Fundamental Limits of Quantum-Secure Covert Communication Over Bosonic Channels

Abstract

We investigate the fundamental limit of quantum-secure covert communication over the lossy thermal noise bosonic channel, the quantum-mechanical model 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.M. S.[4], showing the SRL for discrete memoryless channels (DMCs) [3]-[5], and determining it up to the second order [6]. A tutorial explanation of the SRL and its implications is offered in [7]. Consider an optical channel with additive thermal noise. The use of laser light modulation at the transmitter and coherent detection (homodyne or heterodyne) at the receiver induces an AWGN channel, with covert communication governed by the SRL in [1], [2]. Fundamentally, however, electromagnetic waves are quantum mechanical: they are boson fields. Currently, noises of quantum-mechanical origin limit the performance of advanced high-sensitivity photodetection systems [8]-[10]. Therefore, analysis of the ultimate limits of any communications system requires quantum information theory [11]. This led to the development of the SRL for covert communication over the lossy thermal noise bosonic channel, which is the underlying quantummechanical description of many practical channels, including optical, microwave, and radiofrequency (RF) [12]. The single-mode bosonic channel, depicted in Fig. 1 and formally defined Fig. 1. Single-mode bosonic channel En B η modeled by a beamsplitter with transmissivity η and an environment injecting a thermal stateρn B with mean photon numbern B .â,ê,b, andŵ label input/output modal annihilation operators.in Section II-A, is parametrized by the power coupling (transmissivity) η between the transmitter Alice and the intended receiver Bob, and the mean photon numbern B per mode injected by the environment, where a single spatial-temporal-polarization mode is our fundamental transmission unit. In our analysis (as in [12]) we do not assume a specific receiver structure for the adversary Willie. Willie has access to all transmitted photons that are not captured by Bob, on which he can perform arbitrary quantum information process...

Two-way covert quantum communication in the microwave regime

“…We now discuss the possibility of performing secure quantum communication using the setup depicted in Fig. 2, by exploiting recent results about covert quantum communication (24,35.…”

Demonstration of Entanglement-Enhanced Covert Sensing

“…Quantum covert protocols have recently emerged to offer a feature beyond the scope of these quantum cryptography protocols-the executions of the very protocols, with a high probability, are undetectable from the adversary's perspective [27][28][29][30][31][32][33][34][35], thereby ensuring the data integrity. The covertness of these protocols is fundamentally guaranteed by the indistinguishability between quantum states and hence can be quantified by the quantum measurement theory.…”

“…The covertness of these protocols is fundamentally guaranteed by the indistinguishability between quantum states and hence can be quantified by the quantum measurement theory. In analogy to many quantum cryptography protocols [36][37][38], quantum covert protocols may be solely constructed upon classical transmitters and receivers [27,28,31,32,[39][40][41], but quintessential quantum resources such as entanglement may offer additional performance gains. Indeed, the benefit of entanglement in quantum covert protocols has been recently analyzed [3,32,42], but an experimental realiza-tion for entanglement-enhanced covert systems remains elusive.…”

“…3 dictates that the per-mode probe photon number, N S , needs to scale as 1/ √ M to maintain a constant covertness parameter at a given background noise level, leading to a square-root scaling for the signal-to-noise ratio with respect to the number of employed signalidler mode pairs, viz. MN S /N B ∝ √ M, which is a signature for covert communication and sensing protocols [27,28,[31][32][33][34][35][39][40][41]. We experimentally test the square-root law and report the result in Fig.…”