Search for: All records

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.

 

We consider the numerical analysis of the inchworm Monte Carlo method, which is proposed recently to tackle the numerical sign problem for open quantum systems. We focus on the growth of the numerical error with respect to the simulation time, for which the inchworm Monte Carlo method shows a flatter curve than the direct application of Monte Carlo method to the classical Dyson series. To better understand the underlying mechanism of the inchworm Monte Carlo method, we distinguish two types of exponential error growth, which are known as the numerical sign problem and the error amplification. The former is due to the fast growth of variance in the stochastic method, which can be observed from the Dyson series, and the latter comes from the evolution of the numerical solution. Our analysis demonstrates that the technique of partial resummation can be considered as a tool to balance these two types of error, and the inchworm Monte Carlo method is a successful case where the numerical sign problem is effectively suppressed by such means. We first demonstrate our idea in the context of ordinary differential equations, and then provide complete analysis for the inchworm Monte Carlo method. Several numerical experiments are carried out to verify our theoretical results. 

In 2018, Renes [IEEE Trans. Inf. Theory, vol. 64, no. 1, pp. 577-592 (2018)] developed a general theory of channel duality for classical-input quantum-output channels. His result shows that a number of well-known duality results for linear codes on the binary erasure channel can be extended to general classical channels at the expense of using dual problems which are intrinsically quantum mechanical. One special case of this duality is a connection between coding for error correction on the quantum pure-state channel (PSC) and coding for wiretap secrecy on the classical binary symmetric channel (BSC). Similarly, coding for error correction on the BSC is related to wire-tap secrecy on the PSC. While this result has important implications for classical coding, the machinery behind the general duality result is rather challenging for researchers without a strong background in quantum information theory. In this work, we leverage prior results for linear codes on PSCs to give an alternate derivation of the aforementioned special case by computing closed-form expressions for the performance metrics. The noted prior results include the optimality of square-root measurement for linear codes on the PSC and the Fourier duality of linear codes. 

Quantum technologies are maturing by the day and their near-term applications are now of great interest. Deep-space optical communication involves transmission over the pure-state classical-quantum channel. For optimal detection, a joint measurement on all output qubits is required in general. Since this is hard to realize, current (sub-optimal) schemes perform symbol-by-symbol detection followed by classical post-processing. In this paper we focus on a recently proposed belief propagation algorithm by Renes that passes qubit messages on the factor graph of a classical error-correcting code. More importantly, it only involves single-qubit Pauli measurements during the process. For an example 5-bit code, we analyze the involved density matrices and calculate the error probabilities on this channel. Then we numerically compute the optimal joint detection limit using the Yuen-Kennedy-Lax conditions and demonstrate that the calculated error probabilities for this algorithm appear to achieve this limit. This represents a first step towards achieveing quantum communication advantage. We verify our analysis using Monte-Carlo simulations in practice. 

Discriminating between quantum states is a fundamental task in quantum information theory. Given two quantum states, ρ+ and ρ− , the Helstrom measurement distinguishes between them with minimal probability of error. However, finding and experimentally implementing the Helstrom measurement can be challenging for quantum states on many qubits. Due to this difficulty, there is a great interest in identifying local measurement schemes which are close to optimal. In the first part of this work, we generalize previous work by Acin et al. (Phys. Rev. A 71, 032338) and show that a locally greedy (LG) scheme using Bayesian updating can optimally distinguish between any two states that can be written as a tensor product of arbitrary pure states. We then show that the same algorithm cannot distinguish tensor products of mixed states with vanishing error probability (even in a large subsystem limit), and introduce a modified locally-greedy (MLG) scheme with strictly better performance. In the second part of this work, we compare these simple local schemes with a general dynamic programming (DP) approach. The DP approach finds the optimal series of local measurements and optimal order of subsystem measurement to distinguish between the two tensor-product states.