Discriminating coherent states of light is an important instance of quantum state discrimination that is 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 signals via the recently developed theory of the quantum Chernoff exponent in M-ary multi-copy state discrimination. A receiver 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-resolving single photon detectors. An explicit error probability analysis of the SWN receiver is used to show that it achieves the quantum limit on the error probability exponent, which is shown to be a factor of four greater than the error probability exponent of an ideal heterodyne-detection receiver on the same ensemble. Apart from being of fundamental interest, these results are relevant to communication, sensing, imaging, and quantum information processing systems that use laser light.
Discriminating coherent states of light is an important instance of quantum state discrimination that is 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 signals via the recently developed theory of the quantum Chernoff exponent in M-ary multi-copy state discrimination. A receiver 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-resolving single photon detectors. An explicit error probability analysis of the SWN receiver is used to show that it achieves the quantum limit on the error probability exponent, which is shown to be a factor of four greater than the error probability exponent of an ideal heterodyne-detection receiver on the same ensemble. Apart from being of fundamental interest, these results are relevant to communication, sensing, imaging, and quantum information processing systems that use laser light.
We derive the quantum limit on the error probability exponent for discriminating any M multimode coherent states of light and show that it is four times that of an ideal heterodyne receiver for the same signal set. We then propose a receiver that achieves the quantum limit using auxiliary coherent-state fields, beam splitters, and single-photon detectors. The performance of the receiver is compared to standard measurements for various imaging and communication tasks. A related receiver for discriminating arbitrary multicopy pure quantum states is shown to achieve the M-ary quantum Chernoff exponent and does so using only local operations and classical communication.
The conditions for a quantum measurement to discriminate a set of states with the minimum probability of error were specified by Yuen, Kennedy and Lax, and are often termed the YKL conditions [1]. Since light is quantum mechanical, the ultimate limit on minimum-error discrimination of an optical modulation constellation is determined by the YKL bound. Standard optical receivers (i.e., direct, homodyne or heterodyne detection)-even at their respective ideal operation limits-cannot achieve this performance. Recently, it was shown that a `sequential waveform nulling' (SWN) receiver can, not only discriminate an arbitrary M-ary coherent-state (ideal laser-light) constellation asymptotically at the YKL bound in the high-power limit, but that it achieves a factor of 4 better in the asymptotic error-probability exponent compared with heterodyne detection-the only conventional optical receiver that can in principle be employed for detecting an arbitrary phase-and-amplitude modulated constellation [2]. The SWN receiver can be built with standard optical components; i.e., beamsplitters, local-oscillator lasers, delay loops and single-photon detectors. However on the other hand, in the high power regime, heterodyne detection is known to achieve a reliable communication rate that asymptotically approaches the Holevo capacity of a lossy-noisy optical channel (the ultimate limit to the classical capacity of a quantum channel) [3]. In fact, in the high power regime, heterodyne detection was also shown recently to achieve the optimal second-order coding rate, when using the optimal (Gaussian) input distribution [4]. In this paper, we show that when restricted to the M-ary phase-shift keying (PSK) ensemble, that the SWN receiver's superiority over heterodyne detection in its asymptotic error exponent of the demodulation error probability, translates to a slightly higher capacity and a pronouncedly higher finite blocklength reliable-communication rate. We also quantify, via a numerical calculation, the dependence of the SWN receiver's capacity on the order in which the PSK constellation points are nulled. Our results suggest that for short-latency PSK-modulated optical communication in the high spectral efficiency regime-for which heterodyne detection is the conventional receiver choice-that it may be beneficial to employ the SWN receiver, despite the widely-regarded capacity optimality of heterodyne detection in this operating regime.
Laser light is widely used for communication and sensing applications, so the optimal discrimination of coherent states---the quantum states of light emitted by an ideal laser---has immense practical importance. Due to fundamental limits imposed by quantum mechanics, such discrimination has a finite minimum probability of error. While concrete optical circuits for the optimal discrimination between two coherent states are well known, the generalization to larger sets of coherent states has been challenging. In this paper, we show how to achieve optimal discrimination of any set of coherent states using a resource-efficient quantum computer. Our construction leverages a recent result on discriminating multicopy quantum hypotheses [Blume-Kohout, Croke, and Zwolak, arXiv:1201.6625]. As illustrative examples, we analyze the performance of discriminating a ternary alphabet and show how the quantum circuit of a receiver designed to discriminate a binary alphabet can be reused in discriminating multimode hypotheses. Finally, we show that our result can be used to achieve the quantum limit on the rate of classical information transmission on a lossy optical channel, which is known to exceed the Shannon rate of all conventional optical receivers.
We demonstrate an optical receiver that achieves the quantum Chernoff bound for discriminating coherent states from thermal states in the multicopy scenario. In contrast, we find that repeated use of the receiver approaching the Helstrom bound for single-copy measurement is suboptimal in this multicopy case. Furthermore, for a large class of multicopy 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 2 in error-probability exponent compared to the multicopy quantum Chernoff bound. This behavior has a classical analog in the performance gap between soft-decision and hard-decision receivers for detecting a multicopy signal embedded in white Gaussian noise.
Coherent states of the quantum electromagnetic field, the quantum description of ideal laser light, are a prime candidate as information carriers for optical communications. A large body of literature exists on quantum-limited parameter estimation and discrimination for coherent states. However, very little is known about practical realizations of receivers for unambiguous state discrimination (USD) of coherent states. Here we fill this gap and establish a theory of unambiguous discrimination of coherent states, with receivers that are allowed to employ: passive multimode linear optics, phase-space displacements, un-excited auxiliary input modes, and on-off photon detection. Our results indicate that these currently-available optical components are near optimal for unambiguous discrimination of multiple coherent states in a constellation.
Coherent states of the quantum electromagnetic field, the quantum description of ideal laser light, are prime candidates as information carriers for optical communications. A large body of literature exists on their quantum-limited estimation and discrimination. However, very little is known about the practical realizations of receivers for unambiguous state discrimination (USD) of coherent states. Here we fill this gap and outline a theory of USD with receivers that are allowed to employ: passive multimode linear optics, phase-space displacements, auxiliary vacuum modes, and on-off photon detection. Our results indicate that, in some regimes, these currently-available optical components are typically sufficient to achieve near-optimal unambiguous discrimination of multiple, multimode coherent states.