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Xiaoguang Wang

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Published work

67 published item(s)

preprint2026arXiv

MBP-KT: Learning Global Collaborative Information from Meta-Behavioral Pattern for Enhanced Knowledge Tracing

The emerging collaborative information-based knowledge tracing (KT) has been a promising way to enhance modeling of learners' knowledge states. The core idea is to extract the collaborative information from interaction sequences of other learners to assist the prediction on the target one. Despite effectiveness, existing methods are built on the raw interaction sequences with tailored modules, which inevitably limits their capacity in deeply capturing learning behavioral patterns and generalization. To this end, we propose a general meta-behavioral pattern-aware framework (MBP-KT) for KT. Specifically, MBP-KT introduces a novel meta-behavioral sequence construction to transform the raw interaction sequences into the combinations of different meta-behavioral patterns. In this way, the learning behavioral patterns of learners can be effectively preserved. Then, MBP-KT develops a parameter-free module to extract the global collaborative representations from the constructed meta-behavioral sequences. Moreover, MBP-KT provides general injection strategies to introduce the extracted global collaborative information into various downstream KT models, ensuring the universality of the collaborative information. Extensive results on real-world datasets demonstrate that MBP-KT can consistently boosts the performance of a wide range of KT models.

preprint2022arXiv

Boundaries of capture hyperbolic components

In complex dynamics, the boundaries of higher dimensional hyperbolic components in holomorphic families of polynomials or rational maps are mysterious objects, whose topological and analytic properties are fundamental problems. In this paper, we show that in some typical families of polynomials (i.e. algebraic varieties defined by periodic critical relations), the boundary of a capture hyperbolic component $\mathcal H$ is homeomorphic to the sphere $S^{2\dim_\mathbb{C}(\mathcal{H})-1}$. Furthermore, we establish an unexpected identity for the Hausdorff dimension of $\partial \mathcal H$: $$\operatorname{H{.}dim}(\partial\mathcal{H}) = 2 \dim_\mathbb{C}(\mathcal{H})-2+\max_{f\in\partial\mathcal{H}} \operatorname{H{.}dim}(\partial A^J(f)),$$ where $A^J(f)$ is the union of the bounded attracting Fatou components of $f$ associated with the free critical points in the Julia set $J(f)$. In the proof, some new results with independent interests are discovered.

preprint2022arXiv

Instantaneous indirect measurement principle in quantum mechanics

In quantum systems, the measurement of operators and the measurement of the quantum states of the system are very challenging tasks. In this Letter, we propose a method to obtain the average value of one operator in a certain state by measuring the instantaneous change of the average value of another operator with the assistance of a known reference state. We refer to this measurement method as the instantaneous indirect measurement method. By studying the application of this method to some typical models, we find that this measurement can be applied to the measurement of an arbitrary state of a quantum system. Furthermore, for the system to be measured, we find that such measurement neither significantly affects the wave function of the system nor causes wave function collapse of the system. Also, our study shows that when two independent systems are coupled, the information mapping between them is done instantaneously. Finally, we discuss applying this measurement method to the measurement of quantum Fisher information, which quantizes the limited accuracy of estimating a parameter from a quantum state.

preprint2022arXiv

Quantum interferometry for rotation sensing in an optical microresonator

We theoretically propose a scheme to perform rotation sensing in a Whispering-gallery-mode resonator setup. With the assistance of a large detuned two-level atom, which induces the effective coupling between clockwise and counterclockwise propagating modes in the resonator, we realize an effective interferometry with SU(2) algebraic structure. By studying the quantum Fisher information of the system, we find that the estimate accuracy for the angular velocity of the rotation can achieve and even break the Heisenberg limit in linear and nonlinear setup, respectively. The high performance of quantum metrology is proved to be associated with the state compressibility during the time evolution. We hope that our investigation will be useful in the design of a quantum gyroscope based on spinning resonators.

preprint2021arXiv

Extreme expected values and their applications in quantum information processing

We consider the probability distribution when the monotonic function $F(X)$ of the independent variable $X$ takes the maximum or minimum expected value under the two constraints of a certain probability and a certain expected value of the independent variable $X$. We proposed an equal probability and equal expected value splitting method. With this method, we proved four inequalities, and two of them can be reduced to Jensen's inequalities. Subsequently, we find that after dividing the non-monotone function $H(X)$ into multiple monotone intervals, the problem of solving the maximum and minimum expected values of $H(X)$ can be transformed into the problem of solving the extreme value of a multiple-variable function. Finally, we apply the proved theory to solve three problems in quantum information processing. When studying the quantum parameter estimation in Mach-Zehnder interferometer, for an equal total input photon number, we find an optimal path-symmetric input state that makes the quantum Fisher information take the maximum value, and we prove that the NOON state is the path-symmetric state that makes the quantum Fisher information takes the minimum value. When studying the quantum parameter estimation in Landau-Zener-Jaynes-Cummings model, we find the optimal initial state of the cavity field that makes the system obtain the maximum quantum Fisher information. Finally, for an equal initial average photon number, we find the optimal initial state of the cavity field that makes the Tavis-Cummings quantum battery have the maximum stored energy and the maximum average charging power.

preprint2021arXiv

New Recruiter and Jobs: The Largest Enterprise Data Migration at LinkedIn

In August 2019, we introduced to our members and customers the idea of moving LinkedIn's two core talent products -- Jobs and Recruiter -- onto a single platform to help talent professionals be even more productive. This single platform is called the New Recruiter & Jobs. A critical and difficult part of this effort is migrating their existing data from the legacy database to the new database and ensure there is no data discrepancy and no down time. In this article, we will discuss the general architecture for a successful data migration and the thought process we followed. Then we expand these ideas to our circumstances and explain in more detail about our specific challenges and solutions. In the Ramp Process section, we explain the inherent difficulties in satisfying our success criteria and describe how we overcome these difficulties and fulfill the success criteria practically.

preprint2020arXiv

$\mathcal{PT}$-symmetry-breaking enhanced cavity optomechanical magnetometry

$\mathcal{PT}$-symmetry-breaking enhanced cavity optomechanical magnetometer is proposed, which is achieved by monitoring the change of intensity of a nonlinear four-wave mixing (FWM) process in a gain-cavity-assisted cavity optomechanical system (COMS). Compared with the traditional single loss COMS, the FWM intensity can be enhanced by two orders of magnitude when the gain-cavity-assisted COMS operates at the $\mathcal{PT}$-symmetry-breaking phase. Meanwhile, the sensitivity of magnetic field sensing can be increased from $10^{-9}$T to $10^{-11}$T. This originally comes from the fact that the effective detuning and decay of loss-cavity can be effectively modified in the $\mathcal{PT}$-symmetry-breaking phase. Our work shows that an ultrahigh-sensitivity magnetometer can be achieved in the $\mathcal{PT}$-symmetry-breaking COMS, which will have wide applications in the field of quantum sensing.

preprint2020arXiv

Quantum memory assisted precision rotation sensing

We propose to implement a solid-state rotation sensor by employing a many-body quantum spin system which takes the advantages of the easy controllability of the electron spin and the robustness provided by the collective nuclear spin state. The sensor consists of a central electron spin coupled to many surrounding nuclear spins. Previously, this central spin system has been suggested to realize a quantum memory. Here, we further utilize the collective nuclear spins, which store a certain quantum state, to detect the macroscopic rotation. Different from other nuclear spin-based gyroscopes, our proposal does not directly manipulate nuclear spins via nuclear magnetic resonance technique. We analytically and numerically investigate the effects of partial nuclear polarization and decoherence on the sensitivity. We also briefly introduce the procedure to generate entanglement between nuclear spins through the quantum memory technique and to utilize this entanglement to enhance the sensing performance. Our proposal paves the way to the experimental realization of a compact solid-state, full-electrical and spin-based gyroscope.

preprint2019arXiv

Charging of quantum batteries with general harmonic power

We analyse the charging process of quantum batteries with general harmonic power. To describe the charge efficiency, we introduce the charge saturation and the charging power, and divide the charging mode into the saturated charging mode and the unsaturated charging mode. The relationships between the time-dependent charge saturation and the parameters of general driving field are discussed both analytically and numerically. And according to the Floquet theorem, we give the expressions of time-dependent charge saturation with the quasiengery and the Floquet states of the system. With both the analytical and numerical results, we find the optimal parameters to reach the best charging efficiency.

preprint2019arXiv

Photon-assisted entanglement and squeezing generation and decoherence suppression via a quadratic optomechanical coupling

Entanglement and quantum squeezing have wide applications in quantum technologies due to their non-classical characteristics. Here we study entanglement and quantum squeezing in an open spin-optomechanical system, in which a Rabi model (a spin coupled to the mechanical oscillator) is coupled to an ancillary cavity field via a quadratic optomechanical coupling. We find that their performances can be significantly modulated via the photon of the ancillary cavity, which comes from photon-dependent spin-oscillator coupling and detuning. Specifically, a fully switchable spin-oscillator entanglement can be achieved, meanwhile a strong mechanical squeezing is also realized. Moreover, we study the environment-induced decoherence and dissipation, and find that they can be mitigated by increasing the number of photons. This work provides an effective way to manipulate entanglement and quantum squeezing and to suppress decoherence in the cavity quantum electrodynamics with a quadratic optomechanics.

preprint2019arXiv

Quantum Fisher information matrix and multiparameter estimation

Quantum Fisher information matrix (QFIM) is a core concept in theoretical quantum metrology due to the significant importance of quantum Cramér-Rao bound in quantum parameter estimation. However, studies in recent years have revealed wide connections between QFIM and other aspects of quantum mechanics, including quantum thermodynamics, quantum phase transition, entanglement witness, quantum speed limit and non-Markovianity. These connections indicate that QFIM is more than a concept in quantum metrology, but rather a fundamental quantity in quantum mechanics. In this paper, we summarize the properties and existing calculation techniques of QFIM for various cases, and review the development of QFIM in some aspects of quantum mechanics apart from quantum metrology. On the other hand, as the main application of QFIM, the second part of this paper reviews the quantum multiparameter Cramér-Rao bound, its attainability condition and the associated optimal measurements. Moreover, recent developments in a few typical scenarios of quantum multiparameter estimation and the quantum advantages are also thoroughly discussed in this part.

preprint2016arXiv

Coherent-State Approach for Majorana representation

By representing a quantum state and its evolution with the majorana stars on the Bloch sphere, the Majorana representation (MR) provide us an intuitive way to study a physical system with SU(2) symmetry. In this work, based on coherent states, we propose a method to establish generalization of MR for a general symmetry. By choosing a generalized coherent state as a reference state, we give a more general MR for both finite and infinite systems and the corresponding star equations are given. Using this method, we study the squeezed vacuum states for three different symmetries, Heisenberg-Weyl, SU(2) and SU(1,1), and express the effect of squeezing parameter on the distribution of stars. Furthermore, we also study the dynamical evolution of stars for an initial coherent state driven by a nonlinear Hamiltonian, and find that at a special time point, the stars are distributed on two orthogonal large circles.

preprint2016arXiv

Global topology of hyperbolic components I: Cantor circle case

The hyperbolic components in the moduli space ${M}_d$ of degree $d\geq2$ rational maps are mysterious and fundamental topological objects. For those in the connectedness locus, they are known to be the finite quotients of the Euclidean space $\mathbb{R}^{4d-4}$. In this paper, we study the hyperbolic components in the disconnectedness locus and with minimal complexity: those in the Cantor circle locus. We show that each of them is a finite quotient of the space $\mathbb{R}^{4d-4-n}\times\mathbb{T}^{n}$, where $n$ is determined by the dynamics. The proof relates Riemann surface theory (Abel's Theorem), dynamical system and algebraic topology.

preprint2016arXiv

Moduli space of cubic Newton maps

In this article, we study the topology and bifurcations of the moduli space $\mathcal{M}_3$ of cubic Newton maps. It's a subspace of the moduli space of cubic rational maps, carrying the Riemann orbifold structure $(\mathbb{\widehat{C}}, (2,3,\infty))$. We prove two results: (1). The boundary of the unique unbounded hyperbolic component is a Jordan arc and the boundaries of all other hyperbolic components are Jordan curves. (2).The Head's angle map is surjective and monotone. The fibers of this map are characterized completely. The first result is a moduli space analogue of the first author's dynamical regularity theorem \cite{Ro08}. The second result confirms a conjecture of Tan Lei.

preprint2016arXiv

Quantum Fisher information and symmetric logarithmic derivative via anti-commutators

Symmetric logarithmic derivative (SLD) is a key quantity to obtain quantum Fisher information (QFI) and to construct the corresponding optimal measurements. Here we develop a method to calculate the SLD and QFI via anti-commutators. This method is originated from the Lyapunov representation and would be very useful for cases that the anti-commutators among the state and its partial derivative exhibits periodic properties. As an application, we discuss a class of states, whose squares linearly depend on the states themselves, and give the corresponding analytical expressions of SLD and QFI. A noisy scenario of this class of states is also considered and discussed. Finally, we readily apply the method to the block-diagonal states and the multi-parameter estimation problems.

preprint2016arXiv

Quantum multiparameter metrology with generalized entangled coherent state

We propose a generalized form of entangled coherent states (ECS) and apply them in a multi-arm optical interferometer to estimate multiple phase shifts. We obtain the quantum Cramer-Rao bounds for both the linear and nonlinear parameterization protocols. Through the analysis, we find that, utilizing the simultaneous estimation, this generalized form of ECS gives a better precision than the generalized NOON states [Phys. Rev. Lett. \textbf{111}, 070403 (2013)]. Moreover, comparing with the independent estimation, both the linear and nonlinear protocols have the same advantage in the relation to the number of the parameters.

preprint2015arXiv

A simple and robust single-pixel computational ghost imaging

A simple and robust experiment demonstrating computational ghost imaging with structured illumination and a single-pixel detector has been performed. Our experimental setup utilizes a general computer for generating pseudo-randomly patterns on the liquid crystal display screen to illuminate a partially-transmissive object. With an incoherent light source, this object is imaged. The effects of light source, light path, and the number of measurements on the reconstruction quality of the object are discussed both theoretically and experimentally. The realization of computational ghost imaging with computer liquid crystal display is a further setup toward the practical application of ghost imaging with ordinary incoherent light.

preprint2015arXiv

Identifying the closeness of eigenstates in quantum many-body systems

We propose a new quantity called modulus fidelity to measure the closeness of two quantum pure states. Especially, we use it to investigate the closeness of eigenstates of quantum many-body systems. When the system is integrable, the modulus fidelity of neighbor eigenstates displays a large fluctuation. But the modulus fidelity is close to a constant when system becomes non-integrable with fluctuation reduced drastically. Average modulus fidelity of neighbor eigenstates increases with the increase of parameters that destroy the integrability, which also indicates the integrable-chaos transition. In non-integrable case, it is found two eigenstates are closer to each other if their level spacing is small. We also show that the closeness of eigenstates in non-integrable domain is the underlying mechanism of \emph{eigenstate thermalization hypothesis} (ETH) which explains the thermalization in nonintegrable system we studied.

preprint2015arXiv

Implications and applications of the variance-based uncertainty equalities

In quantum mechanics, the variance-based Heisenberg-type uncertainty relations are a series of mathematical inequalities posing the fundamental limits on the achievable accuracy of the state preparations. In contrast, we construct and formulate two quantum uncertainty equalities, which hold for all pairs of incompatible observables and indicate the new uncertainty relations recently introduced by L. Maccone and A. K. Pati [Phys. Rev. Lett. 113, 260401 (2014)]. Furthermore, we present an explicit interpretation lying behind the derivations and relate these relations to the so-called intelligent states. As an illustration, we investigate the properties of these uncertainty inequalities in the qubit system and a state-independent bound is obtained for the sum of variances. Finally, we apply these inequalities to the spin squeezing scenario and its implication in interferometric sensitivity is also discussed.

preprint2015arXiv

Maximal quantum Fisher information for general su(2) parametrization processes

Quantum Fisher information is a key concept in the field of quantum metrology, which aims to enhance the parameter accuracy by using quantum resources. In this paper, utilizing a representation of quantum Fisher information for a general unitary parametrization process, we study unitary parametrization processes governed by su(2) dynamics. We obtain the analytical expression for the Hermitian operator of the parametrization and the maximal quantum Fisher information. We find that the maximal quantum Fisher information over the parameter space consists of two parts, one is quadratic in the time and the other oscillates with the time. We apply our result to the estimation of a magnetic field and obtained the maximal quantum Fisher information. We further discuss a driving field with a time-dependent Hamiltonian and find the maximal quantum Fisher information of the driving frequency attains optimum when it is in resonance with the atomic frequency.

preprint2015arXiv

Quantum information with conserved quantities

Conserved quantities are crucial in quantum physics. Here we discuss a general scenario of Hamiltonians. All the Hamiltonians within this scenario share a common conserved quantity form. For unitary parametrization processes, the characteristic operator of this scenario is analytically provided, as well as the corresponding quantum Fisher information (QFI). As the application of this scenario, we focus on two classes of Hamiltonians: su(2) category and canonical category. Several specific physical systems in these two categories are discussed in detail. Besides, we also calculate an alternative form of QFI in this scenario.

preprint2015arXiv

Quantum metrology with unitary parametrization processes

Quantum Fisher information is a central quantity in quantum metrology. We discuss an alternative representation of quantum Fisher information for unitary parametrization processes. The highlight of this representation is that all information of parametrization transformation, i.e., the entire dynamical information, is totally involved in a Hermitian operator H. Utilizing this representation, quantum Fisher information is only determined by H and the initial state. We apply this representation in a collective spin system and show the specific expression of H. For a simple case, a spin-half system, the quantum Fisher information is given and the optimal states to access maximum quantum Fisher information are found. Furthermore, for an exponential form initial state, an analytical expression of quantum Fisher information by H operator is provided. The multiparameter quantum metrology is also considered and discussed utilizing this representation in the last.

preprint2014arXiv

Enhanced interferometry using squeezed thermal states and even or odd states

We derive a general expression of the quantum Fisher information for a Mach-Zehnder interferometer, with the port inputs of an \emph{arbitrary} pure state and a squeezed thermal state. We find that the standard quantum limit can be beaten, when even or odd states are applied to the pure-state port. In particular, when the squeezed thermal state becomes a thermal state, all the even or odd states have the same quantum Fisher information for given photon numbers. For a squeezed thermal state, optimal even or odd states are needed to approach the Heisenberg limit. As examples, we consider several common even or odd states: Fock states, even or odd coherent states, squeezed vacuum states, and single-photon-subtracted squeezed vacuum states. We also demonstrate that super-precision can be realized by implementing the parity measurement for these states.

preprint2014arXiv

Fidelity susceptibility and quantum Fisher information for density operators with arbitrary ranks

Taking into account the density matrices with non-full ranks, we show that the fidelity susceptibility is determined by the support of the density matrix. Combining with the corresponding expression of the quantum Fisher information, we rigorously prove that the fidelity susceptibility is proportional to the quantum Fisher information. As this proof can be naturally extended to the full rank case, this proportional relation is generally established for density matrices with arbitrary ranks. Furthermore, we give an analytical expression of the quantum Fisher information matrix, and show that the quantum Fisher information matrix can also be represented in the density matrix's support.

preprint2014arXiv

Multiple phase estimation for arbitrary pure states under white noise

In any realistic quantum metrology scenarios, the ultimate precision in the estimation of parameters is limited not only by the so-called Heisenberg scaling, but also the environmental noise encountered by the underlying system. In the context of quantum estimation theory, it is of great significance to carefully evaluate the impact of a specific type of noise on the corresponding quantum Fisher information (QFI) or quantum Fisher information matrix (QFIM). Here we investigate the multiple phase estimation problem for a natural parametrization of arbitrary pure states under white noise. We obtain the explicit expression of the symmetric logarithmic derivative (SLD) and hence the analytical formula of QFIM. Moreover, the attainability of the quantum Cramér-Rao bound (QCRB) is confirmed by the commutability of SLDs and the optimal estimators are elucidated for the experimental purpose. These findings generalize previously known partial results and highlight the role of white noise in quantum metrology.

preprint2014arXiv

Non-Markovian dynamics of mixed-state geometric phase of dissipative qubits

We investigate the geometric phase of a two-level atom (qubit) coupled to a bosonic reservoir with Lorentzian spectral density, and find that for the non-Markovian dynamics in which rotating-wave approximation (RWA) is performed, geometric phase has a $π$-phase jump at the nodal point. However, the exact result without RWA given by hierarchy equation of motion method shows that there is no such a phase jump or nodal structure in geometric phase. Thus our results demonstrate that the counter-rotating terms significantly contribute to the geometric phase in multi-mode Hamiltonian under certain circumstances.

preprint2014arXiv

Optimal condition for measurement observable via error-propagation

Propagation of error is a widely used estimation tool in experiments, where the estimation precision of the parameter depends on the fluctuation of the physical observable. Thus which observable is chosen will greatly affect the estimation sensitivity. Here we study the optimal observable for the ultimate sensitivity bounded by the quantum Cramér-Rao theorem in parameter estimation. By invoking the Schrödinger-Robertson uncertainty relation, we derive the necessary and sufficient condition for the optimal observables saturating the ultimate sensitivity for single parameter estimate. By applying this condition to Greenberg-Horne-Zeilinger states, we obtain the general expression of the optimal observable for separable measurements to achieve the Heisenberg-limit precision and show that it is closely related to the parity measurement. However, Jose {\em et al} [Phys. Rev. A {\bf 87}, 022330 (2013)] have claimed that the Heisenberg limit may not be obtained via separable measurements. We show this claim is incorrect.

preprint2014arXiv

Quantifying non-Markovianity for a chromophore-qubit pair in a super-Ohmic bath

An approach based on a non-Markovian time-convolutionless polaron master equation is used to probe the quantum dynamics of a chromophore-qubit in a super-Ohmic bath. Utilizing a measure of non-Markovianity based on dynamical fixed points, we study the effects of the environment temperature and the coupling strength on the non-Markovian behavior of the chromophore in a super-Ohmic bath. It is found that an increase in the temperature results in a reduction in the backflow information from the environment to the chromophore, and therefore, a suppression of non-Markovianity. In the weak coupling regime, increasing coupling strength will enhance the non- Markovianity, while the effect is reversed in the strong coupling regime.

preprint2014arXiv

Quantum Fisher information and spin squeezing in one-axis twisting model

We consider the quantum Fisher information and spin squeezing in one-axis twisting model with a coherent spin state $|θ_{0},ϕ_{0}\rangle$. We analytically discuss the dependence of the two parameters: spin squeezing parameter $ξ^2_{K}$ and the average parameter estimation precision $χ^2$ on the polar angle $θ_{0}$ and the azimuth angle $ϕ_0$. Moreover, we discuss the effects of the collisional dephasing on the dynamics of the two parameters. In this case, the analytical solution of $ξ^2_K$ is also obtained.

preprint2014arXiv

Torsion points and the Lattes family

We give a dynamical proof of a result of Masser and Zannier [MZ2, MZ3] about torsion points on the Legendre family of elliptic curves. Our methods also treat points of small height. A key ingredient is the arithmetic equidistribution theorem on $\mathbb{P}^1$ of Baker-Rumely, Chambert-Loir, and Favre-Rivera-Letelier. Torsion points on the elliptic curve coincide with preperiodic points for the degree-4 Lattes family of rational functions. Our main new results concern properties of the bifurcation measures for this Lattes family associated to marked points.

preprint2013arXiv

Broadcasting Quantum Fisher Information

It is well known that classical information can be cloned, but non-orthogonal quantum states cannot be cloned, and non-commuting quantum states cannot be broadcast. We conceive a scenario in which the object we want to broadcast is the statistical distinguishability, as quantified by quantum Fisher information, about a signal parameter encoded in quantum states. We show that quantum Fisher information cannot be cloned, whilst it might be broadcast even when the input states are non-commuting. This situation interpolates between cloning of classical information and no-broadcasting of quantum information, and indicates a hybrid way of information broadcasting which is of particular significance from both practical and theoretical perspectives.

preprint2013arXiv

Conjugacy between polynomial basins

In this article, we study the properties of conjugacies between polynomial basins. For any conjugacy, there is a quasiconformal conjugacy in the same homotopy class minimizing the dilatation. We compute the precise value of the minimal dilatation. The quasiconformal conjugacy minimizing the dilatation is not unique in general. We give a necessary and sufficient condition when the extremal map is unique.

preprint2013arXiv

Dephasing-assisted parameter estimation in the presence of dynamical decoupling

We study the dephasing-assisted precision of parameter estimation (PPE) enhancement in atom interferometer under dynamical decoupling (DD) pulses. Through calculating spin squeezing (SS) and quantum Fisher information (QFI), we find that dephasing noise can improve PPE by inducing SS, and the DD pulses can maximize the improvement. It is indicated that in the presence of DD pulses, the dephasing-induced SS can reach the limit of \textquotedblleft one-axis twisting\textquotedblright\ model, $ξ^2\simeq N^{-2/3}$ with $ξ^2$ being the SS parameter and N the number of atoms. In particular, we find that the DD pulses can amplify the dephasing-induced QFI by a factor of $\simeq N/2$ compared with the noise-free case, which means that under the control of DD pulses, the dephasing noise can enhance the PPE to the scale of $\sqrt{2}/N$, the same order of magnitude of Heisenberg limit (1/N).

preprint2013arXiv

Fisher information under decoherence in Bloch representation

The dynamics of two variants of quantum Fisher information under decoherence are investigated from a geometrical point of view. We first derive the explicit formulas of these two quantities for a single qubit in terms of the Bloch vector. Moreover, we obtain analytical results for them under three different decoherence channels, which are expressed as affine transformation matrices. Using the hierarchy equation method, we numerically study the dynamics of both the two information in a dissipative model and compare the numerical results with the analytical ones obtained by applying the rotating-wave approximation. We further express the two information quantities in terms of the Bloch vector for a qudit, by expanding the density matrix and Hermitian operators in a common set of generators of the Lie algebra $\mathfrak{su}(d)$. By calculating the dynamical quantum Fisher information, we find that the collisional dephasing significantly diminishes the precision of phase parameter with the Ramsey interferometry.

preprint2013arXiv

Non-unital non-Markovianity of quantum dynamics

We show that Breuer-Laine-Piilo (BLP) non-Markovianity cannot capture the dynamical information in the non-unital aspect of the quantum dynamics. Moreover, we provide a measure on the effect of the non-unitality of quantum processes on the infinitesimal non-divisibility. This measure can be used as a supplement to BLP non-Markovianity for non-unital quantum processes. A measure on the degree of the non-unital behavior of quantum processes is also given in this paper.

preprint2013arXiv

Phase matching condition for enhancement of phase sensitivity in quantum metrology

We find a phase matching condition for enhancement of sensitivity in a Mach-Zehnder interferometer illuminated by an arbitrary state in one input port and an odd(even) state in the other port. Under this condition, the Fisher information becomes maximal with respect to the relative phase of two modes and the phase sensitivity is enhanced. For the case with photon losses, we further find that the phase matching condition keeps unchanged with a coherent state and a coherent superposition state as the input states.

preprint2013arXiv

Quantum Fisher Information of Entangled Coherent States in a Lossy Mach-Zehnder Interferometer

We give an analytical result for the quantum Fisher information of entangled coherent States in a lossy Mach-Zehnder Interferometer recently proposed by J. Joo et al. [Phys. Rev. Lett. 107, 083601(2011)]. For small loss of photons, we find that the entangled coherent state can surpass the Heisenberg limit. Furthermore, The formalism developed here is applicable to the study of phase sensitivity of multipartite entangled coherent states.

preprint2012arXiv

A decomposition theorem for Herman maps

In 1980s, Thurston established a topological characterization theorem for postcritically finite rational maps. In this paper, a decomposition theorem for a class of postcritically infinite branched covering termed `Herman map' is developed. It's shown that every Herman map can be decomposed along a stable multicurve into finitely many Siegel maps and Thurston maps, such that the combinations and rational realizations of these resulting maps essentially dominate the original one. This result gives an answer to a problem of McMullen in a sense and enables us to prove a Thurston-type theorem for rational maps with Herman rings.

preprint2012arXiv

Dynamics of McMullen maps

In this article, we develop the Yoccoz puzzle technique to study a family of rational maps termed McMullen maps. We show that the boundary of the immediate basin of infinity is always a Jordan curve if it is connected. This gives a positive answer to a question of Devaney. Higher regularity of this boundary is obtained in almost all cases. We show that the boundary is a quasi-circle if it contains neither a parabolic point nor a recurrent critical point. For the whole Julia set, we show that the McMullen maps have locally connected Julia sets except in some special cases.

preprint2012arXiv

Entanglement Dynamics of Two Qubits in a Common Bath

We derive a set of hierarchical equations for qubits interacting with a Lorentz-broadened cavity mode at zero temperature, without using the rotating-wave, Born, and Markovian approximations. We use this exact method to reexamine the entanglement dynamics of two qubits interacting with a common bath, which was previously solved only under the rotating-wave and single-excitation approximations. With the exact hierarchy equation method used here, we observe significant differences in the resulting physics, compared to the previous results with various approximations. Double excitations due to counter-rotating-wave terms are also found to have remarkable effects on the dynamics of entanglement.

preprint2012arXiv

Fisher information manifestation of dynamical stability and transition to self-trapping for Bose-Einstein condensates

We investigate dynamical stability and self-trapping for Bose-Einstein condensates in a symmetric double well. The relation between the quantum Fisher information and the stability of the fixed point is studied. We find that the quantum Fisher information displays a sharp transition as the fixed point evolving from stable to unstable regime. Moreover, the transition from Josephson oscillation to self-trapping is accompanied by an abrupt change of the quantum Fisher information.

preprint2012arXiv

Hyperbolic components of McMullen maps

In this article, we study the hyperbolic components of McMullen maps. We show that the boundaries of all hyperbolic components are Jordan curves. This settles a problem posed by Devaney. As a consequence, we show that cusps are dense on the boundary of the unbounded hyperbolic component. This is a dynamical analogue of McMullen's theorem that cusps are dense on the Bers' boundary of Teichmüller space.

preprint2012arXiv

Macroscopic quantum coherence in spinor condensates confined in an anisotropic potential

We investigate the macroscopic quantum coherence of a spin-1 Rb condensate confined in an anisotropic potential. Under the single-mode approximation, we show that the system can be modeled as a biaxial quantum magnet due to the interplay between the magnetic dipole-dipole interaction and the anisotropic potential. By applying a magnetic field along the hard-axis, we show that the tunneling splitting oscillates as a function of the field strength. We also propose an experimental scheme to detect the oscillatory behavior of the tunneling splitting by employing the Landau-Zener tunneling.

preprint2012arXiv

Measurement-induced nonlocality based on the relative entropy

We quantify the measurement-induced nonlocality [Luo and Fu, Phys. Rev. Lett. 106, 120401 (2011)] from the perspective of the relative entropy. This quantification leads to an operational interpretation for the measurementinduced nonlocality, namely, it is the maximal entropy increase after the locally invariant measurements. The relative entropy of nonlocality is upper bounded by the entropy of the measured subsystem. We establish a relationship between the relative entropy of nonlocality and the geometric nonlocality based on the Hilbert- Schmidt norm, and show that it is equal to the maximal distillable entanglement. Several trade-off relations are obtained for tripartite pure states. We also give explicit expressions for the relative entropy of nonlocality for Bell-diagonal states.

preprint2012arXiv

Necessary and sufficient condition for saturating the upper bound of quantum discord

We revisit the upper bound of quantum discord given by the von Neumann entropy of the measured subsystem. Using the Koashi-Winter relation, we obtain a trade-off between the amount of classical correlation and quantum discord in the tripartite pure states. The difference between the quantum discord and its upper bound is interpreted as a measure on the classical correlative capacity. Further, we give the explicit characterization of the quantum states saturating the upper bound of quantum discord, through the equality condition for the Araki-Lieb inequality. We also demonstrate that the saturating of the upper bound of quantum discord precludes any further correlation between the measured subsystem and the environment.

preprint2012arXiv

Pairwise Quantum Correlations for Superpositions of Dicke States

Pairwise correlation is really an important property for multi-qubit states. For the two-qubit X states extracted from Dicke states and their superposition states, we obtain a compact expression of the quantum discord by numerical check. We then apply the expression to discuss the quantum correlation of the reduced two-qubit states of Dicke states and their superpositions, and the results are compared with those obtained by entanglement of formation, which is a quantum entanglement measure.

preprint2012arXiv

Photon-assisted Landau-Zener transition: Role of coherent superposition states

We investigate a Landau-Zener (LZ) transition process modeled by a quantum two-level system (TLS) coupled to a photon mode when the bias energy is varied linearly in time. The initial state of the photon field is assumed to be a superposition of coherent states, leading to a more intricate LZ transition. Applying the rotating-wave approximation (RWA), analytical results are obtained revealing the enhancement of the LZ probability by increasing the average photon number. We also consider the creation of entanglement and the change of photon statistics during the LZ process. Without the RWA, we find some qualitative differences of the LZ dynamics from the RWA results, e.g., the average photon number no longer monotonically enhances the LZ probability. The ramifications and implications of these results are explored.

preprint2012arXiv

Spin Squeezing under Non-Markovian Channels by Hierarchy Equation Method

We study spin squeezing under non-Markovian channels, and consider an ensemble of $N$ independent spin-1/2 particles with exchange symmetry. Each spin interacts with its own bath, and the baths are independent and identical. For this kind of open system, the spin squeezing under decoherence can be investigated from the dynamics of the local expectations, and the multi-qubit dynamics can be reduced into the two-qubit one. The reduced dynamics is obtained by the hierarchy equation method, which is a exact without rotating-wave and Born-Markov approximation. The numerical results show that the spin squeezing displays multiple sudden vanishing and revival with lower bath temperature, and it can also vanish asymptotically.

preprint2011arXiv

Optimal measurements to access classical correlations of two-qubit states

We analyze the optimal measurements accessing classical correlations in arbitrary two-qubit states. Two-qubit states can be transformed into the canonical forms via local unitary operations. For the canonical forms, we investigate the probability distribution of the optimal measurements. The probability distribution of the optimal measurement is found to be centralized in the vicinity of a specific von Neumann measurement, which we call the maximal-correlation-direction measurement (MCDM). We prove that for the states with zero-discord and maximally mixed marginals, the MCDM is the very optimal measurement. Furthermore, we give an upper bound of quantum discord based on the MCDM, and investigate its performance for approximating the quantum discord.

preprint2011arXiv

Quantum spin squeezing

This paper reviews quantum spin squeezing, which characterizes the sensitivity of a state with respect to an SU(2) rotation, and is significant for both entanglement detection and high-precision metrology. We first present various definitions of spin squeezing parameters, explain their origin and properties for typical states, and then discuss spin-squeezed states produced with the Ising and the nonlinear twisting Hamiltonians. Afterwards, we explain correlations and entanglement in spin-squeezed states, as well as the relations between spin squeezing and quantum Fisher information, where the latter plays a central role in quantum metrology. We also review the applications of spin squeezing for detecting quantum chaos and quantum phase transitions, as well as the influence of decoherence on spin-squeezed states. Finally, several experiments are discussed including: producing spin squeezed states via particle collisions in Bose-Einstein condensates, mapping photon squeezing onto atomic ensembles, and quantum non-demolition measurements.

preprint2011arXiv

Sudden vanishing and reappearance of nonclassical effects: General occurrence of finite-time decays and periodic vanishings of nonclassicality and entanglement witnesses

Analyses of phenomena exhibiting finite-time decay of quantum entanglement have recently attracted considerable attention. Such decay is often referred to as sudden vanishing (or sudden death) of entanglement, which can be followed by its sudden reappearance (or sudden rebirth). We analyze various finite-time decays (for dissipative systems) and analogous periodic vanishings (for unitary systems) of nonclassical correlations as described by violations of classical inequalities and the corresponding nonclassicality witnesses (or quantumness witnesses), which are not necessarily entanglement witnesses. We show that these sudden vanishings are universal phenomena and can be observed: (i) not only for two- or multi-mode but also for single-mode nonclassical fields, (ii) not solely for dissipative systems, and (iii) at evolution times which are usually different from those of sudden vanishings and reappearances of quantum entanglement.

preprint2010arXiv

Adiabatic Creation of Atomic Squeezing in Dark States vs. Decoherences

We study the multipartite correlations of the multi-atom dark states, which are characterized by the atomic squeezing beyond the pairwise entanglement. It is shown that, in the photon storage process with atomic ensemble via electromagnetically induced transparency (EIT) mechanism, the atomic squeezing and the pairwise entanglement can be created by adiabatically manipulating the Rabi frequency of the classical light field on the atomic ensemble. We also consider the sudden death for the atomic squeezing and the pairwise entanglement under various decoherence channels. An optimal time for generating the greatest atomic squeezing and pairwise entanglement is obtained by studying in details the competition between the adiabatic creation of quantum correlation in the atomic ensemble and the decoherence that we describe with three typical decoherence channels.

preprint2010arXiv

Exact non-Markovian cavity dynamics strongly coupled to a reservoir

The exact non-Markovian dynamics of a microcavity strongly coupled to a general reservoir at arbitrary temperature is studied. With the exact master equation for the reduced density operator of the cavity system, we analytically solve the time evolution of the cavity state and the associated physical observables. We show that the non-Markovian dynamics is completely determined by the propagating (retarded) and correlation Green functions. Compare the non-Markovian behavior at finite temperature with those at zero-temperature limit or Born-Markov limit, we find that the non-Markovian memory effect can dramatically change the coherent and thermal dynamics of the cavity. We also numerically study the dissipation dynamics of the cavity through the mean mode amplitude decay and the average photon number decay in the microwave regime. It is shown that the strong coupling between the cavity and the reservoir results in a long-time dissipationless evolution to the cavity field amplitude, and its noise dynamics undergoes a critical transition from the weak to strong coupling due to the non-Markovian memory effect.

preprint2010arXiv

Geometric measure of quantum discord under decoherence

The dynamics of a geometric measure of the quantum discord (GMQD) under decoherence is investigated. We show that the GMQD of a two-qubit state can be alternatively obtained through the singular values of a $3\times4$ matrix whose elements are the expectation values of Pauli matrices of the two qubits. By using Heisenberg picture, the analytic results of the GMQD is obtained for three typical kinds of the quantum decoherence channels. We compare the dynamics of the GMQD with that of the quantum discord and of entanglement. We show that a sudden change in the decay rate of the GMQD does not always imply that of the quantum discord, and vice versa. We also give a general analysis on the sudden change in behavior and find that at least for the Bell diagonal states, the sudden changes in decay rates of the GMQD and that of the quantum discord occur simultaneously.

preprint2010arXiv

Operator Quantum Geometric Tensor and Quantum Phase Transitions

We extend the quantum geometric tensor from the state space to the operator level,and investigate its properties like the additivity for factorizable models and the splitting of two kinds contributions for the case of stationary reference states. This operator-quantum-geometric tensor (OQGT) is shown to reflect the sensitivity of unitary operations against perturbations of multi parameters. General results for the cases of time evolutions with given stationary reference states are obtained. By this approach, we get exact results for the rotated XY models, and show relations between the OQGT and quantum criticality.

preprint2010arXiv

Quantum Fisher Information Flow in Non-Markovian Processes of Open Systems

We propose to use the quantum Fisher information in characterizing the information flow of open quantum systems. This information-theoretic approach provides a quantitative measure to statistically distinguish Markovian and non-Markovian processes. A basic relation between the QFI flow and non-Markovianity is unveiled for quantum dynamics of open systems. For a class of time-local master equations, the exactly-analytic solution shows that the non-Markovianity is characterized by additive information sub-flows in different non-Markovian channels.

preprint2010arXiv

Spin squeezing and concurrence

We study the relations between spin squeezing and concurrence, and find that they are qualitatively equivalent for an ensemble of spin-1/2 particles with exchange symmetry and parity, if we adopt the spin squeezing criterion given by the recent work (G. Toth et al. Phys. Rev. Lett. 99, 250405 (2007)). This suggests that the spin squeezing has more intimate relations with pairwise entanglement. We exemplify the result by considering a superposition of two Dicke states.

preprint2010arXiv

Spin Squeezing, Negative Correlations, and Concurrence in the Quantum Kicked Top Model

We study spin squeezing, negative correlations, and concurrence in the quantum kicked top model. We prove that the spin squeezing and negative correlations are equivalent for spin systems with only symmetric Dicke states populated. We numerically analyze spin squeezing parameters and concurrence in this model, and find that the maximal spin squeezing direction, which refers to the minimal pairwise correlation direction, is strongly influenced by quantum chaos. Entanglement (spin squeezing) sudden death and sudden birth occur alternatively for the periodic and quasi-periodic cases, while only entanglement (spin squeezing) sudden death is found for the chaotic case.

preprint2010arXiv

Sudden vanishing of spin squeezing under decoherence

In order to witness multipartite correlations beyond pairwise entanglement, spin-squeezing parameters are analytically calculated for a spin ensemble in a collective initial state under three different decoherence channels. It is shown that, in analogy to pairwise entanglement, the spin squeezing described by different parameters can suddenly become zero at different vanishing times. This finding shows the general occurrence of sudden vanishing phenomena of quantum correlations in many-body systems, which here is referred to as spin-squeezing sudden death (SSSD). It is shown that the SSSD usually occurs due to decoherence and that SSSD never occurs for some initial states in the amplitude-damping channel. We also analytically obtain the vanishing times of spin squeezing.

preprint2010arXiv

Testing nonclassicality in multimode fields: a unified derivation of classical inequalities

We consider a way to generate operational inequalities to test nonclassicality (or quantumness) of multimode (or multiparty) bosonic fields that unifies the derivation of many known inequalities and allows to propose new ones. The nonclassicality criteria are based on Vogel's criterion corresponding to analyzing the positivity of multimode P functions or, equivalently, the positivity of matrices of expectation values of, e.g., creation and annihilation operators. We analyze not only monomials, but also polynomial functions of such moments, which can sometimes enable simpler derivations of physically relevant inequalities. As an example, we derive various classical inequalities which can be violated only by nonclassical fields. In particular, we show how the criteria introduced here easily reduce to the well-known inequalities describing: (a) multimode quadrature squeezing and its generalizations including sum, difference and principal squeezing, (b) two-mode one-time photon-number correlations including sub-Poisson photon-number correlations and effects corresponding to violations of the Cauchy-Schwarz and Muirhead inequalities, (c) two-time single-mode photon-number correlations including photon antibunching and hyperbunching, and (d) two- and three-mode quantum entanglement. Other simple inequalities for testing nonclassicality are also proposed. We have found some general relations between the nonclassicality and entanglement criteria, in particular, those resulting from the Cauchy-Schwarz inequality. It is shown that some known entanglement inequalities can be derived as nonclassicality inequalities within our formalism, while some other known entanglement inequalities can be seen as sums of more than one inequality derived from the nonclassicality criterion. This approach enables a deeper analysis of the entanglement for a given nonclassicality.

preprint2009arXiv

Many-body reduced fidelity susceptibility in Lipkin-Meshkov-Glick model

We study the reduced fidelity susceptibility $χ_{r}$ for an $M$-body subsystem of an $N$-body Lipkin-Meshkov-Glick model with $τ=M/N$ fixed. The reduced fidelity susceptibility can be viewed as the response of subsystem to a certain parameter. In noncritical region, the inner correlation of the system is weak, and $χ_{r}$ behaves similar with the global fidelity susceptibility $χ_{g}$, the ratio $η=χ_{r}/χ_{g}$ depends on $τ$ but not $N$. However, at the critical point, the inner correlation tends to be divergent, then we find $χ_{r}$ approaches $χ_{g}$ with the increasing the $N$, and $η=1$ in the thermodynamic limit. The analytical predictions are perfect agreement with the numerical results.

preprint2008arXiv

Ground-state properties of the two-site Hubbard-Holstein model: an exact solution

We revisit the two-site Hubbard-Holstein model by using extended phonon coherent states. The nontrivial singlet bipolaron is studied exactly in the whole coupling regime. The ground-state (GS) energy and the double occupancy probability are calculated. The linear entropy is exploited successfully to quantify bipartite entanglement between electrons and their environment phonons, displaying a maximum entanglement of the singlet-bipolaron in strong coupling regime. A dramatic drop in the crossover regime is observed in the GS fidelity and its susceptibility. The bipolaron properties is also characterized classically by correlation functions. It is found that the crossover from a two-site to single-site bipolaron is more abrupt and shifts to a larger electron-phonon coupling strength as electron-electron Coulomb repulsion increases.

preprint2004arXiv

Entanglement and spin squeezing in the three-qubit transverse Ising model

We study entanglement and spin squeezing in the ground state of three qubits interacting via the transverse Ising model. We give analytical results for the entanglement and spin squeezing, and a quantitative relation between the concurrence, quantifying the entanglement of two spins, and the spin squeezing parameter, measuring the degree of squeezing. Finally, by appropriately choosing the exchange interaction and strengths of the transverse field, we propose a scheme for generating entangled W state from an unentangled initial state with all spins down.

preprint2002arXiv

Quantum entanglement and Bell inequalities in Heisenberg spin chains

We show that in one-dimensional isotropic Heisenberg model two-qubit thermal entanglement and maximal violation of Bell inequalities are directly related with a thermodynamical state function, i.e., the internal energy. Therefore they are completely determined by the partition function, the central object of thermodynamics. For ferromagnetic ring we prove that there is no thermal entanglement at any temperature. Explicit relations between the concurrence and the measure of maximal Bell inequality violation are given.