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arXiv:1611.10020 · Physical Review A

Overarching framework between Gaussian quantum discord and Gaussian quantum illumination

Mark Bradshaw, Syed M. Assad, Jing Yan Haw, Si-Hui Tan, Ping Koy Lam, Mile Gu

Published Feb 23, 2017• 23 citations
arXivHTMLPDF

Abstract

We cast the problem of illuminating an object in a noisy environment into a communication protocol. A probe is sent into the environment, and the presence or absence of the object constitutes a signal encoded on the probe. The probe is then measured to decode the signal. We calculate the Holevo information and bounds to the accessible information between the encoded and received signal with two different Gaussian probes---an Einstein-Podolsky-Rosen (EPR) state and a coherent state. We also evaluate the Gaussian discord consumed during the encoding process with the EPR probe. We find that the Holevo quantum advantage, defined as the difference between the Holevo information obtained from the EPR and coherent state probes, is approximately equal to the discord consumed. These quantities become exact in the typical illumination regime of low object reflectivity and low probe energy. Hence we show that discord is the resource responsible for the quantum advantage in Gaussian quantum illumination.

DOI
10.1103/physreva.95.022333

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We cast the problem of illuminating an object in a noisy environment into a communication protocol. A probe is sent into the environment, and the presence or absence of the object constitutes a signal encoded on the probe. The probe is then measured to decode the signal. We calculate the Holevo information and bounds to the accessible information between the encoded and received signal with two different Gaussian probes---an Einstein-Podolsky-Rosen (EPR) state and a coherent state. We also evaluate the Gaussian discord consumed during the encoding process with the EPR probe. We find that the Holevo quantum advantage, defined as the difference between the Holevo information obtained from the EPR and coherent state probes, is approximately equal to the discord consumed. These quantities become exact in the typical illumination regime of low object reflectivity and low probe energy. Hence we show that discord is the resource responsible for the quantum advantage in Gaussian quantum illumination.
We investigate how the quantum advantage in quantum illumination is determined by an interplay between entanglement and discord of the probe state. In particular, we consider a setup in which the probe is a maximally mixed marginal (MMM) state and the environmental state is completely mixed where the quantum advantage equals the amount of discord consumed for illumination. Through a conditional extremal analysis, we determine the range of accessible advantages for given values of entanglement and discord. At fixed discord, high entanglement restricts the accessible advantage to high values, making high entanglement sufficient for high advantage. Conversely, at fixed entanglement, low discord limits the advantage to low values, indicating that high discord is necessary for high advantage. These conclusions remain unchanged when alternative correlation measures, including relative entropy and Bures entanglement and geometric discord, are used. The consistency of our results across multiple conceptually distinct measures indicates that the observed resource-advantage relation is not an artifact of a specific quantifier, but a robust feature of the protocol within the family of MMM states. We finally find that in the high-noise regime (near-maximally-mixed state), quantum advantage is, to leading order, a linear function of the initial discord highlighting discord as the key resource for resilience to noise in the protocol.
The benefits of entanglement can outlast entanglement itself. In quantum illumination, entanglement is employed to better detect reflecting objects in environments so noisy that all entanglement is destroyed. Here, we show that quantum discord—a more resilient form of quantum correlations—explains the resilience of quantum illumination. We introduce a quantitative relation between the performance gain in quantum illumination and the amount of discord used to encode information about the presence or absence of a reflecting object. This highlights discords role preserving the benefits of entanglement in entanglement breaking noise.
Quantum illumination consists in shining quantum light on a target region immersed in a bright thermal bath with the aim of detecting the presence of a possible low-reflective object. If the signal is entangled with the receiver, then a suitable choice of the measurement offers a gain with respect to the optimal classical protocol employing coherent states. Here, we tackle this detection problem by using quantum estimation techniques to measure the reflectivity parameter of the object, showing an enhancement in the signal-to-noise ratio up to 3 dB with respect to the classical case when implementing only local measurements. Our approach employs the quantum Fisher information to provide an upper bound for the error probability, supplies the concrete estimator saturating the bound, and extends the quantum illumination protocol to non-Gaussian states. As an example, we show how Schrödinger's cat states may be used for quantum illumination.
Proofs of the quantum advantage available in imaging or detecting objects under quantum illumination can rely on optimal measurements without specifying what they are. We use the continuous-variable Gaussian quantum information formalism to show that quantum illumination is better for object detection compared with coherent states of the same mean photon number, even for simple direct photodetection. The advantage persists if signal energy and object reflectivity are low and background thermal noise is high. The advantage is even greater if we match signal beam detection probabilities rather than mean photon number. We perform all calculations with thermal states, even for non-Gaussian conditioned states with negative Wigner functions. We simulate repeated detection using a Monte-Carlo process that clearly shows the advantages obtainable.
Proofs of the quantum advantage available in imaging or detecting objects under quantum illumination can rely on optimal measurements without specifying what they are. We use the continuous-variable Gaussian quantum information formalism to show that quantum illumination is better for object detection compared with coherent states of the same mean photon number, even for simple direct photodetection. The advantage persists if signal energy and object reflectivity are low and background thermal noise is high. The advantage is even greater if we match signal beam detection probabilities rather than mean photon number. We perform all calculations with thermal states, even for non-Gaussian conditioned states with negative Wigner functions. We simulate repeated detection using a Monte-Carlo process that clearly shows the advantages obtainable.
Quantum illumination is a quantum sensing protocol primarily used for object detection, which aims to detect the presence of a target with low reflectivity in the free space using quantum light fields. Here we investigate a quantum illumination scheme using an entangled light source by performing non-Gaussian operations on the two-mode squeezed vacuum (TMSV) state in order to reduce the detection error probability and meanwhile improve the signal-to-noise (SNR) ratio. We demonstrate that under the same squeezing parameter, the non-Gaussian operations can significantly reduce the detection error rate compared with the original TMSV state. Under the same average signal photon number, both the TMSV states with and without non-Gaussian operations can provide smaller error rate than that of the coherent state. In addition, we consider the balanced homodyne detection on idler and return signal photons as joint measurement and find that non-Gaussian operations can enhance the SNR of target detection by about 6--9 dB compared with that using TMSV. These results here demonstrate the advantage of the non-Gaussian entangled source in quantum illumination protocol and can find potential applications in target detection in noisy environment.