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preprint2020arXiv

Quantum nonlinear metasurfaces

We review the latest advances in the generation of quantum light with nonlinear nanoresonators in metasurfaces, which act both as sources of quantum states and nanoantennas shaping the emitted photons. We outline a general quantum theory of spontaneous photon-pair generation in arbitrary nonlinear photonic structures, including nanoresonators and metasurfaces, which provides an explicit analytical solution for the photon state expressed through the classical Green function. We formulate the correspondence between the quantum photon-pair generation and classical sum-frequency process in nonlinear media, and discuss its application in various contexts, including waveguide circuits and nanostructures. We also discuss the first experimental results demonstrating photon-pair generation in a single nonlinear nanoantenna.

preprint2020arXiv

Hilbert space average of transition probabilities

The typicality approach and the Hilbert space averaging method as its technical manifestation are important concepts of quantum statistical mechanics. Extensively used for expectation values we extend them in this paper to transition probabilities. In this context we also find that the transition probability of two random uniformly distributed states is connected to the spectral statistics of the considered operator. Furthermore, within our approach we are capable to consider distributions of matrix elements between states, that are not orthogonal. We will demonstrate our quite general result numerically for a kicked spin chain in the integrable resp. chaotic regime.

preprint2020arXiv

Engineering telecom single-photon emitters in silicon for scalable quantum photonics

We create and isolate single-photon emitters with a high brightness approaching $10^5$ counts per second in commercial silicon-on-insulator (SOI) wafers. The emission occurs in the infrared spectral range with a spectrally narrow zero phonon line in the telecom O-band and shows a high photostability even after days of continuous operation. The origin of the emitters is attributed to one of the carbon-related color centers in silicon, the so-called G center, allowing purification with the $^{12}$C and $^{28}$Si isotopes. Furthermore, we envision a concept of a highly-coherent scalable quantum photonic platform, where single-photon sources, waveguides and detectors are integrated on a SOI chip. Our results provide a route towards the implementation of quantum processors, repeaters and sensors compatible with the present-day silicon technology.

preprint2020arXiv

Variational approach to time-dependent fluorescence of a driven qubit

We employ the Dirac-Frenkel variational principle and multiple Davydov ansatz to study time-dependent fluorescence spectra of a driven qubit in the weak- to strong qubit-reservoir coupling regimes, where both the Rabi frequency and spontaneous decay rate are comparable to the transition frequency of the qubit. Our method agrees well with the time-local master-equation approach in the weak-coupling regime, and offers a flexible way to compute the spectra from the bosonic dynamics instead of two-time correlation functions. While the perturbative master equation breaks down in the strong-coupling regime, our method actually becomes more accurate due to the use of bosonic coherent states under certain conditions. We show that the counter-rotating coupling between the qubit and the reservoir has considerable contributions to the photon number dynamics and the spectra under strong driving conditions even though the coupling is moderately weak. The time-dependent spectra are found to be generally asymmetric, a feature that is derived from photon number dynamics. In addition, it is shown that the spectral profiles can be dramatically different from the Mollow triplet due to strong dissipat

preprint2020arXiv

Cross Entropy Hyperparameter Optimization for Constrained Problem Hamiltonians Applied to QAOA

Hybrid quantum-classical algorithms such as the Quantum Approximate Optimization Algorithm (QAOA) are considered as one of the most encouraging approaches for taking advantage of near-term quantum computers in practical applications. Such algorithms are usually implemented in a variational form, combining a classical optimization method with a quantum machine to find good solutions to an optimization problem. The solution quality of QAOA depends to a high degree on the parameters chosen by the classical optimizer at each iteration. However, the solution landscape of those parameters is highly multi-dimensional and contains many low-quality local optima. In this study we apply a Cross-Entropy method to shape this landscape, which allows the classical optimizer to find better parameter more easily and hence results in an improved performance. We empirically demonstrate that this approach can reach a significant better solution quality for the Knapsack Problem.

preprint2020arXiv

Radiation from an inertial mirror horizon

The purpose of this study is to investigate radiation from asymptotic zero acceleration motion where a horizon is formed and subsequently detected by an outside witness. A perfectly reflecting moving mirror is used to model such a system and compute the energy and spectrum. The trajectory is asymptotically inertial (zero proper acceleration)-ensuring negative energy flux (NEF), yet approaches light-speed with a null ray horizon at a finite advanced time. We compute the spectrum and energy analytically.

preprint2020arXiv

Berry phase for a Bose gas on a one-dimensional ring

We study a system of strongly interacting one-dimensional (1D) bosons on a ring pierced by a synthetic magnetic flux tube. By the Fermi-Bose mapping, this system is related to the system of spin-polarized non-interacting electrons confined on a ring and pierced by a solenoid (magnetic flux tube). On the ring there is an external localized delta-function potential barrier $V(ϕ)=g δ(ϕ-ϕ_0)$. We study the Berry phase associated to the adiabatic motion of delta-function barrier around the ring as a function of the strength of the potential $g$ and the number of particles $N$. The behavior of the Berry phase can be explained via quantum mechanical reflection and tunneling through the moving barrier which pushes the particles around the ring. The barrier produces a cusp in the density to which one can associate a missing charge $Δq$ (missing density) for the case of electrons (bosons, respectively). We show that the Berry phase (i.e., the Aharonov-Bohm phase) cannot be identified with the quantity $Δq/\hbar \oint \mathbf{A}\cdot d\mathbf{l}$. This means that the missing charge cannot be identified as a (quasi)hole. We point out to the connection of this result and recent studies of synth

preprint2020arXiv

Quasi-Fine-Grained Uncertainty Relations

Nonlocality, which is the key feature of quantum theory, has been linked with the uncertainty principle by fine-grained uncertainty relations, by considering combinations of outcomes for different measurements. However, this approach assumes that information about the system to be fine-grained is local, and does not present an explicitly computable bound. Here, we generalize above approach to general quasi-fine-grained uncertainty relations (QFGURs) which applies in the presence of quantum memory and provides conspicuously computable bounds to quantitatively link the uncertainty to entanglement and Einstein-Podolsky-Rosen (EPR) steering, respectively. Moreover, our QFGURs provide a framework to unify three important forms of uncertainty relations, i.e., universal uncertainty relations, uncertainty principle in the presence of quantum memory, and fine-grained uncertainty relation. This result gives a direct significance to the uncertainty principle, and allows us to determine whether a quantum measurement exhibits typical quantum correlations, meanwhile, it reveals a fundamental connection between basic elements of quantum theory, specifically, uncertainty measures, combined outcome

preprint2020arXiv

Combining $T_1$ and $T_2$ estimation with randomized benchmarking and bounding the diamond distance

The characterization of errors in a quantum system is a fundamental step for two important goals. First, learning about specific sources of error is essential for optimizing experimental design and error correction methods. Second, verifying that the error is below some threshold value is required to meet the criteria of threshold theorems. We consider the case where errors are dominated by the generalized damping channel (encompassing the common intrinsic processes of amplitude damping and dephasing) but may also contain additional unknown error sources. We demonstrate the robustness of standard $T_1$ and $T_2$ estimation methods and provide expressions for the expected error in these estimates under the additional error sources. We then derive expressions that allow a comparison of the actual and expected results of fine-grained randomized benchmarking experiments based on the damping parameters. Given the results of this comparison, we provide bounds that allow robust estimation of the thresholds for fault-tolerance.

preprint2020arXiv

Characterization of quantum entanglement via a hypercube of Segre embeddings

A particularly simple description of separability of quantum states arises naturally in the setting of complex algebraic geometry, via the Segre embedding. This is a map describing how to take products of projective Hilbert spaces. In this paper, we show that for pure states of n particles, the corresponding Segre embedding may be described by means of a directed hypercube of dimension n-1, where all edges are bipartite-type Segre maps. Moreover, we describe the image of the original Segre map via the intersections of images of the n-1 edges whose target is the last vertex of the hypercube. This purely algebraic result is then transferred to physics. For each of the last edges of the Segre hypercube, we introduce an observable which measures geometric separability and is related to the trace of the squared reduced density matrix. As a consequence, the hypercube approach gives a novel viewpoint on measuring entanglement, naturally relating bipartitions with $q$-partitions for q>1. We test our observables against well-known states, showing that these provide well-behaved and fine measures of entanglement.

preprint2020arXiv

Quantum photonics with active feedback loops

We develop a unified theoretical framework for the efficient description of multiphoton states generated and propagating in loop-based optical networks which contain nonlinear elements. These active optical components are modeled as nonlinear media, resembling a two-mode squeezer. First, such nonlinear components can be seeded to manipulate quantum states of light, as such enabling photon addition protocols. And, second, they can function as an amplifying medium for quantum light. To prove the practical importance of our approach, the impact of multiple round trips is analyzed for states propagating in experimentally relevant loop configurations of networks, such as time-multiplexed driven quantum walks and iterative photon-number state generation protocols. Our method not only enables us to model such complex systems but also allows us to propose alternative setups that overcome previous limitations. To characterize the systems under study, we provide exact expressions for fidelities with target states, success probabilities of heralding-type measurements, and correlations between optical modes, including many realistic imperfections. Moreover, we provide an easily implementable n

preprint2020arXiv

Finding the optimal Nash equilibrium in a discrete Rosenthal congestion game using the Quantum Alternating Operator Ansatz

This paper establishes the tractability of finding the optimal Nash equilibrium, as well as the optimal social solution, to a discrete congestion game using a gate-model quantum computer. The game is of the type originally posited by Rosenthal in the 1970's. To find the optimal Nash equilibrium, we formulate an optimization problem encoding based on potential functions and path selection constraints, and solve it using the Quantum Alternating Operator Ansatz. We compare this formulation to its predecessor, the Quantum Approximate Optimization Algorithm. We implement our solution on an idealized simulator of a gate-model quantum computer, and demonstrate tractability on a small two-player game. This work provides the basis for future endeavors to apply quantum approximate optimization to quantum machine learning problems, such as the efficient training of generative adversarial networks using potential functions.

preprint2020arXiv

The Garrison-Wong quantum phase operator revisited

We revisit the quantum phase operator $Φ$ introduced by Garrison and Wong. Denoting by $N$ the number operator, we provide a detailed proof of the Heisenberg commutation relation $ΦN - NΦ= iI$ on the natural maximal domain $D(ΦN) \cap D(N Φ)$ as well as the failure of the Weyl commutation relations, and discuss some further interesting properties of this pair.

preprint2020arXiv

Spectral sum rules for the Schrödinger equation

We study the sum rules of the form $Z(s) = \sum_n E_n^{-s}$, where $E_n$ are the eigenvalues of the time--independent Schrödinger equation (in one or more dimensions) and $s$ is a rational number for which the series converges. We have used perturbation theory to obtain an explicit formula for the sum rules up to second order in the perturbation and we have extended it non--perturbatively by means of a Padé--approximant. For the special case of a box decorated with one impurity in one dimension we have calculated the first few sum rules of integer order exactly; the sum rule of order one has also been calculated exactly for the problem of a box with two impurities. In two dimensions we have considered the case of an impurity distributed on a circle of arbitrary radius and we have calculated the exact sum rules of order two. Finally we show that exact sum rules can be obtained, in one dimension, by transforming the Schrödinger equation into the Helmholtz equation with a suitable density.

preprint2020arXiv

Approaches for approximate additivity of the Holevo information of quantum channels

We study quantum channels that are close to another channel with weakly additive Holevo information and derive upper bounds on their classical capacity. Examples of channels with weakly additive Holevo information are entanglement-breaking channels, unital qubit channels, and Hadamard channels. Related to the method of approximate degradability, we define approximation parameters for each class above that measure how close an arbitrary channel is to satisfying the respective property. This gives us upper bounds on the classical capacity in terms of functions of the approximation parameters, as well as an outer bound on the dynamic capacity region of a quantum channel. Since these parameters are defined in terms of the diamond distance, the upper bounds can be computed efficiently using semidefinite programming (SDP). We exhibit the usefulness of our method with two example channels: a convex mixture of amplitude damping and depolarizing noise, and a composition of amplitude damping and dephasing noise. For both channels, our bounds perform well in certain regimes of the noise parameters in comparison to a recently derived SDP upper bound on the classical capacity. Along the way, we

preprint2020arXiv

Transfer efficiency enhancement and eigenstate properties in locally symmetric disordered finite chains

The impact of local reflection symmetry on wave localization and transport within finite disordered chains is investigated. Local symmetries thereby play the role of a spatial correlation of variable range in the finite system. We find that, on ensemble average, the chain eigenstates become more fragmented spatially for intermediate average symmetry domain sizes, depending on the degree of disorder. This is caused by the partial formation of states with approximate local parity confined within fictitious, disorder-induced double wells and perturbed by the coupling to adjacent domains. The dynamical evolution of wave-packets shows that the average site-resolved transfer efficiency is enhanced between regions connected by local symmetry. The transfer may further be drastically amplified in the presence of spatial overlap between the symmetry domains, and in particular when global and local symmetry coexist. Applicable to generic discrete models for matter and light waves, our work provides a perspective to understand and exploit the impact of local order at multiple scales in complex systems.

preprint2020arXiv

Quantum Hierarchical Systems: Fluctuation Force by Coarse-Graining, Decoherence by Correlation Noise

While the issues of dissipation, fluctuations, noise and decoherence in open quantum systems (with autocratic divide) analyzed via Langevin dynamics are familiar subjects, the treatment of corresponding issues in closed quantum systems is more subtle, as witnessed by Boltzmann's explanation of dissipation in a macroscopic system made up of many equal constituents (a democratic system). How to extract useful physical information about a closed democratic system with no obvious ways to distinguish one constituent from another, nor the existence of conservation laws governing certain special kinds of variables, e.g., the hydrodynamic variables -- this is the question we raise in this essay. Taking the inspirations from Boltzmann and Langevin, we study a) how a hierarchical order introduced to a closed democratic system -- defined either by substance or by representation, and b) how hierarchical coarse-graining, executed in a specific order, can facilitate our understanding in how macro-behaviors arise from micro-dynamics. We give two examples in: a) the derivation of correlation noises in the BBGKY hierarchy and how using a Boltzmann-Langevin equation one can study the decoherence

preprint2020arXiv

Simulating quantum dynamics: Evolution of algorithms in the HPC context

Due to complexity of the systems and processes it addresses, the development of computational quantum physics is influenced by the progress in computing technology. Here we overview the evolution, from the late 1980s to the current year 2020, of the algorithms used to simulate dynamics of quantum systems. We put the emphasis on implementation aspects and computational resource scaling with the model size and propagation time. Our mini-review is based on a literature survey and our experience in implementing different types of algorithms.

preprint2020arXiv

Cosmological Decoherence from Thermal Gravitons

We study the effects of gravitationally-driven decoherence on tunneling processes associated with false vacuum decays, such as the Coleman--De~Luccia instanton. We compute the thermal graviton-induced decoherence rate for a wave function describing a perfect fluid of nonzero energy density in a finite region. When the effective cosmological constant is positive, the thermal graviton background sourced by a de Sitter horizon provides an unavoidable decoherence effect, which may have important consequences for tunneling processes in cosmological history. We discuss generalizations and consequences of this effect and comment on its observability and applications to black hole physics.

preprint2020arXiv

Experimental Demonstration of Sequential Quantum Random Access Codes

A random access code (RAC) is a strategy to encode a message into a shorter one in a way that any bit of the original can still be recovered with nontrivial probability. Encoding with quantum bits rather than classical ones can improve this probability, but has an important limitation: due to the disturbance caused by standard quantum measurements, qubits cannot be used more than once. However, as recently shown by Mohan, Tavakoli, and Brunner [New J. Phys. 21 083034, (2019)], weak measurements can alleviate this problem, allowing two sequential decoders to perform better than with the best classical RAC. We use single photons to experimentally show that these weak measurements are feasible and nonclassical success probabilities are achievable by two decoders. We prove this for different values of the measurement strength and use our experimental results to put tight bounds on them, certifying the accuracy of our setting. This proves the feasibility of using sequential quantum RACs for quantum information tasks such as the self-testing of untrusted devices.

preprint2020arXiv

A Direct Product Theorem for One-Way Quantum Communication

We prove a direct product theorem for the one-way entanglement-assisted quantum communication complexity of a general relation $f\subseteq\mathcal{X}\times\mathcal{Y}\times\mathcal{Z}$. For any $\varepsilon, ζ> 0$ and any $k\geq1$, we show that \[ \mathrm{Q}^1_{1-(1-\varepsilon)^{Ω(ζ^6k/\log|\mathcal{Z}|)}}(f^k) = Ω\left(k\left(ζ^5\cdot\mathrm{Q}^1_{\varepsilon + 12ζ}(f) - \log\log(1/ζ)\right)\right),\] where $\mathrm{Q}^1_{\varepsilon}(f)$ represents the one-way entanglement-assisted quantum communication complexity of $f$ with worst-case error $\varepsilon$ and $f^k$ denotes $k$ parallel instances of $f$. As far as we are aware, this is the first direct product theorem for quantum communication. Our techniques are inspired by the parallel repetition theorems for the entangled value of two-player non-local games, under product distributions due to Jain, Pereszlényi and Yao, and under anchored distributions due to Bavarian, Vidick and Yuen, as well as message-compression for quantum protocols due to Jain, Radhakrishnan and Sen. Our techniques also work for entangled non-local games which have input distributions anchored on any one side. In particular, we show that for any game $G

preprint2020arXiv

Open Quantum Entanglement: A study of two atomic system in static patch of de Sitter space

In this work, our prime objective is to study non-locality and long-range effects of two-body correlation using quantum entanglement from the various information-theoretic measures in the static patch of de Sitter space using a two-body Open Quantum System (OQS). The OQS is described by a system of two entangled atoms, surrounded by a thermal bath, which is modelled by a massless probe scalar field. Firstly, we partially trace over the bath field and construct the Gorini Kossakowski Sudarshan Lindblad (GSKL) master equation, which describes the time evolution of the reduced subsystem density matrix. This GSKL master equation is characterized by two components, these are-Spin chain interaction Hamiltonian and the Lindbladian. To fix the form of both of them, we compute the Wightman functions for probe massless scalar field. Using this result along with the large time equilibrium behaviour we obtain the analytical solution for reduced density matrix. Further using this solution we evaluate various entanglement measures, namely Von-Neumann entropy, R$e'$nyi entropy, logarithmic negativity, entanglement of formation, concurrence and quantum discord for the two atomic subsystems on

preprint2020arXiv

Perturbative instability towards delocalization at phase transitions between MBL phases

We examine the stability of marginally Anderson localized phase transitions between localized phases to the addition of many-body interactions, focusing in particular on the spin-glass to paramagnet transition in a disordered transverse field Ising model in one dimension. We find evidence for a perturbative instability of localization at finite energy densities once interactions are added, i.e. evidence for the relevance of interactions - in a renormalization group sense - to the non-interacting critical point governed by infinite randomness scaling. We introduce a novel diagnostic, the "susceptibility of entanglement", which allows us to perturbatively probe the effect of adding interactions on the entanglement properties of eigenstates, and helps us elucidate the resonant processes that can cause thermalization. The susceptibility serves as a much more sensitive probe, and its divergence can detect the perturbative beginnings of an incipient instability even in regimes and system sizes for which conventional diagnostics point towards localization. We expect this new measure to be of independent interest for analyzing the stability of localization in a variety of different

preprint2020arXiv

Symmetry-protected self-correcting quantum memories

A self-correcting quantum memory can store and protect quantum information for a time that increases without bound with the system size and without the need for active error correction. We demonstrate that symmetry can lead to self-correction in 3D spin-lattice models. In particular, we investigate codes given by 2D symmetry-enriched topological (SET) phases that appear naturally on the boundary of 3D symmetry-protected topological (SPT) phases. We find that while conventional on-site symmetries are not sufficient to allow for self-correction in commuting Hamiltonian models of this form, a generalized type of symmetry known as a 1-form symmetry is enough to guarantee self-correction. We illustrate this fact with the 3D "cluster-state" model from the theory of quantum computing. This model is a self-correcting memory, where information is encoded in a 2D SET-ordered phase on the boundary that is protected by the thermally stable SPT ordering of the bulk. We also investigate the gauge color code in this context. Finally, noting that a 1-form symmetry is a very strong constraint, we argue that topologically ordered systems can possess emergent 1-form symmetries, i.e., models w