We demonstrate a sub-shot-noise-limit discrimination of on-off keyed coherent signals by an optimal displacement quantum receiver in which a superconducting transition edge sensor is installed. Use of a transition edge sensor and a fiber beam splitter realizes high total detection efficiency and high interference visibility of the receiver and the observed average error surpasses the shot-noise-limit in a wider range of the signal power. Our technique opens up a new technology for the sub-shot-noise-limit detection of coherent signals in optical communication channels.
We address binary optical communication channels based on phase-shift keyed coherent signals in the presence of phase diffusion. We prove theoretically and demonstrate experimentally that a discrimination strategy based on homodyne detection is robust against this kind of noise for any value of the channel energy. Moreover, we find that homodyne receiver beats the performance of Kennedy receiver as the signal energy increases, and achieves the Helstrom bound in the limit of large noise.
We address binary phase-shift-keyed communication channels based on Gaussian states and prove that squeezing improves state discrimination at fixed energy of the channel, also in the presence of phase diffusion. We then assess performances of homodyne detection against the ultimate quantum limits to discrimination, and show that homodyning achieves optimality in large noise regime. Finally, we consider noise in the preparation of the seed signal (before phase encoding) and show that also in this case squeezing may improve state discrimination in realistic conditions.
Quantum receiver is an important tool for overcoming the standard quantum limit (SQL) of discrimination errors in optical communication. We theoretically study the quantum receivers for discriminating ternary and quaternary phase shift keyed coherent states in terms of average error rate and mutual information. Our receiver consists of on/off-type photon detectors and displacement operations w/o electrical feedforward operations. We show that for the ternary signals, the receiver shows a reasonable gain from the SQL even without feedforward. This scheme is realizable with the currently availab…
The impossibility of perfectly discriminating non orthogonal quantum states imposes far-reaching consequences both on quantum and classical communication schemes. We propose and numerically analyze an optimized quantum receiver for the discrimination of phase encoded signals. Our scheme outperforms the standard quantum limit and approaches the Helstrom bound for any signal power. The discrimination is performed via an optimized, feedback-mediated displacement prior to a photon counting detector. We provide a detailed analysis of the influence of excess noise and technical imperfections on the …
We experimentally investigate a strategy to discriminate between quaternary phase-shift keyed coherent states based on single-shot measurements that is compatible with high-bandwidth communications. We extend previous theoretical work in single-shot measurements to include critical experimental parameters affecting the performance of practical implementations. Specifically, we investigate how the visibility of the optical displacement operations required in the strategy impacts the achievable discrimination error probability, and identify the experimental requirements to outperform an ideal he…
We address the limit of the Gaussian operations and classical communication in the problem of quantum state discrimination. We show that the optimal Gaussian strategy for the discrimination of the binary phase shift keyed (BPSK) coherent signal is a simple homodyne detection. We also propose practical near-optimal quantum receivers that beat the BPSK homodyne limit in all areas of the signal power. Our scheme is simple and does not require realtime electrical feedback.
We numerically study the performance of the displacement based quantum receiver for the discrimination of weak 3- and 4-phase-shift keyed (PSK) coherent state signals. We show that due to the nontrivial asymmetry of the receiver structure, optimization of the prior probability increases the mutual information and achieves sub-shot-noise limit discrimination. Moreover, we estimate the cutoff rate for a 4-PSK signal and confirm that the prior probability optimization shortens the code length for a given decoding error criterion. Such consideration for the asymmetric channel matrix is essential i…
We propose a near-optimum receiver for the discrimination of binary phase-shift-keyed coherent states employing photon-number-resolving detectors. The receiver exploits a discrimination strategy based on both the so-called homodyne-like and the direct detection, thus resulting in a hybrid scheme. We analyse the performance and the robustness of the proposed scheme under realistic conditions, namely, in the presence of inefficient detection and dark counts. We show that the present hybrid setup is near-optimum and beats both the standard-quantum-limit and the performance of the Kennedy receiver…
We provide a description of the problem of the discrimination of two quantum states in terms of receiver operation characteristics analysis, a prevalent approach in classical statistics. Receiveroperation characteristics diagrams provide an expressive representation of the problem, in which quantities such as the fidelity and the trace distance also appear explicitly. In addition we introduce an alternative quantum generalization of the classical Bhattacharyya coefficient. We evaluate our quantum Bhattacharyya coefficient for certain situations and describe some of its properties. These proper…
It is well known that a minimum error quantum measurement for arbitrary binary optical coherent states can be realized by a receiver that comprises interfering with a coherent reference light, photon counting, and feedback control. We show that, for ternary optical coherent states, a minimum error measurement cannot always be realized by such a receiver. The problem of finding an upper bound on the maximum success probability of such a receiver can be formulated as a convex programming. We derive its dual problem and numerically find the upper bound. At least for ternary phase-shift keyed cohe…
We consider the problem of discriminating between two quantum coherent states by interpreting a single state like being a collection of several successive copies of weaker coherent states. By means of recent results on multiple-copy state discrimination, it is possible to give a reinterpretation of the Dolinar receiver, and carry out a quite straightforward analysis of its behavior. We also propose and investigate a suboptimal detection scheme derived from the Dolinar's architecture, which is shown to slightly outperform some other near-optimal schemes available in literature.
We propose and experimentally demonstrate a near-optimal discrimination scheme for the quadrature phase shift keying protocol (QPSK). We show in theory that the performance of our hybrid scheme is superior to the standard scheme - heterodyne detection - for all signal amplitudes and underpin the predictions with our experimental results. Furthermore, our scheme provides the hitherto best performance in the domain of highly attenuated signals. The discrimination is composed of a quadrature measurement, a conditional displacement and a threshold detector.
We propose quantum receivers with optical squeezing and photon-number-resolving detector (PNRD) for the near-optimal discrimination of quaternary phase-shift-keyed coherent state signals. The basic scheme is similar to the previous proposals (e.g. Phys. Rev. A 84, 042328 (2012)) in which displacement operations, on-off detectors, and electrical feedforward operations were used. Here we study two types of receivers where one installs optical squeezings and the other uses PNRDs instead of on-off detectors. We show that both receivers can attain lower error rates than that by the previous scheme …
We investigate quantum measurement strategies capable of discriminating two coherent states probabilistically with significantly smaller error probabilities than can be obtained using non- probabilistic state discrimination. We apply a postselection strategy to the measurement data of a homodyne detector as well as a photon number resolving detector in order to lower the error probability. We compare the two different receivers with an optimal intermediate measurement scheme where the error rate is minimized for a fixed rate of inconclusive results. The photon number resolving (PNR) receiver i…
We investigate the performance of a Kennedy receiver, which is known as a beneficial tool in optical coherent communications, to the quantum state discrimination of the two superpositions of vacuum and single photon states corresponding to the $\hatσ_x$ eigenstates in the single-rail encoding of photonic qubits. We experimentally characterize the Kennedy receiver in vacuum-single photon two-dimensional space using quantum detector tomography and evaluate the achievable discrimination error probability from the reconstructed measurement operators. We furthermore derive the minimum error rate ob…
The Kennedy-like receiver is a quasi-optimal receiver employed in binary phase-shift-keyed communication schemes with coherent states. It is based on the interference of the two signals encoding the message with a reference local oscillator and on/off photodetection. We show both theoretically and experimentally that it is possible to extract useful information about the phase reference by Bayesian processing of the very same data sample used to discriminate the signals shot by shot. We demonstrate that the minimum uncertainty in phase estimation, given by the inverse of the Fisher information…
We demonstrate an optical receiver that achieves the quantum Chernoff bound for discriminating coherent states from thermal states in the multi-copy scenario. In contrast, we find that repeated use of the receiver approaching the Helstrom bound for single-copy measurement is sub-optimal in this multi-copy case. Furthermore, for a large class of multi-copy discrimination tasks between a pure and a mixed state, we prove that any Helstrom-bound achieving single-copy receiver is suboptimal by a factor of at least two in error-probability exponent compared to the multi-copy quantum Chernoff bound. …
Understanding the fundamental sensitivity limit of an optical sensor requires a full quantum mechanical description of the sensing task. In this work, we calculate the fundamental (quantum) limit for discriminating between pure laser light and thermal noise in a photon-starved regime. The Helstrom bound for discrimination error probability for single mode measurement is computed along with error probability bounds for direct detection, coherent homodyne detection and the Kennedy receiver. A generalized Kennedy (GK) receiver is shown to closely approach the Helstrom limit. We present an experim…
The need of discriminating between different quantum states is a fundamental issue in Quantum Information and Communication. The actual realization of generally optimal strategies in this task is often limited by the need of supplemental resources and very complex receivers. We have experimentally implemented two discrimination schemes in a minimum-error scenario based on a receiver featured by a network structure and a dynamical processing of information. The first protocol implemented in our experiment, directly inspired to a recent theoretical proposal, achieves binary optimal discriminatio…
The optimal discrimination of non-orthogonal quantum states with minimum error probability is a fundamental task in quantum measurement theory as well as an important primitive in optical communication. In this work, we propose and experimentally realize a new and simple quantum measurement strategy capable of discriminating two coherent states with smaller error probabilities than can be obtained using the standard measurement devices; the Kennedy receiver and the homodyne receiver.
We experimentally demonstrate a quantum receiver based on Kennedy scheme for discrimination between two phase-modulated weak coherent states. The receiver is assembled entirely from the standard fiber-optic elements and operates at the conventional telecom wavelength 1.55 microns. The local oscillator and the signal are transmitted through different optical fibers, and the displaced signal is measured with a high-efficiency superconducting nanowire single-photon detector. We show the discrimination error rate two times below the shot-noise limit.
In the communication scenario, we consider the problem of the discrimination between the signals of the Quantum Pulse Position Modulation. We propose a receiver scheme that employs repeated local measurements in distinct temporal slots within the symbol time interval, adaptively chosen on the basis of the outcomes in the previous slots. By employing Dynamic Programming to optimize each measurement, we approach the theoretical performance limit much closer than existing receiver schemes.
We present a quantum receiver for 16-QAM signals discrimination with hybrid structure containing a homodyne receiver and a displacement receiver, which can outperform the SQL, and the performance can be improved by an optimized displacement.
Quantum metrology utilizes nonclassical resources, such as entanglement or squeezed light, to realize sensors whose performance exceeds that afforded by classical-state systems. Environmental loss and noise, however, easily destroy nonclassical resources, and thus nullify the performance advantages of most quantum-enhanced sensors. Quantum illumination (QI) is different. It is a robust entanglement-enhanced sensing scheme whose 6 dB performance advantage over a coherent-state sensor of the same average transmitted photon number survives the initial entanglement's eradication by loss and noise.…
Laser light is widely used for communication and sensing applications, so the optimal discrimination of coherent states--the quantum states of light emitted by a laser--has immense practical importance. However, quantum mechanics imposes a fundamental limit on how well different coher- ent states can be distinguished, even with perfect detectors, and limits such discrimination to have a finite minimum probability of error. While conventional optical receivers lead to error rates well above this fundamental limit, Dolinar found an explicit receiver design involving optical feedback and photon c…
The discrimination of non-orthogonal quantum states with reduced or without errors is a fundamental task in quantum measurement theory. In this work, we investigate a quantum measurement strategy capable of discriminating two coherent states probabilistically with significantly smaller error probabilities than can be obtained using non-probabilistic state discrimination. We find that appropriate postselection of the measurement data of a photon number resolving detector can be used to discriminate two coherent states with small error probability. We compare our new receiver to an optimal inter…
A scheme for the detection of low-intensity optical coherent signals was studied which uses a probabilistic amplifier operated in the non-heralded version, as the underlying non-linear operation to improve the detection efficiency. This approach allows us to improve the statistics by keeping track of all possible outcomes of the amplification stage (including failures). When compared with an optimized Kennedy receiver, the resulting discrimination success probability we obtain presents a gain up to ~1.85% and it approaches the Helstrom bound appreciably faster than the Dolinar receiver, when e…
Rydberg states of alkali atoms, where the outer valence electron is excited to high principal quantum numbers, have large electric dipole moments allowing them to be used as sensitive, wideband, electric field sensors. These sensors use electromagnetically induced transparency (EIT) to measure incident electric fields. The characteristic timescale necessary to establish EIT determines the effective speed at which the atoms respond to time-varying RF radiation. Previous studies have predicted that this EIT relaxation rate causes a performance roll-off in EIT-based sensors beginning at a less th…
Discrimination of coherent states beyond the standard quantum limit (SQL) is an important tasknot only for quantum information processing but also for optical coherent communication. In orderto optimize long distance optical fiber networks, it is of practical importance to develop a quantumreceiver beating the SQL and approaching the quantum bound at telecom wavelength. In this paper,we experimentally demonstrate a receiver beating the conventional SQL at telecom wavelength. Ourreceiver is composed of a displacement operation, a single photon counter and a real time adaptivefeedback operation.…
We address quantum $M$-ary phase-shift keyed (PSK) communication channels in the presence of phase diffusion, and analyze the use of probabilistic noiseless linear amplifiers (NLA) to enhance performance of coherent signals. We consider both static and dynamical phase diffusion and assess the performances of the channel for ideal and realistic phase receivers. Our results show that NLA employed at the stage of signal preparations is a useful resource, especially in the regime of weak signals. We also discuss the interplay between the use of NLA, and the memory effects occurring with dynamical …
The use of linearly independent signal states in realistic implementations of quantum key distribution (QKD) enables an eavesdropper to perform unambiguous state discrimination. We explore quantitatively the limits for secure QKD imposed by this fact taking into account that the receiver can monitor to some extend the photon number statistics of the signals even with todays standard detection schemes. We compare our attack to the beamsplitting attack and show that security against beamsplitting attack does not necessarily imply security against the attack considered here.
We present a quantum receiver for quadrature amplitude modulation (QAM) coherent states discrimination with homodyne-displacement hybrid structure. Our strategy is to carry out two successive measurements on parts of the quantum states. The homodyne result of the first measurement reveals partial information about the state and is forward to a displacement receiver, which finally identifies the input state by using feedback to adjust a reference field. Numerical simulation results show that for 16-QAM, the hybrid receiver could outperform the standard quantum limit (SQL) with a reduced number …
We propose a simple architecture based on multimode quantum memories for collective readout of classical information keyed using a pair coherent states, exemplified by the well-known binary phase shift keying format. Such a configuration enables demonstration of the superadditivity effect in classical communication over quantum channels, where the transmission rate becomes enhanced through joint detection applied to multiple channel uses. The proposed scheme relies on the recently introduced idea to prepare Hadamard sequences of input symbols that are mapped by a linear optical transformation …
We propose a long-distance continuous-variable quantum key distribution (CVQKD) with four-state protocol using non-Gaussian state-discrimination detection. A photon subtraction operation, which is deployed at the transmitter, is used for splitting the signal required for generating the non-Gaussian operation to lengthen the maximum transmission distance of CVQKD. Whereby an improved state-discrimination detector, which can be deemed as an optimized quantum measurement that allows the discrimination of nonorthogonal coherent states beating the standard quantum limit, is applied at the receiver …
One of the most fascinating aspects of quantum mechanics is the principle impossibility of deterministic errorless discrimination of nonorthogonal signals, such as coherent states. On the one hand, it prevents perfect cloning of quantum states and enables secure communication. On the other hand, it makes a grand challenge to reach the ultimate measurement precision. Although the minimum possible error rate (the Helstrom bound) has been known for almost five decades, there is no practical way to achieve it. Developing the realistic optimal measurement strategies to attain the Helstrom bound is …
Near-optimal discrimination of displaced squeezed binary signals using displacement, inverse-squeezing, and photon-number-resolving detection
Information Support Force Engineering University（信息支援部队工程大学）；Guangxi Key Laboratory of Multimedia Communications and Network Technology, Guangxi University（广西大学）；Henan Key Laboratory of Quantum Information and Cryptography, SSF IEU（河南量子信息与密码学重点实验室）；Wuhan Maritime Communication Research Institute（武汉海事通信研究所）
We investigate quantum state discrimination with confidentiality. $N$ observers share a given quantum state belonging to a finite set of known states. The observers want to determine the state as accurately as possible and send a discrimination result to a receiver. However, the observers are not allowed to get any information about which state was given. $N-1$ or fewer observers might try to steal the information, but if $N$ observers coexist, the honest ones will keep the dishonest ones from doing anything wrong. Assume that the state set has a certain symmetry, or more precisely, is Abelian…
Non-conventional receivers for phase-coherent states based on non-Gaussian measurements such as photon counting surpass the sensitivity limits of shot-noise-limited coherent receivers, the quantum noise limit (QNL). These non-Gaussian receivers can have a significant impact in future coherent communication technologies. However, random phase changes in realistic communication channels, such as optical fibers, present serious challenges for extracting the information encoded in coherent states. While there are methods for correcting random phase noise with conventional heterodyne detection, pha…
The quantum states of two laser pulses---coherent states---are never mutually orthogonal, making perfect discrimination impossible. Even so, coherent states can achieve the ultimate quantum limit for capacity of a classical channel, the Holevo capacity. Attaining this requires the receiver to make joint-detection measurements on long codeword blocks, optical implementations of which remain unknown. We report the first experimental demonstration of a joint-detection receiver, demodulating quaternary pulse-position-modulation (PPM) codewords at a word error rate of up to 40% (2.2 dB) below that …
The integration of quantum communication functions often requires dedicated opto-electronic components that do not bode well with the technology roadmaps of telecom systems. We investigate the capability of commercial coherent transceiver sub-systems to support quantum random number generation next to classical data transmission, and demonstrate how the quantum entropy source based on vacuum fluctuations can be potentially converted into a true random number generator for this purpose. We discuss two possible implementations, building on a receiver- and a transmitter-centric architecture. In t…
The optimal discrimination of coherent states of light with current technology is a key problem in classical and quantum communication, whose solution would enable the realization of efficient receivers for long-distance communications in free-space and optical fiber channels. In this article, we show that reinforcement learning (RL) protocols allow an agent to learn near-optimal coherent-state receivers made of passive linear optics, photodetectors and classical adaptive control. Each agent is trained and tested in real time over several runs of independent discrimination experiments and has …
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…
Because of the potential applications in quantum information processing tasks, discrimination of binary coherent states using generalized Kennedy receiver with maximum a posteriori probability (MAP) detection has attracted increasing attentions in recent years. In this paper, we analytically study the performance of the generalized Kennedy receiver having optimally displaced threshold detection (ODTD) in a realistic situation with noises and imperfect devices. We first prove that the MAP detection for a generalized Kennedy receiver is equivalent to a threshold detection in this realistic situa…
Uncertainty in discriminating between different received coherent signals is integral to the operation of many free-space optical communications protocols, and is often difficult when the receiver measures a weak signal. Here we design an optical communications scheme that uses balanced homodyne detection in combination with an unsupervised generative machine learning and convolutional neural network (CNN) system, and demonstrate its efficacy in a realistic simulated coherent quadrature phase shift keyed (QPSK) communications system. Additionally, we program the neural network system at the tr…
Coherent states of light, and methods for distinguishing between them, are central to all applications of laser light. We obtain the ultimate quantum limit on the error probability exponent for discriminating among any M multimode coherent-state waveforms via the quantum Chernoff exponent in M-ary multi-copy state discrimination. A receiver, i.e., a concrete realization of a quantum measurement, called the Sequential Waveform Nulling (SWN) receiver, is proposed for discriminating an arbitrary coherent-state ensemble using only auxiliary coherent-state fields, beam splitters, and non-number-res…
