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Published work
Using reinforcement learning, we optimize for practical hardware constraints, including limited FIR filter taps at the transmitter and receiver, mean photon number and finite DAC/ADC resolution. Under these realistic conditions, the proposed approach achieves significant performance improvements.
Device-independent quantum key distribution protocols allow two honest users to establish a secret key with minimal levels of trust on the provider, as security is proven without any assumption on the inner working of the devices used for the distribution. Unfortunately, the implementation of these protocols is challenging, as it requires the observation of a large Bell-inequality violation between the two distant users. Here, we introduce novel photonic protocols for device-independent quantum key distribution exploiting single-photon sources and heralding-type architectures. The heralding process is designed so that transmission losses become irrelevant for security. We then show how the use of single-photon sources for entanglement distribution in these architectures, instead of standard entangled-pair generation schemes, provides significant improvements on the attainable key rates and distances over previous proposals. Given the current progress in single-photon sources, our work opens up a promising avenue for device-independent quantum key distribution implementations.
We consider a communication scenario where classical information is encoded in an ensemble of quantum states that admit a power series expansion in a cost parameter and with the vanishing cost converge to a single zero-cost state. For a given measurement scheme, we derive an approximate expression for mutual information in the leading order of the cost parameter. The general results are applied to selected problems in optical communication, where coherent states of light are used as input symbols and the cost is quantified as the average number of photons per symbol. We show that for an arbitrary individual measurement on phase shift keyed (PSK) symbols, the photon information efficiency is upper bounded by 2 nats of information per photon in the low-cost limit, which coincides with the conventional homodyne detection bound. The presented low-cost approximation facilitates a systematic analysis of few-symbol measurements that exhibit superadditivity of accessible information. For the binary PSK alphabet of coherent states, we present designs for two- and three-symbol measurement schemes based on linear optics, homodyning, and single photon detection that offer respectively 2.49% and 3.40% enhancement relative to individual measurements. We also show how designs for scalable superadditive measurement schemes emerge from the introduced low-cost formalism.
Quantum fingerprinting reduces communication complexity of determination whether two $n$-bit long inputs are equal or different in the simultaneous message passing model. Here we quantify the advantage of quantum fingerprinting over classical protocols when communication is carried out using optical signals with limited power and unrestricted bandwidth propagating over additive white Gaussian noise (AWGN) channels with power spectral density (PSD) much less than one photon per unit time and unit bandwidth. We identify a noise parameter whose order of magnitude separates near-noiseless quantum fingerprinting, with signal duration effectively independent of $n$, from a regime where the impact of AWGN is significant. In the latter case the signal duration is found to scale as $O(\sqrt{n})$, analogously to classical fingerprinting. However, the dependence of the signal duration on the AWGN PSD is starkly distinct, leading to quantum advantage in the form of a reduced multiplicative factor in $O(\sqrt{n})$ scaling.
This tutorial reviews the Holevo capacity limit as a universal tool to analyze the ultimate transmission rates in a variety of optical communication scenarios, ranging from conventional optically amplified fiber links to free-space communication with power-limited optical signals. The canonical additive white Gaussian noise model is used to describe the propagation of the optical signal. The Holevo limit exceeds substantially the standard Shannon limit when the power spectral density of noise acquired in the course of propagation is small compared to the energy of a single photon at the carrier frequency per unit time-bandwidth area. General results are illustrated with a discussion of efficient communication strategies in the photon-starved regime.
The information capacity of an optical channel under power constraints is ultimately limited by the quantum nature of transmitted signals. We discuss currently available and emerging photonic technologies whose combination can be shown theoretically to enable nearly quantum-limited operation of a noisy optical communication link in the photon-starved regime, with the information rate scaling linearly in the detected signal power. The key ingredients are quantum pulse gating to facilitate mode selectivity, photon-number-resolved direct detection, and a photon-efficient high-order modulation format such as pulse position modulation, frequency shift keying, or binary phase shift keyed Hadamard words decoded optically using structured receivers.
We consider the problem of estimating the spatial separation between two mutually incoherent point light sources using the super-resolution imaging technique based on spatial mode demultiplexing with noisy detectors. We show that in the presence of noise the resolution of the measurement is limited by the signal-to-noise ratio (SNR) and the minimum resolvable spatial separation has a characteristic dependence of $\sim$SNR$^{-1/2}$. Several detection techniques, including direct photon counting, as well as homodyne and heterodyne detection are considered.
The spatial structure of single photons is becoming an extensively explored resource used for facilitating the free-space quantum key distribution and quantum computation as well as for benchmarking the limits of quantum entanglement generation with orbital angular momentum modes or reduction of the photon free-space propagation speed. Albeit nowadays an accurate tailoring of photon's spatial structure is routinely performed using methods employed for shaping classical optical beams, the reciprocal problem of retrieving the spatial phase-amplitude structure of an unknown single photon cannot be solved using complimentary classical holography techniques exhibiting excellent interferometric precision. Here we introduce a method to record a hologram of a single photon (HSP) probed by another reference photon, based on essentially different concept of quantum interference between two-photon probability amplitudes. Similarly to classical holograms, HSP encodes full information about photon's "shape", i.e. its quantum wavefunction whose local amplitude and phase are retrieved in the demonstrated experiment.
Quantum metrology overcomes standard precision limits by exploiting collective quantum superpositions of physical systems used for sensing, with the prominent example of non-classical multiphoton states improving interferometric techniques. Practical quantum-enhanced interferometry is, however, vulnerable to imperfections such as partial distinguishability of interfering photons. Here we introduce a method where appropriate design of the modal structure of input photons can alleviate deleterious effects caused by another, experimentally inaccessible degree of freedom. This result is accompanied by a laboratory demonstration that a suitable choice of spatial modes combined with position-resolved coincidence detection restores entanglement-enhanced precision in the full operating range of a realistic two-photon Mach-Zehnder interferometer, specifically around a point which otherwise does not even attain the shot-noise limit due to the presence of residual distinguishing information in the spectral degree of freedom. Our method highlights the potential of engineering multimode physical systems in metrologic applications.
We analyze the effect of phase fluctuations in an optical communication scheme based on collective detection of sequences of binary coherent state symbols using linear optics and photon counting. When the phase noise is absent, the scheme offers qualitatively improved nonlinear scaling of the spectral efficiency with the mean photon number in the low-power regime compared to individual detection. We show that this feature, providing a demonstration of superaddivitity of accessible information in classical communication over quantum channels, is preserved if random phases imprinted on transmitted symbols fluctuate around a reference fixed over the sequence length.
In this paper, we propose a method for the generation of higher dimensional modal entanglement through type II spontaneous parametric down conversion process using a three waveguide directional coupler in a periodically poled lithium niobate substrate. We show that by a proper design, it is possible to achieve an output state of two photons occupying three different spatial modes. The advantage of using such waveguide structure is its flexibility and the design space availability to achieve desired characteristics of the photon pairs generated in the down conversion process
We analyze the performance of on-off keying (OOK) and its restricted version pulse position modulation (PPM) over a lossy narrowband optical channel under the constraint of a low average photon number, when direct detection is used at the output. An analytical approximation for the maximum PPM transmission rate is derived, quantifying the effects of photon statistics on the communication efficiency in terms of the $g^{(2)}$ second-order intensity correlation function of the light source. Enhancement attainable through the use of sub-Poissonian light is discussed.
A key ingredient in emerging quantum-enhanced technologies is the ability to coherently manipulate and detect superpositions of basis states. In integrated optics implementations, transverse spatial modes supported by multimode structures offer an attractive carrier of quantum superpositions. Here we propose an integrated dynamic mode converter based on the electro-optic effect in nonlinear channel waveguides for deterministic transformations between mutually non-orthogonal bases of spatial modes. We theoretically show its capability to demonstrate a violation of a Bell-type Clauser-Horne-Shimony-Holt inequality by measuring spatially mode-entangled photon pairs generated by an integrated photon pair source. The proposed configuration, numerically studied for the potassium titanyl phosphate (KTP) material, can be easily implemented using standard integrated optical fabrication technology.
We analyze the ultimate quantum limit on the accessible information for an optical communication scheme when time bins carry coherent light pulses prepared in one of several orthogonal modes and the phase undergoes diffusion after each channel use. This scheme, an example of a quantum memory channel, can be viewed as noisy pulse position modulation (PPM) keying with phase fluctuations occurring between consecutive PPM symbols. We derive a general expression for the output states in the Fock basis and implement a numerical procedure to calculate the Holevo quantity. Using asymptotic properties of Toeplitz matrices, we also present an analytic expression for the Holevo quantity valid for very weak signals and sufficiently strong dephasing when the dominant contribution comes from the single-photon sector in the Hilbert space of signal states. Based on numerical results we conjecture an inequality for contributions to the Holevo quantity from multiphoton sectors which implies that in the asymptotic limit of weak signals, for arbitrarily small dephasing the accessible information scales linearly with the average number of photons contained in the pulse. Such behaviour presents a qualitative departure from the fully coherent case.
We present a method for spatially resolved multiphoton counting based on an intensified camera with the retrieval of multimode photon statistics fully accounting for non-linearities in the detection process. The scheme relies on one-time quantum tomographic calibration of the detector. Faithful, high-fidelity reconstruction of single- and two-mode statistics of multiphoton states is demonstrated for coherent states and their statistical mixtures. The results consistently exhibit classical values of Mandel and Fano parameters in contrast to raw statistics of camera photo-events. Detector operation is reliable for illumination levels up to the average of one photon per an event area, substantially higher than in previous approaches to characterize quantum statistical properties of light with spatial resolution.
We report measurements of two-photon interference using a cw-pumped type-II spontaneous parametric down-conversion source based on a multimode perodically poled potassium titanyl phosphate waveguide. We have used the recently demonstrated technique of controlling the spatial characteristics of the down-conversion process via intermodal dispersion to generate photon pairs in fundamental transverse modes, thus ensuring their spatial indistinguishability. Good spatial overlap of photon modes within pairs has been verified using the Hong-Ou-Mandel interferometer and the preparation of polarization entanglement in the Shih-Alley configuration, yielding visibilities consistently above 90%.
We study the operation of linear optics schemes for entanglement distribution based on nonlocal photon subtraction when input states, produced by imperfect single-photon sources, exhibit both vacuum and multiphoton contributions. Two models for realistic photon statistics with radically different properties of the multiphoton "tail" are considered. The first model assumes occasional emission of double photons and linear attenuation, while the second one is motivated by heralded sources utilizing spontaneous parametric down-conversion. We find conditions for the photon statistics that guarantee generation of entanglement in the relevant qubit subspaces and compare it with classicality criteria. We also quantify the amount of entanglement that can be produced with imperfect single-photon sources, optimized over setup parameters, using as a measure entanglement of formation. Finally, we discuss verification of the generated entanglement by testing Bell's inequalities. The analysis is carried out for two schemes. The first one is the well-established one-photon scheme, which produces a photon in a delocalized superposition state between two nodes, each of them fed with one single photon at the input. As the second scheme, we introduce and analyze a linear-optics analog of the robust scheme based on interfering two Stokes photons emitted by atomic ensembles, which does not require phase stability between the nodes.
The fundamental quantum interferometry bound limits the sensitivity of an interferometer for a given total rate of photons and for a given decoherence rate inside the measurement device.We theoretically show that the recently reported quantum-noise limited sensitivity of the squeezed-light-enhanced gravitational-wave detector GEO600 is exceedingly close to this bound, given the present amount of optical loss. Furthermore, our result proves that the employed combination of a bright coherent state and a squeezed vacuum state is generally the optimum practical approach for phase estimation with high precision on absolute scales. Based on our analysis we conclude that neither the application of Fock states nor N00N states or any other sophisticated nonclassical quantum states would have yielded an appreciably higher quantum-noise limited sensitivity.
We analyze theoretically performance of four-state quantum key distribution protocols implemented with a realistic heralded single-photon source. The analysis assumes a noisy model for the detector heralding generation of individual photons via spontaneous parametric down-conversion, including dark counts and imperfect photon number resolution. We identify characteristics of the heralding detector that defines the attainable cryptographic key rate and the maximum secure distance. Approximate analytical formulas are applied to multiplexed detection and compared with results of numerical calculations.
For a particle travelling through an interferometer, the trade-off between the available which-way information and the interference visibility provides a lucid manifestation of the quantum mechanical wave-particle duality. Here we analyze this relation for a particle possessing an internal degree of freedom such as spin. We quantify the trade-off with a general inequality that paints an unexpectedly intricate picture of wave-particle duality when internal states are involved. Strikingly, in some instances which-way information becomes erased by introducing classical uncertainty in the internal degree of freedom. Furthermore, even imperfect interference visibility measured for a suitable set of spin preparations can be sufficient to infer absence of which-way information. General results are illustrated with a proof-of-principle single photon experiment.
We report generation of near-infrared photon pairs in fundamental spatial modes via type-II spontaneous parametric down-conversion in a periodically poled potassium titanyl phosphate (KTiOPO4) nonlinear waveguide supporting multiple transverse modes. This demonstrates experimentally a versatile scheme for controlling the spatial characteristics of the produced nonclassical light based on exploitation of intermodal dispersion. The down-converted photons are characterized by the measurement of the beam quality factors in the heralded regime.
We present experimental realization of type-II spontaneous parametric down-conversion in a periodically poled potassium titanyl phosphate (KTiOPO4) nonlinear waveguide. We demonstrate that by careful exploitation of intermodal dispersion in the waveguide it is feasible to produce photon pairs in well defined transverse modes without any additional spatial filtering at the output. Spatial characteristics is verified by measurements of the M2 beam quality factors. We also prepared a postselected polarization-entangled two-photon state shown to violate Bell's inequality. Similar techniques based on intermodal dispersion can be used to generate spatial entanglement and hyperentanglement.
We report experimental generation of a noisy entangled four-photon state that exhibits a separation between the secure key contents and distillable entanglement, a hallmark feature of the recently established quantum theory of private states. The privacy analysis, based on the full tomographic reconstruction of the prepared state, is utilized in a proof-of-principle key generation. The inferiority of distillation-based strategies to extract the key is exposed by an implementation of an entanglement distillation protocol for the produced state.
We demonstrate that for an ensemble of qudits, subjected to collective decoherence in the form of perfectly correlated random SU(d) unitaries, quantum superpositions stored in the decoherence free subspace are fully immune against the removal of one particle. This provides a feasible scheme to protect quantum information encoded in the polarization state of a sequence of photons against both collective depolarization and one photon loss, and can be demonstrated with photon quadruplets using currently available technology.
While it is usually known that the mean value of a single observable is enough to detect entanglement or its distillability, the counterpart of such an approach in the case of quatum privacy has been missing. Here we develop the concept of a privacy witness, i.e. a single observable that may detect presence of the secure key even in the case of bound entanglement. Then we develop the notion of secret key estimation based on few observables and discuss the witness decomposition into local measurements. The surprising property of the witness is that with the help of a low number of product mesurements involved it may still report the key values that are {\it strictly above} distillable entanglement of the state. For an exemplary four-qubit state studied in a recent experiment [K. Dobek {\em et al.}, Phys. Rev. Lett. {\bf 106}, 030501 (2011)] this means 6 Pauli operator product measurements versus 81 needed to carry out the complete quantum state tomography. The present approach may be viewed as a paradigm for the general program of experimentally friendly detection and estimation of task-dedicated quantum entanglement.
We derive an inequality bounding the strength of temporal correlations for a pair of light beams prepared in a separable state and propagating through dispersive media with opposite signs of group velocity dispersion. The presented inequality can be violated by entangled states of light, such as photon pairs produced in spontaneous parametric down-conversion. Because the class of separable states covers the entire category of classical fields as a particular case, this result provides an unambiguously quantum feature of nonlocal dispersion cancellation that cannot be reproduced within the classical theory of electromagnetic radiation.
We report experimental determination of the phase-matching function for type-II three-wave mixing in a periodically poled KTiOPO_4 waveguide in the 792-815 nm spectral region. The measurement was performed by sum-frequency generation of spectrally tuned fundamental components. Strong dependence of the observed signal on the excited spatial modes in the waveguide has been observed and fully interpreted. These results indicate a route to employ the waveguide for spontaneous parametric down-conversion producing photon pairs in well-defined spatial modes.
We employed an electrically-driven polarization controller to implement anisotropic depolarizing quantum channels for the polarization state of single photons. The channels were characterized by means of ancilla-assisted quantum process tomography using polarization-entangled photons generated in the process of spontaneous parametric down-conversion. The demonstrated depolarization method offers good repeatability, low cost, and compatibility with fiber-optic setups. It does not perturb the modal structure of single photons, and therefore can be used to verify experimentally protocols for managing decoherence effects based on multiphoton interference.
We analyze the strength of polarization correlations between two light beams that can be achieved in the semiclassical regime using statistical mixtures of coherent states and binary on/off detectors. Under certain symmetry assumptions, the visibility of polarization correlations is shown to be bounded by 1/3, which is in a striking contrast with perfect 100% correlations exhibited by photon pairs prepared in the singlet state. The semiclassical limit is demonstrated in a measurement performed on a pair of laser beams undergoing correlated depolarization. This result illustrates the dramatic difference between predictions of quantum mechanics and the semiclassical theory of electromagnetic radiation for the polarization degree of freedom.
Recent progress in manipulating quantum states of light and matter brings quantum-enhanced measurements closer to prospective applications. The current challenge is to make quantum metrologic strategies robust against imperfections.
We discuss characterization of single-photon wave packets by measuring Hong-Ou-Mandel interference with a weak coherent pulse. A complete multimode calculation is presented and effects of multiphoton terms in the coherent field as well as the impact of source and detection imperfections are discussed.
We derive the general structure of noiseless subsystems for optical radiation contained in a sequence of pulses undergoing collective depolarization in an optical fiber. This result is used to identify optimal ways to implement quantum communication over a collectively depolarizing channel, which in general combine various degrees of freedom, such as polarization and phase, into joint hybrid schemes for protecting quantum coherence.
Detectors that can resolve photon number are needed in many quantum information technologies. In order to be useful in quantum information processing, such detectors should be simple, easy to use, and be scalable to resolve any number of photons, as the application may require great portability such as in quantum cryptography. Here we describe the construction of a time-multiplexed detector, which uses a pair of standard avalanche photodiodes operated in Geiger mode. The detection technique is analysed theoretically and tested experimentally using a pulsed source of weak coherent light.
We present a complete statistical analysis of quantum optical measurement schemes based on photodetection. Statistical distributions of quantum observables determined from a finite number of experimental runs are characterized with the help of the generating function, which we derive using the exact statistical description of raw experimental outcomes. We use the developed formalism to point out that the statistical uncertainty results in substantial limitations of the determined information on the quantum state: though a family of observables characterizing the quantum state can be safely evaluated from experimental data, its further use to obtain the expectation value of some operators generates exploding statistical errors. These issues are discussed using the example of phase-insensitive measurements of a single light mode. We study reconstruction of the photon number distribution from photon counting and random phase homodyne detection. We show that utilization of the reconstructed distribution to evaluate a simple well-behaved observable, namely the parity operator, encounters difficulties due to accumulation of statistical errors. As the parity operator yields the Wigner function at the phase space origin, this example also demonstrates that transformation between various experimentally determined representations of the quantum state is a quite delicate matter.
A phase space description of the fractional Talbot effect, occurring in a one-dimensional Fresnel diffraction from a periodic grating, is presented. Using the phase space formalism a compact summation formula for the Wigner function at rational multiples of the Talbot distance is derived. The summation formula shows that the fractional Talbot image in the phase space is generated by a finite sum of spatially displaced Wigner functions of the source field.
We study the application of squeezed states in a quantum optical scheme for direct sampling of the phase space by photon counting. We prove that the detection setup with a squeezed coherent probe field is equivalent to the probing of the squeezed signal field with a coherent state. An example of the Schroedinger cat state measurement shows that the use of squeezed states allows one to detect clearly the interference between distinct phase space components despite losses through the unused output port of the setup.
We study the accuracy of determining the phase space quasidistribution of a single quantized light mode by a photon counting experiment. We derive an exact analytical formula for the error of the experimental outcome. This result provides an estimation for the experimental parameters, such as the number of events, required to determine the quasidistribution with assumed precision. Our analysis also shows that it is in general not possible to compensate the imperfectness of the photodetector in a numerical processing of the experimental data. The discussion is illustrated with Monte Carlo simulations of the photon counting experiment for the coherent state, the one photon Fock state, and the Schroedinger cat state.