An optical transmitter that uses entangled light generated by spontaneous parametric downconversion (SPDC), in conjunction with an optimal quantum-optical receiver (whose implementation is not yet known) is in principle capable of obtaining up to a 6 dB gain in the error-probability exponent over the optimum-reception un-entangled coherent-state lidar to detect the presence of a far-away target subject to entanglement-breaking loss and noise in the free-space link [Lloyd'08, Tan'08]. We present an explicit design of a structured quantum-illumination receiver, which in conjunction with the SPDC transmitter is shown to achieve up to a 3 dB error-exponent advantage over the classical sensor. Apart from being fairly feasible for a proof-of-principle demonstration, this is to our knowledge the first structured design of a quantum-optical sensor for target detection that outperforms the comparable best classical lidar sensor appreciably in a low-brightness, lossy and noisy operating regime.
A quantum receiver is an essential element of quantum illumination (QI) which outperforms its classical counterpart, called classical-illumination (CI). However, there are only few proposals for realizable quantum receiver, which exploits nonlinear effects leading to increasing the complexity of receiver setups. To compensate this, in this article, we design a quantum receiver with linear optical elements for Gaussian QI. Rather than exploiting nonlinear effect, our receiver consists of a 50:50 beam splitter and homodyne detection. Using double homodyne detection after the 50:50 beam splitter,…
Quantum illumination (QI) promises unprecedented performances in target detection but there are various problems surrounding its implementation. Where target ranging is a concern, signal and idler recombination forms a crucial barrier to the protocol's success. This could potentially be mitigated if performing a measurement on the idler mode could still yield a quantum advantage. In this paper we investigate the QI protocol for a generically correlated Gaussian source and study the phase-conjugating (PC) receiver, deriving the associated SNR in terms of the signal and idler energies, and their…
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 p…
In quantum illumination, the signal mode of light, entangled with an idler mode, is dispatched towards a suspected object bathed in thermal noise and the returning mode, along with the stored idler mode, is measured to determine the presence or absence of the object. In this process, entanglement is destroyed but its benefits in the form of classical correlations and enlarged Hilbert space survive. Here, we propose the use of probe state hyperentangled in two degrees of freedom - polarization and frequency, to achieve a significant 12dB performance improvement in error probability exponent ove…
We propose observable bounds for Gaussian illumination to maximize the signal-to-noise ratio, which minimizes the discrimination error between the presence and absence of a low-reflectivity target using Gaussian states. The observable bounds are achieved with mode-by-mode measurements. In the quantum regime using a two-mode squeezed vacuum state, our observable receiver outperforms the other feasible receivers whereas it cannot approach the quantum Chernoff bound. The corresponding observable cannot be implemented with heterodyne detections due to the additional vacuum noise. In the classical …
Quantum illumination is a powerful sensing technique that employs entangled signal-idler photon pairs to boost the detection efficiency of low-reflectivity objects in environments with bright thermal noise. The promised advantage over classical strategies is particularly evident at low signal powers, a feature which could make the protocol an ideal prototype for non-invasive biomedical scanning or low-power short-range radar. In this work we experimentally investigate the concept of quantum illumination at microwave frequencies. We generate entangled fields using a Josephson parametric convert…
This research note II introduces a way to understand a basic concept of the quantum enigma cipher. The conventional cipher is designed by a mathematical algorithm and its security is evaluated by the complexity of the algorithm in security analysis and ability of computers. This kind of cipher can be decrypted with probability one in principle by the Brute force attack in which an eavesdropper tries all the possible keys based on the correct ciphertext and some known plaintext. A cipher with quantum effects in physical layer may protect the system from the Brute force attack by means of the qu…
We propose Gaussian quantum illumination(QI) protocol exploiting asymmetrically squeezed two-mode(ASTM) state that is generated by applying single-mode squeezing operations on each mode of an initial two-mode squeezed vacuum(TMSV) state, in order to overcome the limited brightness of a TMSV state. We show that the performance of the optimal receiver is enhanced by local squeezing operation on a signal mode whereas the performance of a realistic receiver can be enhanced by local squeezing operations on both input modes. Under a fixed mean photon number of the signal mode, the ASTM state can be …
With the aim to loosen the entanglement requirements of quantum illumination, we study the performance of a family of Gaussian states at the transmitter, combined with an optimal and joint quantum measurement at the receiver. We find that maximal entanglement is not strictly necessary to achieve quantum advantage over the classical benchmark of a coherent-state transmitter, in both settings of symmetric and asymmetric hypothesis testing. While performing this quantum-classical comparison, we also investigate a suitable regime of parameters for potential short-range radar (or scanner) applicati…
In Quantum Illumination (QI), a signal beam initially entangled with an idler beam held at the receiver interrogates a target region bathed in thermal background light. The returned beam is measured jointly with the idler in order to determine whether a weakly reflecting target is present. Using tools from quantum information theory, we derive lower bounds on the average error probability of detecting both specular and fading targets and on the mean squared error of estimating the reflectance of a detected target, which are obeyed by any QI transmitter satisfying a signal energy constraint. Fo…
Loss and noise quickly destroy quantum entanglement. Nevertheless, recent work has shown that a quadrature-entangled light source can reap a substantial performance advantage over all classical-state sources of the same average transmitter power in scenarios whose loss and noise makes them entanglement breaking, standoff target-detection being an example. In this paper, we make a first step in extending this quantum illumination paradigm to the optical imaging domain, viz., to obtain better spatial resolution for standoff optical sensing. Our canonical imaging scenario---restricted, for simpli…
We consider the problem of estimating unknown transmittance $θ$ of a target bathed in thermal background light. As quantum estimation theory yields the fundamental limits, we employ the lossy thermal-noise bosonic channel model, which describes sensor-target interaction quantum mechanically in many practical active-illumination systems (e.g., using emissions at optical, microwave, or radio frequencies). We prove that quantum illumination using two-mode squeezed vacuum (TMSV) states asymptotically achieves minimal quantum Cramér-Rao bound (CRB) over all quantum states (not necessarily Gaussian)…
Quantum illumination (QI) provides entanglement-based target detection---in an entanglement-breaking environment---whose performance is significantly better than that of optimum classical-illumination target detection. QI's performance advantage was established in a Bayesian setting with the target presumed equally likely to be absent or present and error probability employed as the performance metric. Radar theory, however, eschews that Bayesian approach, preferring the Neyman-Pearson performance criterion to avoid the difficulties of accurately assigning prior probabilities to target absence…
By harnessing the quantum states of light for illumination, precise phase and absorption estimations can be achieved with precision beyond the standard quantum limit. Despite their significance for precision measurements, quantum states are fragile in noisy environments which leads to difficulties in revealing the quantum advantage. In this work, we propose a scheme to improve optical absorption estimation precision by using the correlated photon pairs from spontaneous parametric down-conversion as the illumination. This scheme performs better than clasical illumination when the loss is below …
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 lidar applicati…
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 imple…
Quantum illumination can utilize entangled light to detect the low-reflectivity target that is hidden in a bright thermal background. This technique is applied to the detection of an object in the curved spacetime of the Earth, in order to explore how the curvature of spacetime affects quantum illumination. It is found that the spatial quantum illumination with entangled state transmitter outperforms that with coherent-state transmitter in the near-Earth curved spacetime. Moreover, either the quantum illumination system or the coherent-state system is employed, and gravity can enhance the spac…
Quantum illumination (QI) theoretically promises up to a 6dB error-exponent advantage in target detection over the best classical protocol. The advantage is maximised by a regime which includes a very high background, which occurs naturally when one considers microwave operation. Such a regime has well-known practical limitations, though it is clear that, theoretically, knowledge of the associated classical benchmark in the microwave is lacking. The requirement of amplifiers for signal detection necessarily renders the optimal classical protocol here different to that which is traditionally us…
Quantum target detection is an emerging application that utilizes entanglement to enhance the sensing of the presence of an object. Although several experimental demonstrations for certain situations have been reported recently, the single-shot detection limit imposed by the Helstrom limit has not been reached because of the unknown optimum measurements. Here we report an experimental demonstration of quantum target detection, also known as quantum illumination, in the single-photon limit. In our experiment, one photon of the maximally entangled photon pair is employed as the probe signal and …
Quantum metrology utilizes nonclassical resources, such as entanglement or squeezed light, to realize sensors whose performance exceeds that afforded by classical-state systems. Environmental loss and noise, however, easily destroy nonclassical resources, and thus nullify the performance advantages of most quantum-enhanced sensors. Quantum illumination (QI) is different. It is a robust entanglement-enhanced sensing scheme whose 6 dB performance advantage over a coherent-state sensor of the same average transmitted photon number survives the initial entanglement's eradication by loss and noise.…
Quantum target detection aims to utilise quantum technologies to achieve performances in target detection not possible through purely classical means. Quantum illumination is an example of this, based on signal-idler entanglement, promising a potential 6 dB advantage in error exponent over its optimal classical counterpart. So far, receiver designs achieving this optimal reception remain elusive with many proposals based on Gaussian processes appearing unable to utilise quantum information contained within Gaussian state sources. This paper considers the employment of a noiseless linear amplif…
In this paper, we propose a novel quantum backscatter communications (QBC) protocol, inspired by the quantum illumination (QI) concept. In the QBC paradigm, the transmitter generates entangled photon pair. The signal photon is transmitted and the idler photon is kept at the receiver. The tag antenna communicates by performing the pulse amplitude modulation (PAM), binary phase shift keying (BPSK) or quadratic phase shift keying (QPSK) on the signal impinging at the antenna. Using the sum-frequency-generation receiver, our QBC protocol achieves a 6 dB error exponent gain for PAM and BPSK, and 3 …
The general problem of performance advantage obtainable by the use of nonclassical transmitted states over classical ones is considered. Attention is focused on the situation where system loss is significant and additive Gaussian noise may be present at the receiver. Under the assumption that the total received state is classical, rigorous output density operator representations and their trace distance bounds are developed for classical and nonclassical transmitted states. For applications with high loss in all modes, a practical No-Go theorem is enunciated that rules out the possibility of s…
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 $\hatθ_n$ scales as $\langle (θ-\hatθ_n)^2\rangle=\mathcal{O}(1/\sqrt{n})$; 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, e…
