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arXiv:2001.03934 · IEEE International Symposium on Information Theory (ISIT)

Infinite-fold enhancement in communications capacity using pre-shared entanglement

Saikat Guha, Quntao Zhuang, Boulat A. Bash

Published Jun 1, 2020• 19 citations
arXivHTMLPDF

Abstract

Pre-shared entanglement can significantly boost communication rates in the regime of high thermal noise, and a low-brightness transmitter. In this regime, the ratio between the entanglement-assisted capacity and the Holevo capacity, the maximum reliable-communication rate permitted by quantum mechanics without any pre-shared entanglement as a resource, is known to scale as log(1/N̅S), where N̅S≪ 1 is the mean transmitted photon number per mode. This is especially promising in enabling a large boost to radio-frequency communications in the weak-transmit-power regime, by exploiting pre-shared optical-frequency entanglement, e.g., distributed by the quantum internet. In this paper, we propose a structured design of a quantum transmitter and receiver that leverages continuous-variable pre-shared entanglement from a downconversion source, which can harness this purported infinite-fold capacity enhancement- a problem that has been open for over a decade. Its implication to the breaking of the well-known square root law for covert communications, with entanglement assistance, is discussed.

DOI
10.1109/isit44484.2020.9173940

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Pre-shared entanglement can significantly boost communication rates in the regime of high thermal noise, and a low-brightness transmitter. In this regime, the ratio between the entanglement-assisted capacity and the Holevo capacity, the maximum reliable-communication rate permitted by quantum mechanics without any pre-shared entanglement as a resource, is known to scale as log(1/N̅S), where N̅S≪ 1 is the mean transmitted photon number per mode. This is especially promising in enabling a large boost to radio-frequency communications in the weak-transmit-power regime, by exploiting pre-shared optical-frequency entanglement, e.g., distributed by the quantum internet. In this paper, we propose a structured design of a quantum transmitter and receiver that leverages continuous-variable pre-shared entanglement from a downconversion source, which can harness this purported infinite-fold capacity enhancement- a problem that has been open for over a decade. Its implication to the breaking of the well-known square root law for covert communications, with entanglement assistance, is discussed.
Preshared entanglement can significantly boost communication rates in the high thermal-noise and low-brightness transmitter regime. In this regime, for a lossy bosonic channel with additive thermal noise, the ratio between the entanglement-assisted capacity and the Holevo capacity---the maximum reliable communication rate permitted by quantum mechanics without any preshared entanglement---scales as log(1/N‾S)\mathrm{log}(1/{\overline{N}}_{S})log(1/NS​), where the mean transmitted photon number per mode, ${\overline{N}}_{S}\ensuremath{\ll}1$. Thus, preshared entanglement, e.g., distributed by the quantum internet or a satellite-assisted quantum link, promises to significantly improve low-power radio-frequency communications. In this paper, we propose a pair of structured quantum transceiver designs that leverage continuous-variable preshared entanglement (generated, e.g., from a down-conversion source), binary phase modulation, and non-Gaussian joint detection over a codeword block, to achieve this scaling law of capacity enhancement. Furthermore, we describe a modification to the aforesaid receiver using a frontend that uses sum-frequency generation sandwiched with dynamically programmable in-line two-mode squeezers, and a receiver backend that takes full advantage of the output of the receiver's frontend by employing a nondestructive multimode vacuum-or-not measurement to achieve the entanglement-assisted classical communication capacity.
We establish the fundamental limits of covert communication over quantum channels, focusing on both finite-dimensional classical-quantum (CQ) channels and the infinite-dimen\-sional lossy thermal-noise bosonic channel. For general memoryless CQ channels, we characterize when covert communication is possible and prove a square root law (SRL): at most Ln+o(n)L\sqrt{n} + o(\sqrt{n})Ln​+o(n​) bits can be reliably transmitted covertly over nnn uses of the channel where LLL is the channel-dependent covert capacity. We derive a single-letter expression for LLL and show that the required pre-shared secret key also scales as n\sqrt{n}n​ under mild conditions. We also identify and characterize corner cases where either constant-rate or zero-rate covert communication is possible. For the bosonic channel, we prove that the SRL holds and derive exact covert capacities under different resource assumptions. In particular, we show that the covert secrecy and covert entanglement generation capacities both equal the covert classical capacity without entanglement-assistance, Lno-EAL_{\text{no-EA}}Lno-EA​, and show that the required pre-shared classical secret key scales as n\sqrt{n}n​. We also find that quadrature phase-shift keying (QPSK) achieves the optimal covert capacity, outperforming binary modulation in contrast to the classical channel setting. When Alice and Bob instead share entanglement, the covert classical capacity improves to LEAnlog⁡n+o(nlog⁡n)L_{\text{EA}} \sqrt{n} \log n + o(\sqrt{n} \log n)LEA​n​logn+o(n​logn), though this scaling is sensitive to noise in the entangled resource. Finally, we propose a practical covert transceiver and simulate its performance compared to recently experimentally-tested transceivers under realistic conditions.
We investigate the fundamental limit of quantumsecure covert communication over the lossy thermal noise bosonic channel, the quantum-mechanical mode underlying many practical channels. We assume that the adversary has unlimited quantum information processing capabilities as well as access to all transmitted photons that do not reach the legitimate receiver. Given existence of noise that is uncontrolled by the adversary, the square root law (SRL) governs covert communication: up to c√(n) covert bits can be transmitted reliably in n channel uses. Attempting to surpass this limit results in detection with unity probability as n → ∞. Here we present the expression for c, characterizing the SRL for the bosonic channel. We also prove that discrete-valued coherent state quadrature phase shift keying (QPSK) constellation achieves the optimal c, which is the same as that achieved by a circularly-symmetric complex-valued Gaussian prior on coherent state amplitude. Finally, while binary phase shift keying (BPSK) achieves the Holevo capacity for non-covert bosonic channels in the low received signal-to-noise ratio regime, we show that it is strictly sub-optimal for covert communication.
Entanglement underpins a variety of quantum-enhanced communication, sensing, and computing capabilities. Entanglement-assisted communication (EACOMM) leverages entanglement preshared by communicating parties to boost the rate of classical information transmission. Pioneering theory works showed that EACOMM can enable a communication rate well beyond the ultimate classical capacity of optical communications, but an experimental demonstration of any EACOMM advantage remains elusive. In this Letter we report the implementation of EACOMM surpassing the classical capacity over lossy and noisy bosonic channels. We construct a high-efficiency entanglement source and a phase-conjugate quantum receiver to reap the benefit of preshared entanglement, despite entanglement being broken by channel loss and noise. We show that EACOMM beats the Holevo-Schumacher-Westmoreland capacity of classical communication by up to 16.3%, when both protocols are subject to the same power constraint at the transmitter. As a practical performance benchmark, we implement a classical communication protocol with the identical characteristics for the encoded signal, showing that EACOMM can reduce the bit-error rate by up to 69% over the same bosonic channel. Our work opens a route to provable quantum advantages in a wide range of quantum information processing tasks.
We study quantum-secure covert-communication over lossy thermal-noise bosonic channels, the quantum mechanical model for many practical channels. We derive the expressions for the covert capacity of these channels: Lno-EA, when Alice and Bob share only a classical secret, and LEA, when they benefit from entanglement assistance. Entanglement assistance alters the fundamental scaling law for covert communication. Instead of Lno-EA√n-rno-EA(n), rno-EA(n) = o(√n), entanglement assistance allows LEA√n log n - rEA(n), rEA(n) = o(√n log n), covert bits to be transmitted reliably over n channel uses. However, noise in entanglement storage erases the log n gain from our achievability; work on the matching converse is ongoing.