Demonstration of Entanglement-Enhanced Covert Sensing

Shuhong Hao, Haowei Shi, Christos N. Gagatsos, Mayank Mishra, Boulat Bash, Ivan Djordjevic, Saikat Guha, Quntao Zhuang, and Zheshen Zhang

Phys. Rev. Lett. 129, 010501 – Published 27 June 2022

Abstract

The laws of quantum physics endow superior performance and security for information processing: quantum sensing harnesses nonclassical resources to enable measurement precision unmatched by classical sensing, whereas quantum cryptography aims to unconditionally protect the secrecy of the processed information. Here, we present the theory and experiment for entanglement-enhanced covert sensing, a paradigm that simultaneously offers high measurement precision and data integrity by concealing the probe signal in an ambient noise background so that the execution of the protocol is undetectable with a high probability. We show that entanglement offers a performance boost in estimating the imparted phase by a probed object, as compared to a classical protocol at the same covertness level. The implemented entanglement-enhanced covert sensing protocol operates close to the fundamental quantum limit by virtue of its near-optimum entanglement source and quantum receiver. Our work is expected to create ample opportunities for quantum information processing at unprecedented security and performance levels.

Received 10 December 2021
Accepted 25 May 2022

DOI:https://doi.org/10.1103/PhysRevLett.129.010501

Physics Subject Headings (PhySH)

Quantum information processing with continuous variables Quantum metrology Quantum sensing

Quantum Information, Science & Technology

Authors & Affiliations

Shuhong Hao ¹, Haowei Shi², Christos N. Gagatsos², Mayank Mishra ², Boulat Bash^3,2, Ivan Djordjevic^3,2, Saikat Guha^2,3, Quntao Zhuang ^3,2, and Zheshen Zhang ^1,3,2,*

¹Department of Materials Science and Engineering, University of Arizona, Tucson, Arizona 85721, USA
²James C. Wyant College of Optical Sciences, University of Arizona, Tucson, Arizona 85721, USA
³Department of Electrical and Computer Engineering, University of Arizona, Tucson, Arizona 85721, USA

^*zsz@arizona.edu

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Issue

Vol. 129, Iss. 1 — 1 July 2022

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Images

Figure 1
Configuration for entanglement-enhanced covert sensing. Entanglement transmitter generates entangled signal and idler and sends the signal to probe an object. The quantum receiver performs a joint measurement on the signal returned from a lossy and noisy environment and the locally stored idler. Willie takes the optimal quantum measurement to detect the sensing attempt.
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Figure 2
Experimental setups for (a) entanglement-enhanced covert sensing and (b) covert sensing based on thermal light. Willie’s apparatus to detect the sensing attempt is illustrated in Ref. [44]. PPLN, periodically poled lithium niobate; PM, phase modulator.
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Figure 3
Phase estimation in entanglement-enhanced covert sensing (blue) and classical covert sensing (red). Dots are experiment data, each obtained from averaging over 2000 consecutive measurements. Error bars represent rms errors. Shades represent the theoretical rms. Inset: estimation of $\cos (θ)$ . The probed phase values for classical (entanglement-enhanced) covert sensing are shifted on abscissa by 0.015 ( $- 0.015$ ) for readability. $N_{S} = 8 \times 10^{- 4}$ , $N_{B} = 160$ , $T = 125 μ s$ , and $κ = 0.0165$ .
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Figure 4
MSE errors versus background-noise levels for entanglement-enhanced covert sensing (blue) and classical covert sensing (red). Experimental data (triangles) and theoretical model (dashed curves) in the fixed covertness regime; experimental data (circles) and theoretical model (solid curves) in the fixed probe power regime. Dotted lines: QCRBs in the fixed probe power regime. Inset: covertness parameter versus noise photons per mode for the fixed covertness (dashed line) and fixed probe power (solid line) regimes. $θ = π / 2$ , $T = 125 μ s$ , $κ = 0.0165$ . $N_{S} = 8 \times 10^{- 4}$ for solid curves and QCRB; $N_{S} / N_{B} = 10^{- 6}$ for dashed curves.
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Figure 5
Test of Willie’s detection error probability when the square-root law is obeyed (black) or violated (red). Thermal-loss sensing channel emulated by a $50 ∶ 50$ beam splitter ( $κ_{E} = 0.5$ ). $N_{B} = 1280$ . $κ N_{S} \sqrt{M} = 200$ to obey the square-root law (black and blue dashed curve). $κ N_{S} / N_{B} = 6.25 \times 10^{- 5}$ to violate the square-root law (red and blue curves). Dots: experimental data. Red and black curves: theory. Blue curves: lower bound for Willie’s detection error probability. Inset: corresponding MSEs for classical (solid) and entanglement-enhanced (dotted) covert sensing around $θ = π / 2$ , showing different scaling behaviors in obeying or violating the square-root law. MSE data for entanglement-enhanced covert sensing not taken due to limited photon flux at the source.
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