We provide a proof that Gaussian entanglement can provide up to 6dB of advantage in the error probability exponent compared to using a classical light source of the same signal brightness for the task of discriminating between the presence of two arbitrary objects (whose shapes are known). The proof is based on a perturbative expansion in the high loss and low signal brightness regime of the joint state of the reflected signal and the stored idler mode with which the signal is entangled.
We provide a proof that Gaussian entanglement can provide up to 6dB of advantage in the error probability exponent compared to using a classical light source of the same signal brightness for the task of discriminating between the presence of two arbitrary objects (whose shapes are known). The proof is based on a perturbative expansion in the high loss and low signal brightness regime of the joint state of the reflected signal and the stored idler mode with which the signal is entangled.
Quantum illumination (QI) is the task of querying a scene using a transmitter probe whose quantum state is entangled with a reference beam retained in ideal storage, followed by optimally detecting the target-returned light together with the stored reference, to make decisions on characteristics of targets at stand-off range, at precision that exceeds what is achievable with a classical transmitter of the same brightness and otherwise identical conditions. Using tools from perturbation theory, we show that in the limit of low transmitter brightness, high loss, and high thermal background, there is a factor of four improvement in the Chernoff exponent of the error probability in discriminating any number of apriori-known reflective targets when using a Gaussian-state entangled QI probe, over using classical coherent-state illumination (CI). While this advantage was known for detecting the presence or absence of a target, it had not been proven for the generalized task of discriminating between arbitrary target libraries. In proving our result, we derive simple general analytic expressions for the lowest-order asymptotic expansions of the quantum Chernoff exponents for QI and CI in terms of the signal brightness, loss, thermal noise, and the modal expansion coefficients of the target-reflected light's radiant exitance profiles when separated by a spatial mode sorter after entering the entrance pupil of the receiver's aperture.
An optical transmitter irradiates a target region containing a bright thermal-noise bath in which a low-reflectivity object might be embedded. The light received from this region is used to decide whether the object is present or absent. The performance achieved using a coherent-state transmitter is compared with that of a quantum-illumination transmitter, i.e., one that employs the signal beam obtained from spontaneous parametric down-conversion. By making the optimum joint measurement on the light received from the target region together with the retained spontaneous parametric down-conversion idler beam, the quantum-illumination system realizes a 6 dB advantage in the error-probability exponent over the optimum reception coherent-state system. This advantage accrues despite there being no entanglement between the light collected from the target region and the retained idler beam.
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.
The signal half of an entangled twin beam, generated using spontaneous parametric downconversion, interrogates a region of space that is suspected of containing a target and has high loss and high (entanglement-breaking) background noise. A joint measurement is performed on the returned light and the idler beam that was retained at the transmitter. An optimal quantum receiver, whose implementation is not yet known, was shown to achieve 6 dB gain in the error-probability exponent relative to that achieved with a single coherent-state (classical) laser transmitter and the optimum receiver. We present two structured optical receivers that achieve up to 3 dB gain in the error exponent over that attained with the classical sensor. These are designs of quantum-optical sensors for target detection, which can be readily implemented in a proof-of-concept experiment, that appreciably outperform the best classical sensor in the low-signal-brightness, high-loss, and high-noise operating regime.
Quantum illumination exploits entanglement between a transmitted signal and a retained idler to improve the error-probability exponent of target detection by roughly a factor of four (6 dB) over that with a coherent state of the same transmitted energy. This advantage presumes a known return phase. In practice, the phase is set by the range to the target and the condition of its surface, and is difficult to know in advance. Whether the advantage survives when this phase is unknown is not obvious. Here, we cast target detection as a composite hypothesis test in which the return phase is an unknown constant common to all trials, and we restrict the receiver to independent and identical measurements on each copy. We bound the worst-case error exponent at low reflectivity for every such measurement and every input state of a single signal mode and an idler of any dimension. We then show that unentangled coherent light with heterodyne detection already saturates this bound, for every value of the phase. Entanglement therefore confers no advantage in this setting. The class of independent and identical measurements contains many implementable quantum-illumination receivers, including the optical parametric amplifier and phase-conjugate receivers. Our result shows that none of them can offer a quantum advantage in the worst case over the phase, to leading order in the reflectivity.
Quantum illumination (QI) is an entanglement-enhanced sensing system whose performance advantage over a comparable classical system survives its usage in an entanglement-breaking scenario plagued by loss and noise. In particular, QI's error-probability exponent for discriminating between equally likely hypotheses of target absence or presence is 6 dB higher than that of the optimum classical system using the same transmitted power. This performance advantage, however, presumes that the target return, when present, has known amplitude and phase, a situation that seldom occurs in light detection and ranging (lidar) applications. At lidar wavelengths, most target surfaces are sufficiently rough that their returns are speckled, i.e., they have Rayleigh-distributed amplitudes and uniformly distributed phases. QI's optical parametric amplifier receiver---which affords a 3 dB better-than-classical error-probability exponent for a return with known amplitude and phase---fails to offer any performance gain for Rayleigh-fading targets. We show that the sum-frequency generation receiver [Zhuang et al., Phys. Rev. Lett. 118, 040801 (2017)]---whose error-probability exponent for a nonfading target achieves QI's full 6 dB advantage over optimum classical operation---outperforms the classical system for Rayleigh-fading targets. In this case, QI's advantage is subexponential: its error probability is lower than the classical system's by a factor of $1/ln(M\overline{\ensuremath{\kappa}}{N}_{S}/{N}_{B})$, when $M\overline{\ensuremath{\kappa}}{N}_{S}/{N}_{B}\ensuremath{\gg}1$, with $M\ensuremath{\gg}1$ being the QI transmitter's time-bandwidth product, ${N}_{S}\ensuremath{\ll}1$ its brightness, $\overline{\ensuremath{\kappa}}$ the target return's average intensity, and NB the background light's brightness.