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arXiv:2109.00432 · Physical Review A

Quantum channel-position finding using single photons

Athena Karsa, Jacques Carolan, Stefano Pirandola

Published Feb 7, 2022• 3 citations
arXivHTMLPDF

Abstract

Channel-position finding is the task of determining the location of a single target channel among an ensemble of background channels. It has many potential applications, including quantum sensing, quantum reading, and quantum spectroscopy. In particular, it could allow for simple detection protocols to be extended to ones of measurement, for example, target ranging with quantum illumination. The use of quantum states and entanglement in such protocols has shown to yield quantum advantages over their optimal classical counterparts. Here we consider quantum channel-position finding using sources specified by at most one single photon on average per mode, using the discrete-variable formalism. By considering various quantum sources, it is shown through the derivation of performance bounds that a quantum enhancement may be realized.

DOI
10.1103/physreva.105.023705

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Channel-position finding is the task of determining the location of a single target channel among an ensemble of background channels. It has many potential applications, including quantum sensing, quantum reading, and quantum spectroscopy. In particular, it could allow for simple detection protocols to be extended to ones of measurement, for example, target ranging with quantum illumination. The use of quantum states and entanglement in such protocols has shown to yield quantum advantages over their optimal classical counterparts. Here we consider quantum channel-position finding using sources specified by at most one single photon on average per mode, using the discrete-variable formalism. By considering various quantum sources, it is shown through the derivation of performance bounds that a quantum enhancement may be realized.
Quantum channels model many physical processes. For this reason, hypothesis testing between quantum channels is a fundamental task in quantum information theory. Here we consider the paradigmatic case of channel position finding, where the aim is to determine the position of a target quantum channel within a sequence of background channels. We explore this model in the setting of bosonic systems, considering Gaussian channels with the same transmissivity (or gain) but different levels of environmental noise. Thus the goal of the problem becomes detecting the position of a target environment among a number of identical background environments, all acting on an input multi-mode system. We derive bounds for the ultimate error probability affecting this multi-ary discrimination problem and find an analytic condition for quantum advantage over protocols involving classical input states. We also design an explicit protocol that gives numerical bounds on the ultimate error probability and often achieves quantum advantage. Finally, we consider direct applications of the model for tasks of thermal imaging (finding a warmer pixel in a colder background) and quantum communication (for localizing a different level of noise in a sequence of lines or a frequency spectrum).
Quantum hypothesis testing is a central task in the entire field of quantum information theory. Understanding its ultimate limits will give insight into a wide range of quantum protocols and applications, from sensing to communication. Although the limits of hypothesis testing between quantum states have been completely clarified by the pioneering works of Helstrom in the 1970s, the more difficult problem of hypothesis testing with quantum channels, i.e., channel discrimination, is less understood. This is mainly due to the complications coming from the use of input entanglement and the possibility of employing adaptive strategies. In this Letter, we establish a lower limit for the ultimate error probability affecting the discrimination of an arbitrary number of quantum channels. We also show that this lower bound is achievable when the channels have certain symmetries. As an example, we apply our results to the problem of channel position finding, where the goal is to identify the location of a target channel among multiple background channels. In this general setting, we find that the use of entanglement offers a great advantage over strategies without entanglement, with nontrivial implications for data readout, target detection, and quantum spectroscopy.
Quantum hypothesis testing has been greatly advanced for the binary discrimination of two states, or two channels. In this setting, we already know that quantum entanglement can be used to enhance the discrimination of two bosonic channels. Here, we remove the restriction of binary hypotheses and show that entangled photons can remarkably boost the discrimination of multiple bosonic channels. More precisely, we formulate a general problem of channel-position finding where the goal is to determine the position of a target channel among many background channels. We prove that, using entangled photons at the input and a generalized form of conditional nulling receiver at the output, we may outperform any classical strategy. Our results can be applied to enhance a range of technological tasks, including the optical readout of sparse classical data, the spectroscopic analysis of a frequency spectrum, and the determination of the direction of a target at fixed range.
Abstract Quantum hypothesis testing has been greatly advanced for the binary discrimination of two states, or two channels. In this setting, we already know that quantum entanglement can be used to enhance the discrimination of two bosonic channels. Here, we remove the restriction of binary hypotheses and show that entangled photons can remarkably boost the discrimination of multiple bosonic channels. More precisely, we formulate a general problem of channel-position finding where the goal is to determine the position of a target channel among many background channels. We prove that, using entangled photons at the input and a generalized form of conditional nulling receiver at the output, we may outperform any classical strategy. Our results can be applied to enhance a range of technological tasks, including the optical readout of sparse classical data, the spectroscopic analysis of a frequency spectrum, and the determination of the direction of a target at fixed range.
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 the corresponding optimum measurement is implemented at the receiver. We explore the detection problem in different regions of the parameter space and verify that the quantum advantage exists even in a forbidden region of the conventional illumination, where all classical schemes become useless. Our results indicate that quantum illumination breaks the classical limit for up to 40%, while approaching the quantum limit imposed by the Helstrom limit. These results not only demonstrate the advantage of quantum illumination, but also manifest its valuable potential of target detection.
The final goal of quantum hypothesis testing is to achieve quantum advantage over all possible classical strategies. In the protocol of quantum reading this advantage is achieved for information retrieval from an optical memory, whose generic cell stores a bit of information in two possible lossy channels. For this protocol, we show, theoretically and experimentally, that quantum advantage is obtained by practical photon-counting measurements combined with a simple maximum-likelihood decision. In particular, we show that this receiver combined with an entangled two-mode squeezed vacuum source is able to outperform any strategy based on statistical mixtures of coherent states for the same mean number of input photons. Our experimental findings demonstrate that quantum entanglement and simple optics are able to enhance the readout of digital data, paving the way to real applications of quantum reading and with potential applications for any other model that is based on the binary discrimination of bosonic loss.