We introduce a filter using a noise-free quantum buffer with large optical bandwidth that can both filter temporal-spectral modes, as well as inter-convert them and change their frequency. We show that such quantum buffers optimally filter out temporal-spectral noise; producing identical single-photons from many distinguishable noisy single-photon sources with the minimum required reduction in brightness. We then experimentally demonstrate a noise-free quantum buffer in a warm atomic system that is well matched to quantum dots and can outperform all intensity (incoherent) filtering schemes for increasing indistinguishability.
A stochastic model for a continuous photon counting and heterodyne measurement of a coherent source is proposed. A nonlinear filtering equation for the posterior state of a single-mode field in a cavity is derived by using the methods of quantum stochastic calculus. The posterior dynamics is found for the observation of a Bose field being initially in a coherent state. The filtering equations for counting and diffusion processes are given.
We derive the form of the quantum filter equation describing the continuous observation of the phase of a quantum system in an arm of an interferometer via non-demolition measurements when the statistics of an input field used for the indirect measurement are in a general coherent state. Both quadrature homodyne detection and photon-counting dection schemes are covered, and we solve the linearized filter for a specific application.
We propose and experimentally demonstrate non-destructive and noiseless removal (filtering) of vacuum states from an arbitrary set of coherent states of continuous variable systems. Errors i.e. vacuum states in the quantum information are diagnosed through a weak measurement, and on that basis, probabilistically filtered out. We consider three different filters based on on/off detection phase stabilized and phase randomized homodyne detection. We find that on/off etection, optimal in the ideal theoretical setting, is superior to the homodyne strategy in a practical setting.
Coherent temporal filtering of multimode parametric down-conversion using a quantum pulse gate
Integrated Quantum Optics Group, Institute for Photonic Quantum Systems (PhoQS), Paderborn University（帕德博恩大学光子量子系统研究所）；School of Mathematics and Physics, University of Queensland（昆士兰大学数学与物理学院）
Probabilistic quantum filtering is proposed to properly adapt sequential independent quantum channels in order to stop sudden death of entanglement. In the adaptation, the quantum filtering does not distill or purify more entanglement, it rather properly prepares entangled state to the subsequent quantum channel. For example, the quantum adaptation probabilistically eliminates the sudden death of entanglement of two-qubit entangled state with isotropic noise injected into separate amplitude damping channels. The result has a direct application in quantum key distribution through noisy channels…
Number state filtering in coherent states leads to sub-Poissonian photon statistics. These states are more suitable for phase estimation when compared with the coherent states. Nonclassicality of these states is quantified in terms of the negativity of the Wigner function and the entanglement potential. Filtering of the vacuum from a coherent state is almost like the photon-addition. However, filtering makes the state more resilient against dissipation than photon-addition. Vacuum state filtered coherent states perform better than the photon-added coherent states for a two-way quantum key dist…
Security of a continuous-variable quantum key distribution protocol based on noisy coherent states and channel is analyzed. Assuming the noise of coherent states is induced by Fred, a neutral party relative to others, we prove that the prepare and measurement scheme and entanglement-based scheme are equivalent. Then, we show that this protocol is secure against Gaussian collective attacks even if the channel is lossy and noisy, and further, a lower bound to the secure key rate is derived.
We investigate the non-Markovian dynamics of a qubit-oscillator system embedded in a noisy environment by employing the hierarchical equations of motion approach. It is found that the decoherence rate of the whole qubit-oscillator-bath system can be significantly suppressed by enhancing the coupling strength between the qubit and the harmonic oscillator. Moreover, we find that the non-Markovian memory character of the bath is able to facilitate a robust quantum coherent dynamics in this qubit-oscillator-bath system. Our findings may be used to engineer some tunable coherent manipulations in me…
We present methods for the direct characterization of quantum dynamics (DCQD) in which both the principal and ancilla systems undergo noisy processes. Using a concatenated error detection code, we discriminate between located and unlocated errors on the principal system in what amounts to filtering of ancilla noise. The example of composite noise involving amplitude damping and depolarizing channels is used to demonstrate the method, while we find the rate of noise filtering is more generally dependent on code distance. Our results indicate the accuracy of quantum process characterization can …
A basic feasible probabilistic purification of unknown noisy coherent states, outgoing from different state preparations with unknown mean number of thermal photons, is proposed. The scheme is based only on a linear-optical network with an avalanche photo-diode or heterodyne (homodyne) detection used to post-select a successful processing. The suggested probabilistic method can produce an output state with a lower noise than both quantum deterministic and classical probabilistic distillation method. The purification applied in the state preparation can increase classical capacity of communicat…
Time-frequency (TF) filtering of analog signals has played a crucial role in the development of radio-frequency communications, and is currently being recognized as an essential capability for communications, both classical and quantum, in the optical frequency domain. How best to design optical time-frequency (TF) filters to pass a targeted temporal mode (TM), and to reject background (noise) photons in the TF detection window? The solution for coherent TF filtering is known, the quantum pulse gate, whereas the conventional, more common method is implemented by a sequence of incoherent spectr…
A precise security analysis of practical quantum key distribution (QKD) systems is an important step for improving their performance. Here we consider a class of quantum soft filtering operations, which generalizes the unambiguous state discrimination (USD) technique. These operations can be applied as a basis for a security analysis of the original coherent one-way (COW) QKD protocol since their application interpolates between beam-splitting (BS) and USD attacks. We demonstrate that a zero-error attack based on quantum soft filtering operations gives a larger amount of the information for Ev…
Quantum-limited amplifiers increase the amplitude of quantum signals at the price of introducing additional noise. Quantum purification protocols operate in the reverse way, by reducing the noise while attenuating the signal. Here we investigate a scenario that interpolates between these two extremes. We search for the optimal physical process that generates $M$ approximate copies of pure and amplified coherent state, starting from $N$ copies of a noisy coherent state with Gaussian modulation. We prove that the optimal deterministic processes are always Gaussian, whereas non-Gaussianity powers…
We derive the form of the Belavkin-Kushner-Stratonovich equation describing the filtering of a continuous observed quantum system via non-demolition measurements when the statistics of the input field used for the indirect measurement are in a general coherent state.
We propose a hybrid quantum-classical atomic clock protocol where the interrogation of an ensemble of uncorrelated atoms in a spin-coherent state is used to feedback one (or more) spin-squeezed atomic ensembles toward their optimal phase sensitivity point. This protocol overcomes the stability of a single Ramsey clock and it reaches a Heisenberg-limited stability while avoiding non-destructive measurements. Analytical predictions are compared with numerical simulations of clocks operations including correlated 1/f local oscillator noise.
We address security of the quantum key distribution scheme based on the noisy modulation of coherent states and investigate how it is robust against noise in the modulation regardless of the particular technical implementation. As the trusted preparation noise is shown to be security breaking even for purely lossy channels, we reveal the essential difference between two types of trusted noise, namely sender-side preparation noise and receiver-side detection noise, the latter being security preserving. We consider the method of sender-side state purification to compensate the preparation noise …
Many quantum mechanical experiments can be viewed as multi-round interactive protocols between known quantum circuits and an unknown quantum process. Fully quantum "coherent" access to the unknown process is known to provide an advantage in many discrimination tasks compared to when only incoherent access is permitted, but it is unclear if this advantage persists when the process is noisy. Here, we show that a quantum advantage can be maintained when distinguishing between two noisy single qubit rotation channels. Numerical and analytical calculations reveal a distinct transition between optim…
The problem of measuring a time-varying phase, even when the statistics of the variation is known, is considerably harder than that of measuring a constant phase. In particular, the usual bounds on accuracy - such as the $1/(4\bar{n})$ standard quantum limit with coherent states - do not apply. Here, restricting to coherent states, we are able to analytically obtain the achievable accuracy - the equivalent of the standard quantum limit - for a wide class of phase variation. In particular, we consider the case where the phase has Gaussian statistics and a power-law spectrum equal to $κ^{p-1}/|ω…
Inspired by the works of [F. Caruso, New J. Phys. 16, 055015 (2014)] and [T. Scholak et al, J. Phys. B: At. Mol. Opt. Phys. 44 184012 (2011)], which state that for a large class of complex noisy networks, the optimal efficiency of quantum transport is universally obtained by mixing coherent (Hamiltonian) and incoherent (noisy) parts where the contribution of the coherent part is strictly more than incoherent one, we examine the effect of oscillatory deformations on two simple prototypes in order to study their effects on the efficiency of coherent and incoherent energy transport. The prototype…
We identify and discuss nonlinear phase noise arising in Kerr self-phase modulation of a coherent light pulse propagating through an attenuating medium with third-order nonlinearity in a dispersion-free setting. This phenomenon, accompanying the standard unitary Kerr transformation of the optical field, is described with high accuracy as Gaussian phase diffusion with parameters given by closed expressions in terms of the system properties. We show that the irreversibility of the nonlinear phase noise ultimately limits the ability to transmit classical information in the phase variable over a l…
We consider coherent feedback control of quantum transport and focus on the application of simple controllers and the effects of a finite bias voltage. We show that simple single-parameter controllers can give rise to a range of useful effects such as amplification of changes in plant transmission, increased resolution of energy filtration, and the detection of differences between otherwise indistinguishable plants. We explore how these effects are impacted by the phase-averaging effects associated with the application of a finite bias and identify important voltage scales for the maintenance …
General quantum correlations measures like quantum discord, one norm geometric quantum discord, exhibit freezing, sudden change, double sudden change behavior in their decay rates under different noisy channels. Therefore, one may attempt to investigate how the freezing behavior and other dynamical features are affected under application of local quantum operations. In this work, we demonstrate the effect of local filtering on the dynamical evolution of quantum correlations. We have found that using local filtering one may remove freezing depending upon the filtering parameter.
We present the Belavkin filtering equation for the intense balanced heterodyne detection in a unitary model of an indirect observation. The measuring apparatus modelled by a Bose field is initially prepared in a coherent state and the observed process is a diffusion one. We prove that this filtering equation is relaxing: any initial square-integrable function tends asymptotically to a coherent state with an amplitude depending on the coupling constant and the initial state of the apparatus. The time-development of a squeezed coherent state is studied and compared with the previous results obta…
The use of an interferometer to perform an ultra-precise parameter estimation under noisy conditions is a challenging task. Here we discuss nearly optimal measurement schemes for a well known,sensitive input state, squeezed vacuum and coherent light. We find that a single mode intensity measurement, while the simplest and able to beat the shot-noise limit, is outperformed by other measurement schemes in the low-power regime. However, at high powers, intensity measurement is only outperformed by a small factor. Specifically, we confirm, that an optimal measurement choice under lossless conditio…
We propose a new technique for comparing two Raman active samples. The method employs optical interference of the signals generated via coherent anti-Stokes Raman scattering (CARS) of broadband laser pulses with noisy spectra. It does not require spectrally resolved detection, and no prior knowledge about either the Raman spectrum of the samples, or the spectrum of the incident light is needed. We study the proposed method theoretically, and demonstrate it in a proof-of-principle experiment on Toluene and ortho-Xylene samples.
It is the first scheme which allows the detection apparatus to achieve both the photon number of arriving signals and quantum bit error rate of the multiphoton pulses precisely. We show that the upper bound of the fraction of the tagged multiphoton pulses counts is $μ$, which is independent of the channel loss and the intensity of the decoy source. Such upper bound is $inherent$ and cannot be reduced any longer as long as the weak coherent scouces and high lossy channel are used. We show that our scheme can be implemented even if the channel loss is very high. A stronger intensity of the pulse…
Noisy quantum channels may be used in many information carrying applications. We show that different applications may result in different channel capacities. Upper bounds on several of these capacities are proved. These bounds are based on the coherent information, which plays a role in quantum information theory analogous to that played by the mutual information in classical information theory. Many new properties of the coherent information and entanglement fidelity are proved. Two non-classical features of the coherent information are demonstrated: the failure of subadditivity, and the fail…
Coherent population trapping is a well-known quantum phenomenon in a driven $Λ$ system, with many applications across quantum optics. However, when a stochastic bath is present in addition to vacuum noise, the observed trapping is no longer perfect. Here we derive a time-convolutionless master equation describing the equilibration of the $Λ$ system in the presence of additional temporally correlated classical noise, with an unknown decay parameter. Our simulations show a one-to-one correspondence between the decay parameter and the depth of the characteristic dip in the photoluminescence spect…
Machine learning techniques are increasingly being used in fundamental research to solve various challenging problems. Here we explore one such technique to address an important problem in quantum communication scenario. While transferring quantum information through a noisy quantum channel, the utility of the channel is characterized by its quantum capacity. Quantum channels, however, display an intriguing property called super-additivity of coherent information. This makes the calculation of quantum capacity a hard computational problem involving optimization over an exponentially increasing…
This paper proposes a multi-mode Gaussian modulated continuous variable quantum key distribution (CV-QKD) scheme able to operate at high bandwidth despite using conventional noisy, coherent detectors. We demonstrate enhancement in shotnoise sensitivity as well as reduction in the electronic noise variance of the coherent receiver of the multi-mode CV-QKD system. A proof-of-concept simulation is presented using multiple modes; this demonstrates an increase in signal-to-noise ratio and secure key rate at various transmission distances with increasing signal modes.
We introduce here a coherent technique to inject, extract, and velocity filter neutral atoms in a ring trap coupled via tunneling to two additional waveguides. By adiabatically following the transverse spatial dark state, the proposed technique allows for an efficient and robust velocity dependent atomic population transfer between the ring and the input/output waveguides. We have derived explicit conditions for the spatial adiabatic passage that depend on the atomic velocity along the input waveguide as well as on the initial population distribution among the transverse vibrational states. Th…
Highly quantum non-linear interactions between different bosonic modes lead to the generation of quantum non-Gaussian states, i.e. states that cannot be written as mixtures of Gaussian states. A paradigmatic example is given by Schroedinger's cat states, that is coherent superpositions of coherent states with opposite amplitude. We here consider a novel quantum non-Gaussianity criterion recently proposed in the literature and prove its effectiveness on Schroedinger cat states evolving in a lossy bosonic channel. We prove that quantum non-Gaussianity can be effectively detected for high values …
Basing on unified approach to {\it all} kinds of quantum capacities we show that the rate of quantum information transmission is bounded by the maximal attainable rate of coherent information. Moreover, we show that, if for any bipartite state the one-way distillable entanglement is no less than coherent information, then one obtains Shannon-like formulas for all the capacities. The inequality also implies that the decrease of distillable entanglement due to mixing process does not exceed of corresponding loss information about a system.
We exploit the non-dissipative dynamics of a pair of electrons in a large square quantum dot to perform singlet-triplet spin measurement through a single charge detection and show how this may be used for entanglement swapping and teleportation. The method is also used to generate the AKLT ground state, a further resource for quantum computation. We justify, and derive analytic results for, an effective charge-spin Hamiltonian which is valid over a wide range of parameters and agrees well with exact numerical results of a realistic effective-mass model. Our analysis also indicates that the met…
We use the noisy entanglement-assisted classical capacity formula [arXiv:1609.08592] to create a coherent-attack security framework for Gaussian two-way quantum key distribution protocols in the asymptotic region.
Experimental Simulation of Two Pulses and Three Pulses Coherent One Way Quantum Key Distribution Protocol in Noisy/Noiseless and Wired/Wireless Environment
We show that the full statistics of the two detectors outputs in a balanced homodyne detection setup involving a local oscillator in an ideal coherent state is experimentally accessible despite the excess noise existing in actual laser sources. This possibility is illustrated using phase randomized coherent states signals from which the statistics of Fock states can accurately be obtained. The experimental verification of the recently predicted [Kühn and Vogel, Phys. Rev. A, \textbf{98}, 013832 (2018)] two-detector correlation probability for Fock states is presented for states $\vert 1 \rangl…
We study the exact dynamics of optical qubits encoded via coherent states with opposite phases which are interacting with an environment modeled as a collection of simple harmonic oscillators. Making use of a coherent-state path integral formulation, we are able to study memory effects on the dynamics of the coherent-state qubits due to strong environment coupling. We apply this formulation to examine the time evolution of a noisy quantum channel formed by two coherent-state qubits that are subject to uncorrelated local environment noises. In particular, we examine the time evolution of entang…
Error filtration is a method for encoding the quantum state of a single particle into a higher dimensional Hilbert space in such a way that it becomes less sensitive to phase noise. We experimentally demonstrate this method by distributing a secret key over an optical fiber whose noise level otherwise precludes secure quantum key distribution. By filtering out the phase noise, a bit error rate of 15.3% +/- 0.1%, which is beyond the security limit, can be reduced to 10.6% +/- 0.1%, thereby guaranteeing the cryptographic security.
The main aim of the paper is to present the analytical solution of the Belavkin quantum filtering equation for damped harmonic oscillator being initially in the squeezed coherent state for diffusion observation with complex white noise. The comparison of the a priori and a posteriori mean value of the optical quadrature operators and the photon number operator is given.
In this paper, we show how to use low-fidelity operations to control the dynamics of quantum systems. Noisy operations usually drive a system to evolve into a mixed state and damage the coherence. Sometimes frequent noisy operations result in the coherent evolution of a subsystem, and the dynamics of the subsystem is controlled by tuning noisy operations. Based on this, we find that universal quantum computation can be carried out by low-fidelity (fidelity $<90\%$) operations.
We give a proof that entanglement purification, even with noisy apparatus, is sufficient to disentangle an eavesdropper (Eve) from the communication channel. Our proof applies to all possible attacks (individual and coherent). Due to the quantum nature of the entanglement purification protocol, it is also possible to use the obtained quantum channel for secure transmission of quantum information.
The successful implementation of algorithms on quantum processors relies on the accurate control of quantum bits (qubits) to perform logic gate operations. In this era of noisy intermediate-scale quantum (NISQ) computing, systematic miscalibrations, drift, and crosstalk in the control of qubits can lead to a coherent form of error which has no classical analog. Coherent errors severely limit the performance of quantum algorithms in an unpredictable manner, and mitigating their impact is necessary for realizing reliable quantum computations. Moreover, the average error rates measured by randomi…
Noisy mean field annealing (NMFA) is an algorithm that mimics a coherent Ising machine (CIM), which is an optical system for solving Ising problems. The NMFA has reproduced the solver performance of the CIM for systems of limited size even though it simplifies the interaction between spins with a mean-field approximation. However, recent experiments observing various thermodynamic quantities have revealed that the CIM can capture the phase transitions of the two-dimensional Ising models that the mean field cannot capture. This situation leads to a fundamental question as to how well the NMFA c…
Using Gardiner and Collet's input-output model and the concept of cascade system, we determine the filtering equation for a quantum system driven by chosen non-classical states of light. The quantum system and electromagnetic field are described by making use of quantum stochastic unitary evolution. We consider two examples of the non-classical states of the field: a combination of vacuum and single photon states and a mixture of two coherent states. We describe the stochastic evolution conditioned on the results of the photon counting and quadrature measurements.
Quantum optics experiments frequently involve interfering single photons and coherent states. In the case of multi-photon experiments this requires that all photons are frequency degenerate. We report a simple and practical approach to generate coherent states that can be readily tuned to any wavelength required, for example by non-degenerate photon pair creation. We demonstrate this by performing a two-photon (Hong-Ou-Mandel) interference experiment between a coherent state and a pure heralded single photon source. No spectral filtering is required on either source, the coherent state constra…
Quantum Filtering (Quantum Trajectories) for Systems Driven by Fields in Single Photon States and Superposition of Coherent States
Aberystwyth University（阿伯里斯特威斯大学）；ARC Centre for Quantum Computation and Communication Technology（量子计算与通信技术ARC中心）；Research School of Engineering, Australian National University（澳大利亚国立大学工程研究学院）；School of Electrical Engineering and Telecommunications, The University of New South Wales（新南威尔士大学电气工程和电信学院）；Department of Physics and Astronomy, University of New Mexico（新墨西哥大学物理与天文学系）
The quantum discrimination of two non-coherent states draws much attention recently. In this letter, we first consider the quantum discrimination of two noiseless displaced number states. Then we derive the Fock representation of noisy displaced number states and address the problem of discriminating between two noisy displaced number states. We further prove that the optimal quantum discrimination of two noisy displaced number states can be achieved by the Kennedy receiver with threshold detection. Simulation results verify the theoretical derivations and show that the error probability of on…
