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arXiv:1812.10743 · Physical Review A

Covert sensing using floodlight illumination

Christos N. Gagatsos, Boulat A. Bash, Animesh Datta, Zheshen Zhang, Saikat Guha

Published Jun 18, 2019• 15 citations
arXivHTMLPDF

Abstract

We propose a scheme for covert active sensing using floodlight illumination from a terahertz-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 narrow-band 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 or extendible for various practical optical sensing applications.

DOI
10.1103/physreva.99.062321

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We propose a scheme for covert active sensing using floodlight illumination from a terahertz-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 narrow-band 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 or extendible for various practical optical sensing applications.
We present a square root law for active sensing of phase θθθ 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 nnn-mode covert optical probe, the mean squared error (MSE) of the resulting estimator θ^n\hatθ_nθ^n​ scales as ⟨(θ−θ^n)2⟩=O(1/n)\langle (θ-\hatθ_n)^2\rangle=\mathcal{O}(1/\sqrt{n})⟨(θ−θ^n​)2⟩=O(1/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.
This thesis presents three studies in quantum-enhanced sensing and target detection. The first study explores covert target detection using optical or microwave probes, establishing quantum-mechanical limits on the error probabilities of entanglement-assisted detection methods while maintaining the sender's covertness. It identifies the minimal energy required to preserve covertness and reduce error probabilities, compares two-mode squeezed vacuum probes and coherent states against these limits, and extends the analysis to discriminating thermal loss channels and non-adversarial quantum illumination. The second study focuses on phase-insensitive optical amplifiers, determining the quantum limit on the precision of gain estimation using multimode probes possibly entangled with ancillary systems. It finds that the average photon number and the number of input modes are interchangeable resources for achieving optimal gain sensing precision, contrasting classical probes with quantum probes and highlighting the advantages of the latter, even with single-photon inputs and inefficient photodetection. It also provides a closed-form expression for the energy-constrained Bures distance between two amplifier channels. The third study compares three probe states -- coherent state, two-mode squeezed vacuum (TMSV), and single-photon entangled state (SPES) -- in quantum-enhanced target detection, assessing their performance under signal energy constraints relevant to covert radar sensing. SPES is uniquely positioned as a practical probe due to its non-classical properties after thermal loss and ease of generation. Numerical analysis shows that at low signal energies, the error exponent of TMSV aligns with SPES, indicating comparable detection capabilities and that SPES surpasses the best classical state-the coherent state-in accuracy for certain signal strengths.
We present a square root law for active sensing of phase θ 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 θnscales as 〈(θ-θ̂n)2〉 = O(1/√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.
In covert target detection, Alice attempts to send optical or microwave probes to determine the presence or absence of a weakly reflecting target embedded in thermal background radiation within a target region, while striving to remain undetected by an adversary, Willie, who is co-located with the target and collects all 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. We demonstrate how Alice can approach this performance limit using two-mode squeezed vacuum probes in the regime of small to moderate background brightness, and how such protocols can outperform any conventional approach using Gaussian-distributed coherent states. In addition, we derive a universal performance bound for nonadversarial quantum illumination without requiring the passive-signature assumption.
Motivated by application to quantum radar and the known benefits of quantum illumination in the high-noise low-reflectance regime, we study the design of signaling schemes for covertly probing a distant target over a lossy and noisy bosonic channel. Specifically, we analyze the performance of diffuse and sparse signaling schemes, which achieve covertness by spreading a constant number of photons in many modes or in a few modes, respectively. We benchmark the performance against a converse bound that holds for arbitrary covert quantum illumination schemes. Numerical results suggest the superior performance of the diffuse signaling scheme, which we conjecture outperforms any other covert quantum illumination scheme.
Amplified spontaneous emission (ASE) light is a common noise in optical communication systems with optical amplification, and a suitable optical carrier for optical covert communication. To deeply covert the secure signal, an in-band subnoise optical covert communication scheme is proposed and demonstrated by a proof-of-concept experiment. The power spectral density of optical secure channel is 10 dB less than the optical noise in the public channel. The covert signal is hidden in both optical and electrical domain, and can be transmitted with error-free. The trade-off between covertness and availability is discussed.