There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

Quantum theory: Concepts and methods

心臓病診療プラクティス 16. 心不全を癒す

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.

/pdf/advances-in-photonic-quantum-sensing-14r9l01qa3.pdf

Advances in photonic quantum sensing

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.

/pdf/advances-in-photonic-quantum-sensing-wdwvgrc1if.pdf

Advances in Photonic Quantum Sensing

The Rayleigh criterion specifies the minimum separation between two incoherent point sources that may be resolved into distinct objects. We revisit this problem by examining the Fisher information required for resolving the two sources. The resulting Cramer–Rao bound gives the minimum error achievable for any unbiased estimator. When only the intensity in the image plane is recorded, this bound diverges as the separation between the sources tends to zero, an effect that has been dubbed the Rayleigh curse. Nonetheless, this curse can be lifted with suitable measurements. Here, we work out optimal strategies and present a realization for Gaussian and slit apertures, which is accomplished with digital holographic techniques. Our results confirm immunity to the Rayleigh curse and an unprecedented experimental precision.

Achieving the ultimate optical resolution

We establish the multiparameter quantum Cram\'er-Rao bound for simultaneously estimating the centroid, the separation, and the relative intensities of two incoherent optical point sources using a linear imaging system. For equally bright sources, the Cram\'er-Rao bound is independent of their separation, which confirms that the Rayleigh resolution limit is just an artifact of the conventional direct imaging and can be overcome with an adequate strategy. For the general case of unequally bright sources, the amount of information one can gain about the separation falls to zero, but we show that there is always a quadratic improvement in an optimal detection in comparison with the intensity measurements. This advantage can be of utmost importance in realistic scenarios, such as observational astronomy.

Multiparameter quantum metrology of incoherent point sources: Towards realistic superresolution

We establish the conditions to attain the ultimate resolution predicted by quantum estimation theory for the case of two incoherent point sources using a linear imaging system. The solution is closely related to the spatial symmetries of the detection scheme. In particular, for real symmetric point spread functions, any complete set of projections with definite parity achieves the goal.

Optimal measurements for resolution beyond the Rayleigh limit

By projecting onto complex optical mode profiles, it is possible to estimate arbitrarily small separations between objects with quantum-limited precision, free of uncertainty arising from overlapping intensity profiles. Here we extend these techniques to the time-frequency domain using mode-selective sum-frequency generation with shaped ultrafast pulses. We experimentally resolve temporal and spectral separations between incoherent mixtures of single-photon level signals ten times smaller than their optical bandwidths with a tenfold improvement in precision over the intensity-only Cramer-Rao bound.

Quantum-Limited Time-Frequency Estimation through Mode-Selective Photon Measurement.

It has been argued that, for a spatially invariant imaging system, the information one can gain about the separation of two incoherent point sources decays quadratically to zero with decreasing separation The effect is termed Rayleigh’s curse Contrary to this belief, we identify a class of point-spread functions (PSFs) with a linear information decrease Moreover, we show that any well-behaved symmetric PSF can be converted into such a form with a simple nonabsorbing signum filter We experimentally demonstrate significant superresolution capabilities based on this idea

Martin Paúr

Papers

Achieving the ultimate optical resolution

Multiparameter quantum metrology of incoherent point sources: Towards realistic superresolution

Optimal measurements for resolution beyond the Rayleigh limit

Quantum-Limited Time-Frequency Estimation through Mode-Selective Photon Measurement.

Tempering Rayleigh's curse with PSF shaping