Fundamental limits of quantum-secure covert optical sensing

We present a square root law for active sensing of phase $\theta$ of a single pixel using optical probes that pass through a single-mode lossy thermal-noise bosonic channel. Specifically, we show that, when the sensor uses an $n$-mode covert optical probe, the mean squared error (MSE) of the resulting estimator $\hat{\theta}_n$ scales as $\langle (\theta-\hat{\theta}_n)^2\rangle=\mathcal{O}(1/\sqrt{n})$; improving the scaling necessarily leads to detection by the adversary with high probability. We fully characterize this limit and show that it is achievable using laser light illumination and a heterodyne receiver, even when the adversary captures every photon that does not return to the sensor and performs arbitrarily complex measurement as permitted by the laws of quantum mechanics.Comment: 13 pages, 1 figure, submitted to ISIT 201

Covert Communication over Classical-Quantum Channels

The square root law (SRL) is the fundamental limit of covert communication over classical memoryless channels (with a classical adversary) and quantum lossy-noisy bosonic channels (with a quantum-powerful adversary). The SRL states that $\mathcal{O}(\sqrt{n})$ covert bits, but no more, can be reliably transmitted in $n$ channel uses with $\mathcal{O}(\sqrt{n})$ bits of secret pre-shared between the communicating parties. Here we investigate covert communication over general memoryless classical-quantum (cq) channels with fixed finite-size input alphabets, and show that the SRL governs covert communications in typical scenarios. %This demonstrates that the SRL is achievable over any quantum communications channel using a product-state transmission strategy, where the transmitted symbols in every channel use are drawn from a fixed finite-size alphabet. We characterize the optimal constants in front of $\sqrt{n}$ for the reliably communicated covert bits, as well as for the number of the pre-shared secret bits consumed. We assume a quantum-powerful adversary that can perform an arbitrary joint (entangling) measurement on all $n$ channel uses. However, we analyze the legitimate receiver that is able to employ a joint measurement as well as one that is restricted to performing a sequence of measurements on each of $n$ channel uses (product measurement). We also evaluate the scenarios where covert communication is not governed by the SRL

Complete elimination of information leakage in continuous-variable quantum communication channels

In all lossy communication channels realized to date, information is inevitably leaked to a potential eavesdropper. Here we present a communication protocol that does not allow for any information leakage to a potential eavesdropper in a purely lossy channel. By encoding information into a restricted Gaussian alphabet of squeezed states we show, both theoretically and experimentally, that the Holevo information between the eavesdropper and the intended recipient can be exactly zero in a purely lossy channel while minimized in a noisy channel. This result is of fundamental interest, but might also have practical implications in extending the distance of secure quantum key distribution.Comment: 9 pages, 5 figure

Fundamental Limits of Thermal-noise Lossy Bosonic Multiple Access Channel

Bosonic channels describe quantum-mechanically many practical communication links such as optical, microwave, and radiofrequency. We investigate the maximum rates for the bosonic multiple access channel (MAC) in the presence of thermal noise added by the environment and when the transmitters utilize Gaussian state inputs. We develop an outer bound for the capacity region for the thermal-noise lossy bosonic MAC. We additionally find that the use of coherent states at the transmitters is capacity-achieving in the limits of high and low mean input photon numbers. Furthermore, we verify that coherent states are capacity-achieving for the sum rate of the channel. In the non-asymptotic regime, when a global mean photon-number constraint is imposed on the transmitters, coherent states are the optimal Gaussian state. Surprisingly however, the use of single-mode squeezed states can increase the capacity over that afforded by coherent state encoding when each transmitter is photon number constrained individually.Comment: 8 pages, 3 figure

Covert sensing using floodlight illumination

We propose a scheme for covert active sensing using floodlight illumination from a THz-bandwidth amplified spontaneous emission (ASE) source and heterodyne detection. We evaluate the quantum-estimation-theoretic performance limit of covert sensing, wherein a transmitter's attempt to sense a target phase is kept undetectable to a quantum-equipped passive adversary, by hiding the signal photons under the thermal noise floor. Despite the quantum state of each mode of the ASE source being mixed (thermal), and hence inferior compared to the pure coherent state of a laser mode, the thousand-times higher optical bandwidth of the ASE source results in achieving a substantially superior performance compared to a narrowband laser source by allowing the probe light to be spread over many more orthogonal temporal modes within a given integration time. Even though our analysis is restricted to single-mode phase sensing, this system could be applicable extendible for various practical optical sensing applications.Comment: We present new results and discuss some results found in arXiv:1701.06206. Comments are welcom

Optimal Throughput for Covert Communication Over a Classical-Quantum Channel

This paper considers the problem of communication over a memoryless classical-quantum wiretap channel subject to the constraint that the eavesdropper on the channel should not be able to learn whether the legitimate parties are using the channel to communicate or not. Specifically, the relative entropy between the output quantum states at the eavesdropper when a codeword is transmitted and when no input is provided must be sufficiently small. Extending earlier works, this paper proves the "square-root law" for a broad class of classical-quantum channels: the maximum amount of information that can be reliably and covertly transmitted over $n$ uses of such a channel scales like $\sqrt{n}$. The scaling constant is also determined.Comment: Corrected version of a paper presented at ITW 2016. In the ITW paper, the denominator in the main formula (10) was incorrect. The current version corrects this mistake and adds an appendix for its derivatio

Quantum limits of covert target detection

In covert target detection, Alice attempts to send optical or microwave probes to detect whether or not a weakly-reflecting target embedded in thermal background radiation is present in a target region while remaining undetected herself by an adversary Willie who is co-located with the target and collects all the light that does not return to Alice. We formulate this problem in a realistic setting and derive quantum-mechanical limits on Alice's error probability performance in entanglement-assisted target detection for any fixed level of her detectability by Willie. In particular, we show that Alice must expend a minimum energy in her probe light to maintain a given covertness level, but is also able to achieve a nonzero error probability exponent while remaining perfectly covert. We compare the performance of two-mode squeezed vacuum probes and Gaussian-distributed coherent states to our performance limits. We also obtain quantum limits for discriminating any two thermal loss channels and for non-adversarial quantum illumination without the no-passive-signature assumption.Comment: 18 pages, 5 figure