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arXiv:2311.10432 · Physical Review A

Improving continuous-variable quantum channels with unitary averaging

S. Nibedita Swain, Ryan J. Marshman, Peter P. Rohde, Austin P. Lund, Alexander S. Solntsev, Timothy C. Ralph

Published Sep 23, 2024• 3 citations
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Abstract

A significant hurdle for quantum information and processing using bosonic systems is stochastic phase errors which occur as the photons propagate through a channel. These errors will reduce the purity of states passing through the channel and therefore reduce the channels capacity. We present a scheme of passive linear optical unitary averaging for protecting unknown Gaussian states transmitted through an optical channel. The scheme reduces the effect of phase noise on purity, squeezing, and entanglement, thereby enhancing the channel via a probabilistic-error-correcting protocol. The scheme is robust to loss and typically succeeds with high probability. We provide both numerical simulations and analytical approximations tailored for relevant parameters with the improvement of practical and current technology. We also show the asymptotic nature of the protocol, highlighting both current and future relevance.

DOI
10.1103/physreva.110.032622

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A significant hurdle for quantum information and processing using bosonic systems is stochastic phase errors which occur as the photons propagate through a channel. These errors will reduce the purity of states passing through the channel and therefore reduce the channels capacity. We present a scheme of passive linear optical unitary averaging for protecting unknown Gaussian states transmitted through an optical channel. The scheme reduces the effect of phase noise on purity, squeezing, and entanglement, thereby enhancing the channel via a probabilistic-error-correcting protocol. The scheme is robust to loss and typically succeeds with high probability. We provide both numerical simulations and analytical approximations tailored for relevant parameters with the improvement of practical and current technology. We also show the asymptotic nature of the protocol, highlighting both current and future relevance.
We improve Gaussian-boson-sampling circuits by integrating the unitary-averaging (UA) protocol, previously demonstrated to protect unknown Gaussian states from phase errors [Swain et al., Phys. Rev. A 110, 032622 (2024)]. Our work extends the applicability of UA to mitigate arbitrary interferometric noise, including beam-splitter and phase-shifter imperfections. Through comprehensive numerical analysis, we demonstrate that UA consistently achieves higher fidelity and success probability than unprotected circuits, establishing its robustness in noisy conditions. Remarkably, enhancement is maintained across varying numbers of modes with respect to the noise. We further derive a power-law formula predicting performance gains in large-scale systems, including 100-mode and 216-mode configurations. A detailed step-by-step algorithm for implementing the UA protocol is also provided, offering a practical road map for advancing near-term quantum technologies.
The classical capacity of a noisy optical channel is the maximum rate at which information can be transmitted reliably, given a constraint on the mean input energy. For the ubiquitous bosonic Gaussian channels, which include standard models of loss and noise in fibre and free-space optical links, determining this rate requires addressing whether entanglement between channel uses or non-Gaussian signals can outperform Gaussian encodings. More precisely, the question is whether the energy-constrained Holevo information is additive across arbitrarily many channel uses and coincides with its Gaussian counterpart. We answer these fundamental questions in the affirmative for every single-mode bosonic Gaussian channel at every input energy. Namely, we prove that independently prepared Gaussian states with Gaussian-distributed random displacements achieve the capacity, including in the low-energy regime where squeezing the signals competes with encoding information in their displacement. Our proof connects an entanglement inequality to a sharp, additive lower bound on output entropy. We then characterise communication above capacity: under a strict total photon-number cutoff, the probability of correct decoding decreases exponentially with the number of channel uses, and we derive explicit bounds on the decay exponent. When only the mean photon number is constrained, a simple energy-rescaling formula determines exactly the entire asymptotic rate--error trade-off: the capacity at mean photon number NNN and allowed average decoding error εεε equals the vanishing-error capacity at mean photon number N/(1−ε)N/(1-ε)N/(1−ε). Together, these results identify the ultimate limits of classical communication for some of the most fundamental models of optical communication.
We demonstrate that continuous-variable quantum error correction based on Gaussian ancilla states and Gaussian operations (for encoding, syndrome extraction, and recovery) can be very useful to suppress the effect of non-Gaussian error channels. For a certain class of stochastic error models, reminiscent of those typically considered in the qubit case, quantum error correction codes designed for single-channel errors may enhance the transfer fidelities even when errors occur in every channel employed for transmitting the encoded state. In fact, in this case, the error-correcting capability of the continuous-variable scheme turns out to be higher than that of its discrete-variable analogues.
Noiseless linear amplifiers (NLAs) serve as an effective means to enable long-distance continuous-variable (CV) quantum key distribution (QKD), even under realistic conditions with non-unit reconciliation efficiency. Separately, unitary averaging has been suggested to mitigate some stochastic noise, including phase noise in continuous-variable states. In this work, we combine these two protocols to simultaneously compensate for thermal-loss effects and suppress phase noise, thereby enabling long-distance CV QKD that surpasses the repeaterless bound, the fundamental rate-distance limit, for repeaterless quantum communication systems.
The technological progress of the last few decades has brought us the ability of exploiting quantum effects to accomplish a variety of relevant tasks. Yet, quantum phenomena are fragile, and with the ability to engineer quantum information protocols comes the problem of keeping such information safe from the detrimental effects of noise and losses. In the present work we investigate continuous variables Gaussian quantum information in noisy environments, studying the effects of various noise sources in the cases of a quantum metrological task, an error correction scheme and discord-type correlations. We engage each of the topics from a theoretical point of view, successively delving into the details of the experimental realizations and concluding with a survey of the results. In particular, we present experimental implementation of an ab initio, deterministic, real-time adaptive phase estimation protocol in a realistic thermalized scenario, we investigate the performance of an error correction scheme for elimination of correlated noise in a quantum channel, and we study the robustness of discord-type quantum correlations when subject to additive noise and attenuation.