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The Quantum Illumination Story The Quantum Illumination Story Jeffrey H. Shapiro1, ∗ 1Research Laboratory of Electronics Massachusetts Institute of Technology Cambridge, Massachusetts 02139, USA Superposition and entanglement, the quintessential characteristics of quantum physics, have been shown to provide communication, computation, and sensing capabilities that go beyond what clas- sical physics will permit. It is natural, therefore, to explore their application to radar, despite the fact that decoherence|caused by the loss and noise encountered in radar sensing|destroys these fragile quantum properties. This paper tells the story of \quantum illumination", an entanglement- based approach to quantum radar, from its inception to its current understanding. Remarkably, despite loss and noise that destroy its initial entanglement, quantum illumination does offer a target- detection performance improvement over a classical radar of the same transmitted energy. A realistic assessment of that improvement's utility, however, shows that its value is severely limited. Nev- ertheless, the fact that entanglement can be of value on an entanglement-breaking channel|the meta-lesson of the quantum illumination story|should spur continued research on quantum radar. INTRODUCTION two scenarios shown in Fig. 1. In both scenarios an op- tical transmitter illuminates a region of space in which Superposition and entanglement|Schr¨odinger's cat a weakly-reflecting target is equally likely to be absent being simultaneously alive and dead [1], and the \spooky or present within always-present background light. In action at a distance" that Einstein found disturbing [2]| Fig. 1(a), the transmitter's signal beam is a sequence are quantum-mechanical phenomena that are moving of N high time-bandwidth product (M = TW 1), from fundamental studies into scientific and engineering single-photon pulses. The receiver, for this single-photon applications. Quantum computers, if realized at suffi- (SP) scenario, makes a minimum error-probability deci- ciently large scale, will vastly outstrip the capability of sion between hypotheses H0 (target absent) and H1 (tar- classical machines for a variety of problems in simula- get present) from observation of the light returned from tion [3], optimization [4], and machine learning [5]. Those the interrogated region. In Fig. 1(b), the transmitter il- large-scale quantum computers|running Shor's quan- luminates the region of interest with a sequence of N tum factoring algorithm [6]|will also break the public- high time-bandwidth product (M = TW 1), single- key infrastructure on which Internet commerce currently photon signal pulses, each of which is entangled with a relies. Quantum communication, in the form of quantum companion single-photon idler pulse; see Appendix A for key distribution [7], however, may thwart that quantum the details. The receiver, for this quantum illumination threat. In other work, quantum-enhanced sensing is mov- (QI) scenario, makes its minimum error-probability deci- ing out of the laboratory and into real use, the most no- sion between H0 and H1 from observation of the retained table example being the incorporation of squeezed-state idler light and the light returned from the interrogated light into the laser interferometric gravitational-wave ob- region. servatory (LIGO) [8]. A natural question to ask, there- The crucial assumptions in Lloyd's analysis of the un- fore, is whether quantum techniques can bring perfor- entangled and entangled scenarios are as follows. mance gains to radar sensing. This paper will follow one • avenue of quantum radar research from its inception to When the target is present, the roundtrip now: quantum illumination. transmitter-to-target-to-receiver transmissivity for the signal beam is 0 < κ 1. arXiv:1910.12277v4 [quant-ph] 23 Dec 2019 • The background light's average photon number per LLOYD'S QUANTUM ILLUMINATION temporal mode, NB, satisfies the low-brightness condition NB 1. Lloyd [9] coined the term \quantum illumination" for his entanglement-based approach to improving an optical • For each transmitted signal pulse, at most one radar's capability to detect a weakly-reflecting target em- photon is returned to the receiver, regardless of bedded in background noise that can be much stronger whether the target is absent or present, implying than the target return. His work, which built on Sacchi's that MNB 1. earlier studies of quantum operation discrimination [10], [11], compared the target-detection performance for the Under these assumptions, Lloyd identified two operating regimes, the \good" and the \bad", for his SP and QI scenarios, and compared their error probabilities' quan- tum Chernoff bounds [12] in these regimes. In their good ∗ [email protected] regimes, SP and QI's error probabilities have the same 2 ? ? (a) unentangled (b) entangled FIG. 1. Scenarios presumed in Lloyd's treatment of quantum illumination (QI). (a) Unentangled operation, in which the transmitter illuminates the region of interest with a sequence of N single-photon signal pulses. Target absence or presence is decided from observation of the returned light. (b) Entangled operation, in which the transmitter illuminates the region of interest with a sequence of N single-photon signal pulses, each of which is entangled with a companion single-photon idler pulse. Target absence or presence is decided from observation of the retained idler and the returned light. bound, Despite the idealized nature of Lloyd's QI analysis| it presumes an on-demand source of high-TW entan- −Nκ −Nκ Pr(e)SP ≤ e =2 and Pr(e)QI ≤ e =2; (1) gled signal-idler photon pairs, lossless idler storage, and perfect realization of an optimum quantum receiver| which, because Nκ equals the average number of signal its enormous predicted performance enhancement in the photons returned when the target is present, whereas 0 bad regime motivated a great deal of follow-on research. is the average number of signal photons returned when Some of that research, unfortunately, took much of the the object is absent, equals the signal shot-noise limit for air out of QI's balloon, as we will describe below. Before laser communication with on-off-keying (OOK) modula- doing so, however, a brief preface about classical versus tion. Despite (1)'s applying to SP and QI's good regimes, quantum radar is in order. QI still enjoys a substantial good-regime performance ad- We were careful, earlier in this section, not to describe vantage over SP, because SP's good regime is limited to the comparison between SP and QI operation as one be- κ NB, whereas QI's extends to the much larger pa- tween a classical radar (SP) and a quantum radar (QI). rameter region in which κ NB=M. In quantum optics, see, e.g., [15], [16], it is conventional The comparison between SP and QI operation is rad- to reserve the appellation \quantum" for those systems ically different in their bad regimes. Here Lloyd found whose performance analysis requires the quantum theory that of photodetection. In particular, their performance can- 2 not be correctly quantified from the semiclassical theory Pr(e) ≤ e−Nκ =8NB =2; for κ N ; (2) SP B of photodetection, in which light is treated as a classical and (possibly stochastic) electromagnetic wave and the dis- creteness (quantization) of the electron charge gives rise 2 −Nκ M=8NB Pr(e)QI ≤ e =2; for κ NB=M: (3) to shot noise. Furthermore, measurements of light beams that are in coherent states [17], or classically-random These bounds mimic the background-limited error prob- mixtures thereof, in any of the three basic photodetec- ability of OOK laser communication, with NB being the tion paradigms|direct detection, homodyne detection, background's brightness for SP operation, and NB=M or heterodyne detection|do not require quantum pho- being that brightness for QI operation. The bad-regime todetection theory to obtain correct measurement statis- results reveal a double advantage for QI: first, its bad tics [15]. Hence such states are called classical states. regime applies in a smaller κ range than that of SP; Systems that employ nonclassical states|states other and second, when both systems are in their bad regimes, than coherent states or their random mixtures|require QI enjoys a factor-of-M greater error-probability expo- the use of quantum photodetection theory. In this re- nent (effective signal-to-noise ratio). At optical frequen- gard, we note that single-photon states and entangled cies, high time-bandwidth product is easy to obtain, e.g., states are not classical states, and hence Lloyd's perfor- a 1 µs pulse at 300 THz center frequency (1 µm wave- mance comparison is between two quantum radars, one length) with 1 THz (1/3-percent fractional) bandwidth of which employs entanglement (QI) while the other (SP) yields M = 106, in which case Lloyd's bad-regime QI has does not. a 60 dB higher effective signal-to-noise ratio than its SP A coherent state|other than the zero-photon (vac- competitor. Moreover, and remarkably, this advantage uum) state|contains a random number of photons. So, is afforded despite the background noise's destroying the Shapiro and Lloyd [18] compared Lloyd's QI to a classi- initial entanglement, i.e., the retained and returned light cal radar by replacing Lloyd's SP transmitter in Fig. 1(a) are not entangled. with a coherent-state transmitter (an ideal laser) that 3 produces a sequence of N pulses, each of which has unity term this operating regime the \bad" regime for Tan et average photon number. The quantum Chernoff bound al.'s CS and QI systems. Lloyd's bad-regime QI system for their coherent-state radar, offered an M-fold error-probability exponent improve- ment over its SP counterpart, where a time-bandwidth p p 2 −Nκ( 1+NB − NB ) 6 Pr(e)CS ≤ e =2; (4) product M ≥ 10 is easily attainable.
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