We describe a general quantum receiver protocol that maps laser-light-modulated classical communications signals into quantum processors for decoding with quantum logic gates. The quantum gates enable joint quantum measurements over a code word to achieve the quantum limit of communication capacity. Our receiver design requires qubit resources that only logarithmically increase with the size of the code word and accommodates practically relevant coherent-state modulation containing multiple photons per pulse. Focusing on classical-quantum polar codes, we outline the necessary quality of quantum operations and code-word lengths to demonstrate a quantum-processing-enhanced communication rate surpassing that of any known classical optical receiver-decoder pair. Specifically, we show that a small quantum receiver of four qubits with operational errors of approximately 0.2 % can already provide a 5% gain in the communication rate in the weak-signal limit. Additionally, we outline a possible hardware implementation of the receiver where efficient spin-photon interfaces such as cavity-coupled diamond color centers or atomic qubits are used to input the received photonic signal to a small-scale quantum processor for decoding. Our results outline a promising route for potential quantum advantage in classical communication with near-term, small-scale quantum computers.
We describe a general quantum receiver protocol that maps laser-light-modulated classical communications signals into quantum processors for decoding with quantum logic gates. The quantum gates enable joint quantum measurements over a code word to achieve the quantum limit of communication capacity. Our receiver design requires qubit resources that only logarithmically increase with the size of the code word and accommodates practically relevant coherent-state modulation containing multiple photons per pulse. Focusing on classical-quantum polar codes, we outline the necessary quality of quantum operations and code-word lengths to demonstrate a quantum-processing-enhanced communication rate surpassing that of any known classical optical receiver-decoder pair. Specifically, we show that a small quantum receiver of four qubits with operational errors of approximately 0.2 % can already provide a 5% gain in the communication rate in the weak-signal limit. Additionally, we outline a possible hardware implementation of the receiver where efficient spin-photon interfaces such as cavity-coupled diamond color centers or atomic qubits are used to input the received photonic signal to a small-scale quantum processor for decoding. Our results outline a promising route for potential quantum advantage in classical communication with near-term, small-scale quantum computers.
For space-based laser communications, when the mean photon number per received optical pulse is much smaller than one, there is a large gap between communications capacity---measured in bits communicated per pulse---achievable with a receiver that detects (converts from optical to electrical domain) each modulated pulse one at a time, versus with the quantum-optimal joint-detection receiver that acts on a long codeword comprised of n modulated pulses; an effect often termed superadditive capacity. The action of this receiver cannot be described as the detection of each individual pulse, interspersed with classical feedforward and soft-information post-processing. In this paper, we consider the simplest scenario where a large superadditive capacity is known: a pure-loss channel with a coherent-state binary phase-shift keyed (BPSK) modulation. The two BPSK states can be mapped conceptually to two non-orthogonal states of a single qubit, described by an inner product that is a function of the mean photon number of each BPSK pulse. Using this map, we derive an explicit construction of the quantum circuit of a joint-detection receiver based on a recent idea of belief-propagation with quantum messages (BPQM) [arXiv:1607.04833]. We analyze this scheme rigorously and show that it achieves the quantum limit of minimum average error probability in discriminating 8 (BPSK) codewords of a length-5 binary linear code with a tree factor graph. We quantify its performance improvement over the (Dolinar) receiver that optimally detects one pulse at a time. Our result suggests that a BPQM-receiver might attain the Holevo capacity, the quantum limit of classical communication capacity, of this BPSK-modulated pure-loss channel. This suggests a new application for a small, special-purpose, photonic quantum computer capable of so-called cat-basis universal qubit logic.
Abstract Optical communication is the standard for high-bandwidth information transfer in today’s digital age. The increasing demand for bandwidth has led to the maturation of coherent transceivers that use phase- and amplitude-modulated optical signals to encode more bits of information per transmitted pulse. Such encoding schemes achieve higher information density, but also require more complicated receivers to discriminate the signaling states. In fact, achieving the ultimate limit of optical communication capacity, especially in the low light regime, requires coherent joint detection of multiple pulses. Despite their superiority, such joint detection receivers are not in widespread use because of the difficulty of constructing them in the optical domain. In this work we describe how optomechanical transduction of phase information from coherent optical pulses to superconducting qubit states followed by the execution of trained short-depth variational quantum circuits can perform joint detection of communication codewords with error probabilities that surpass all classical, individual pulse detection receivers. Importantly, we utilize a model of optomechanical transduction that captures non-idealities such as thermal noise and loss in order to understand the transduction performance necessary to achieve a quantum advantage with such a scheme. We also execute the trained variational circuits on an IBM-Q device with the modeled transduced states as input to demonstrate that a quantum advantage is possible even with current levels of quantum computing hardware noise.
Abstract For space-based laser communications, when the mean photon number per received optical pulse is much smaller than one, there is a large gap between communications capacity achievable with a receiver that performs individual pulse-by-pulse detection, and the quantum-optimal “joint-detection receiver” that acts collectively on long codeword-blocks of modulated pulses; an effect often termed “superadditive capacity”. In this paper, we consider the simplest scenario where a large superadditive capacity is known: a pure-loss channel with a coherent-state binary phase-shift keyed (BPSK) modulation. The two BPSK states can be mapped conceptually to two non-orthogonal states of a qubit, described by an inner product that is a function of the mean photon number per pulse. Using this map, we derive an explicit construction of the quantum circuit of a joint-detection receiver based on a recent idea of “belief-propagation with quantum messages” (BPQM). We quantify its performance improvement over the Dolinar receiver that performs optimal pulse-by-pulse detection, which represents the best “classical” approach. We analyze the scheme rigorously and show that it achieves the quantum limit of minimum average error probability in discriminating 8 (BPSK) codewords of a length-5 binary linear code with a tree factor graph. Our result suggests that a BPQM receiver might attain the Holevo capacity of this BPSK-modulated pure-loss channel. Moreover, our receiver circuit provides an alternative proposal for a quantum supremacy experiment, targeted at a specific application that can potentially be implemented on a small, special-purpose, photonic quantum computer capable of performing cat-basis universal qubit logic.
Demonstrations of quantum advantage have largely focused on computational speedups and on quantum simulation of many-body physics, limited by fidelity and the capability of current devices. Discriminating laser-pulse-modulated classical-communication code words at the minimum allowable probability of error using universal-quantum processing presents a promising parallel direction, one that is of both fundamental importance in quantum state discrimination and technological relevance in deep-space laser communications. Here we present an experimental realization of a quantum joint detection receiver for binary phase shift keying modulated code words of a 3-bit linear tree code using a recently proposed quantum algorithm: belief propagation with quantum messages. The receiver, translated to a quantum circuit, was experimentally implemented on a trapped-ion device---the recently released Honeywell LT-1.0 system using 171Yb+ ions, which possesses all-to-all connectivity and midcircuit measurement capabilities that are essential to this demonstration. We conclusively realize a previously postulated but hitherto not demonstrated joint quantum detection scheme and provide an experimental framework that surpasses the quantum limit on the minimum average decoding error probability associated with pulse-by-pulse detection in the low-mean-photon-number limit. The full joint detection scheme bridges across photonic and trapped-ion-based quantum information science, mapping the photonic coherent states of the modulation alphabet onto inner product-preserving states of single-ion qubits. Looking ahead, our work opens new avenues in hybrid realizations of quantum-enhanced receivers with applications in astronomy and emerging space-based platforms.
Born about a century ago, Quantum Mechanics has revolutionized the description and the interpretation of Physics at sub-microscopic level. In the last decades, due to the influence of mathematical and engineering research fields, Quantum Mechanics has given birth to related research areas like Quantum Computation, Quantum Information and Quantum Communication. With the discovery of the laser, and later the development of fiber optics and satellite networks, Quantum Communication and Quantum Optics seems to have a natural field of application in Communication Systems. Despite this, the interest in this technology and studies for communication purpose has been overshadowed by the great results in communication networks achieved in the last decades with classical paradigms. However, due to the increasing demand of communication data rate, system designers are now looking at Quantum Mechanics for new and more performanting solutions in communication purposes. Early theoretical studies on Quantum Discrimination Theory and Quantum Information predict better performance for Communication Systems that take advantage of the quantum laws. In addition, Quantum Mechanics provides the deepest description of the physical phenomena, and there are scenarios where a quantum model fits best, as in in deep space communications, where the received signal is really weak, or in a satellite networks, where we are interested in strongly reducing the power of transmitted signals, possibly without sacrificing performance significantly. However, if on one side Quantum Communication Theory promises great gains in the performance of communication systems, on the other hand it fails to describe how to implement physical devices that reach these ultimate limits. So far, only a few architectures achieving these performances are known, and only for simple modulation formats. We are interested in the scenario of optical communications, where the message transmitted is encoded in a sequence of coherent states. Transmitter devices for coherent modulation are well known and consist in laser pulse generators. Instead, receiver implementations working at the quantum limit performance limit are yet to be found. In this Thesis I deal with different topics in the quantum transmission scenario. First, I review existing classical (suboptimal) and quantum (suboptimal and optimal) receiver schemes for the binary coherent modulation. I present a new formulation of the optimal scheme known as Dolinar Receiver with the multiple copies problem, focusing on the information gained during the measurement. Second, I analyze the binary communication in a noisy environment, studying the error probability and the capacity of the binary channel induced. Given the description of the quantum channel, I optimize both the transmitted quantum states and the measurement operators employed in the communication. Third, I consider the Pulse Position Modulation, that is particularly suitable for space and satellite communication due to its simplicity of implementation and high capacity. I review some known suboptimal receivers, and I propose a receiver scheme which approaches the limit performance predicted with quantum theory outperforming the existing schemes. To sum up the results of this Thesis, in order to approach the limit performance predicted by Quantum Mechanics, an optimization is always necessary to exceed the classical effects and trigger the quantum phenomena. In particular, the information gained during the measurement plays an important role, for example in the definition of adaptive receivers. In this Thesis both these aspects have been deeply investigated.
Laser-light (coherent-state) modulation is sufficient to achieve the ultimate (Holevo) capacity of classical communication over a lossy and noisy optical channel, but requires a receiver that jointly detects long modulated code words with highly nonlinear quantum operations, which are near-impossible to realize using current technology. We analyze the capacity of the lossy-noisy optical channel when the transmitter uses coherent-state modulation but the receiver is restricted to a general quantum-limited Gaussian receiver, i.e., one that may involve arbitrary combinations of Gaussian operations [passive linear optics: beam splitters and phase shifters; second-order nonlinear optics (or active linear optics): squeezers, along with homodyne or heterodyne detection measurements] and any amount of classical feedforward within the receiver. Under these assumptions, we show that the Gaussian receiver that attains the maximum mutual information is either homodyne detection, heterodyne detection, or time sharing between the two, depending upon the received power level. In other words, our result shows that to exceed the theoretical limit of conventional coherent optical communication, one has to incorporate non-Gaussian, i.e., third- or higher-order nonlinear operations in the receiver. Finally we compare our Gaussian receiver limit with experimentally feasible non-Gaussian receivers and show that in the regime of low received photon flux, it is possible to overcome the Gaussian receiver limit by relatively simple non-Gaussian receivers based on photon counting.