Quantum sensing has become a broad field. It is generally related with the idea of using quantum resources to boost the performance of a number of practical tasks, including the radar-like detection of faint objects, the readout of information from optical memories, and the optical resolution of extremely close point-like sources. Here, we first focus on the basic tools behind quantum sensing, discussing the most recent and general formulations for the problems of quantum parameter estimation and hypothesis testing. With this basic background in hand, we then review emerging applications of quantum sensing in the photonic regime both from a theoretical and experimental point of view. Besides the state of the art, we also discuss open problems and potential next steps. This Review discusses emerging applications of photonic quantum sensing. The theoretical and experimental developments of quantum reading of classical data, quantum illumination of targets, and optical resolution beyond the Rayleigh limit are described.

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Advances in photonic quantum sensing

Quantum metrology shows that it is always possible to estimate the separation of two stars, no matter how close together they are.

Quantum Theory of Superresolution for Two Incoherent Optical Point Sources

This is the fifth edition of H Dieter Zeh's classic text on the physical foundations of time-irreversibility in the phenomena. A forerunner of this book was the 1984 German text 'Die Physik der Zeitrichtung' of about 80 pages, which appeared as volume 200 in the Springer series Lecture Notes in Physics. It was soon followed by a largely revised and extended English edition of about twice the length. Since then each new edition has been thoroughly revised and, edition by edition, new topics and chapters have been added. As the author says in the introduction: 'The prime intention of this book is to discuss the relations between various arrows of time, and to search for a universal master arrow'. Correspondingly, after a short chapter on 'the physical concept of time', the author systematically discusses in the remaining five chapters the time arrows in electromagnetic radiation theory, in thermodynamics, in quantum mechanics, in black-hole physics and cosmology, and in quantum cosmology. The chapters on thermodynamics and quantum mechanics slightly outweigh the others in terms of length. The fifth edition now includes two new section on 'cosmic probabilities and history' and 'quantum computers', and the section on the 'expansion of the universe' has been restructured and extended. Other changes concentrate on the sections on radiation damping, decoherence, interpretation of quantum theory, and quantum cosmology. It should also be mentioned that the author maintains a regularly updated website for the book at www.time-direction.de. The reading is always highly stimulating and uses results and ideas from a very broad range of physics, with interspersed historical and philosophical comments. Somehow outstanding and of particular interest is the chapter on quantum cosmology, which raises novel interpretational issues that cannot be found in any other textbook I know of on time asymmetry. As regards the mathematical prerequisites, the reader is assumed to have some knowledge on Green functions, special-relativistic electrodynamics, Hamiltonian mechanics, the formalisms of phenomenological and statistical thermodynamics, quantum mechanics, and general relativity. At some rare places the author avowedly shows a certain impatience with mathematical details, in particular if they do not fit with his expectations based on personal intuition. This stands in peculiar contrast to the conceptual depth and thoroughness that otherwise characterizes most of the book. Quite generally, the reader should be prepared to encounter provoking and partially controversial statements, but this should not be too surprising in such a complex and partially highly speculative field. All this certainly sets high standards for the reader's intellectual independence and maturity, but this is definitely in accord with the philosophy of Springer's 'Frontiers Collection'. On the other hand, from personal experience I can say that already the original German text has been very popular with beginning graduate students who had a serious interest in foundational issues. (I obtained my first personal copy as a birthday present from a fellow student.) This is essentially due to the fact that the author's genuine urge to understand, rather than just describe, gives the text a characteristic flair of freshness and authenticity to which beginning researchers are particularly susceptible. Being provocative at places is just part of that. This spirit has essentially survived the various editions, thanks to the author's constant efforts to improve the existing presentation, and also by adding modern topics. However, the negative side of this constant streamlining of presentation according to the author's evolving understanding is that it tends to amplify the already existing idiosyncratic tendencies, sometimes resulting in cryptic remarks which fail their intended clarifying purpose. This already applies to the fairly steep introduction, where the author attempts to clarify in a few lines the central issue of what it means (structurally) to say that a particular dynamical law is (a)symmetric under time reversal. Here I think it would definitely be necessary to give more detailed explanations, e.g., by elaborating on the author's own discussion in 'Note on the time reversal asymmetry of equations of motion' (1999 Found. Phys. Lett. 12 193?96). Also, the structural relations between the operation of time reversal and other space-time symmetries are hardly mentioned. This may be excused insofar as T symmetry in quantum-field theory is not generally addressed in this book (which itself may be regretted), but as part of a structural characterization of the operation of time reversal it would certainly have been useful. The books provides an extensive bibliography which seems (as far as I can tell) fairly complete, though sometimes and for no obvious reason, preprints posted on web-archives are cited instead of the corresponding journal articles. Each reference comes with the page numbers of where it is cited in the text, which is very useful indeed. The positive aspects by far outweigh the critical ones. The new edition of H Dieter Zeh's classic text is highly recommended to anybody interested in foundational issues and ready to take the challenge to follow the sometimes intuitive approach of someone who has spent much time and effort to understand the conceptual intricacies and variations of this indisputably difficult and demanding subject.

https://iopscience.iop.org/article/10.1088/0264-9381/25/20/209003/pdf

The Physical Basis of the Direction of Time

Quantum sensing has become a mature and broad field. It is generally related with the idea of using quantum resources to boost the performance of a number of practical tasks, including the radar-like detection of faint objects, the readout of information from optical memories or fragile physical systems, and the optical resolution of extremely close point-like sources. Here we first focus on the basic tools behind quantum sensing, discussing the most recent and general formulations for the problems of quantum parameter estimation and hypothesis testing. With this basic background in our hands, we then review emerging applications of quantum sensing in the photonic regime both from a theoretical and experimental point of view. Besides the state-of-the-art, we also discuss open problems and potential next steps.

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Advances in Photonic Quantum Sensing

We determine the ultimate potential of quantum imaging for boosting the resolution of a far-field, diffraction-limited, linear imaging device within the paraxial approximation. First, we show that the problem of estimating the separation between two pointlike sources is equivalent to the estimation of the loss parameters of two lossy bosonic channels, i.e., the transmissivities of two beam splitters. Using this representation, we establish the ultimate precision bound for resolving two pointlike sources in an arbitrary quantum state, with a simple formula for the specific case of two thermal sources. We find that the precision bound scales with the number of collected photons according to the standard quantum limit. Then, we determine the sources whose separation can be estimated optimally, finding that quantum-correlated sources (entangled or discordant) can be superresolved at the sub-Rayleigh scale. Our results apply to a variety of imaging setups, from astronomical observation to microscopy, exploiting quantum detection as well as source engineering.

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Ultimate Precision Bound of Quantum and Subwavelength Imaging.

The Rayleigh limit has so far applied to all microscopy techniques that rely on linear optical interaction and detection in the far field. Here we demonstrate that detecting the light emitted by an object in higher-order transverse electromagnetic modes (TEMs) can help in achieving sub-Rayleigh precision for a variety of microscopy-related tasks. Using optical heterodyne detection in TEM01, we measure the position of coherently and incoherently emitting objects to within 0.0015 and 0.012 of the Rayleigh limit, respectively, and determine the distance between two incoherently emitting objects positioned within 0.28 of the Rayleigh limit with a precision of 0.019 of the Rayleigh limit. Heterodyne detection in multiple higher-order TEMs enables full imaging with a resolution significantly below the Rayleigh limit in a way that is reminiscent of quantum tomography of optical states.

Far-field linear optical superresolution via heterodyne detection in a higher-order local oscillator mode

We demonstrate that a photon echo can be implemented by all-optical means using an array of on-chip high-finesse ring cavities whose parameters are chirped in such a way as to support equidistant spectra of cavity modes. When launched into such a system, a classical or quantum optical signal—even a single-photon field—becomes distributed between individual cavities, giving rise to prominent coherence echo revivals at well-defined delay times, controlled by the chirp of cavity parameters. This effect enables long storage times for high-throughput broadband optical delay and quantum memory.

All-optical photon echo on a chip

A scheme of a multiqubit quantum computer on atomic ensembles using a quantum transistor implementing two qubit gates is proposed. We demonstrate how multiatomic ensembles permit one to work with a large number of qubits that are represented in a logical encoding in which each qubit is recorded on a superposition of single-particle states of two atomic ensembles. The access to qubits is implemented by appropriate phasing of quantum states of each of atomic ensembles. An atomic quantum transistor is proposed for use when executing two qubit operations. The quantum transistor effect appears when an excitation quantum is exchanged between two multiatomic ensembles located in two closely positioned QED cavities connected with each other by a gate atom. The dynamics of quantum transfer between atomic ensembles can be different depending on one of two states of the gate atom. Using the possibilities of control for of state of the gate atom, we show the possibility of quantum control for the state of atomic ensembles and, based on this, implementation of basic single and two qubit gates. Possible implementation schemes for a quantum computer on an atomic quantum transistor and their advantages in practical implementation are discussed.

A quantum computer in the scheme of an atomic quantum transistor with logical encoding of qubits

We have found a new hidden symmetry of time reversal light-atom interaction in the photon echo quantum memory with Raman atomic transition. The time-reversed quantum memory creates generalized conditions for ideal compression/decompression of time duration of the input light pulses and its wavelength. Based on a general analytical approach to this scheme, we have studied the optimal conditions for the light field compression/decompression in resonant atomic systems characterized by realistic spectral properties. 
The demonstrated necessary conditions for the effective quantum conversion of the light waveform and wavelength are also discussed for various possible realizations of the quantum memory scheme. The performed study promises new capabilities for fundamental study of the light-atom interaction and deterministic quantum manipulation of the light field, significant for quantum communication and quantum computing.

Scalable time reversal of Raman echo quantum memory and quantum waveform conversion of light pulse

The Rayleigh limit has so far applied to all microscopy techniques that rely on linear optical interaction and detection in the far field. Here we demonstrate that detecting the light emitted by an object in higher-order transverse electromagnetic modes (TEMs) can help achieving sub-Rayleigh precision for a variety of microscopy-related tasks. Using optical heterodyne detection in TEM01, we measure the position of coherently and incoherently emitting objects to within 0.0015 and 0.012 of the Rayleigh limit, respectively, and determine the distance between two incoherently emitting slits positioned within 0.28 of the Rayleigh limit with a precision of 0.019 of the Rayleigh limit. Extending our technique to higher-order TEMs enables full imaging with resolution significantly below the Rayleigh limit in a way that is reminiscent of quantum tomography of optical states.

E. S. Moiseev

Papers

Far-field linear optical superresolution via heterodyne detection in a higher-order local oscillator mode

All-optical photon echo on a chip

A quantum computer in the scheme of an atomic quantum transistor with logical encoding of qubits

Scalable time reversal of Raman echo quantum memory and quantum waveform conversion of light pulse

Far-field linear optical superresolution via heterodyne detection in a higher-order local oscillator mode