arXiv subjects

Mankei Tsang

Publications and source records attributed to Mankei Tsang.

At least 37 records · Page 2Linked to original sources

arXiv2020

Quantum Semiparametric Estimation

In the study of quantum limits to parameter estimation, the high dimensionality of the density operator and that of the unknown parameters have long been two of the most difficult challenges. Here we propose a theory of quantum semiparametric estimation that can circumvent both challenges and produce simple analytic bounds for a class of problems in which the dimensions are arbitrarily high, few prior assumptions about the density operator are made, but only a finite number of the unknown parameters are of interest. We also relate our bounds to Holevo's version of the quantum Cramér-Rao bound, so that they can inherit the asymptotic attainability of the latter in many cases of interest. The theory is especially relevant to the estimation of a parameter that can be expressed as a function of the density operator, such as the expectation value of an observable, the fidelity to a pure state, the purity, or the von Neumann entropy. Potential applications include quantum state characterization for many-body systems, optical imaging, and interferometry, where full tomography of the quantum state is often infeasible and only a few select properties of the system are of interest.

quant-ph↗

arXiv2020

Resolving starlight: a quantum perspective

The wave-particle duality of light introduces two fundamental problems to imaging, namely, the diffraction limit and the photon shot noise. Quantum information theory can tackle them both in one holistic formalism: model the light as a quantum object, consider any quantum measurement, and pick the one that gives the best statistics. While Helstrom pioneered the theory half a century ago and first applied it to incoherent imaging, it was not until recently that the approach offered a genuine surprise on the age-old topic by predicting a new class of superior imaging methods. For the resolution of two sub-Rayleigh sources, the new methods have been shown theoretically and experimentally to outperform direct imaging and approach the true quantum limits. Recent efforts to generalize the theory for an arbitrary number of sources suggest that, despite the existence of harsh quantum limits, the quantum-inspired methods can still offer significant improvements over direct imaging for subdiffraction objects, potentially benefiting many applications in astronomy as well as fluorescence microscopy.

quant-ph↗

arXiv2019

Semiparametric estimation for incoherent optical imaging

The theory of semiparametric estimation offers an elegant way of computing the Cramér-Rao bound for a parameter of interest in the midst of infinitely many nuisance parameters. Here I apply the theory to the problem of moment estimation for incoherent imaging under the effects of diffraction and photon shot noise. Using a Hilbert-space formalism designed for Poisson processes, I derive exact semiparametric Cramér-Rao bounds and efficient estimators for both direct imaging and a quantum-inspired measurement method called spatial-mode demultiplexing (SPADE). The results establish the superiority of SPADE even when little prior information about the object is available.

eess.IV↗

arXiv2019

Quantum limit to subdiffraction incoherent optical imaging

The application of quantum estimation theory to the problem of imaging two incoherent point sources has recently led to new insights and better measurements for incoherent imaging and spectroscopy. To establish a more general limit beyond the case of two sources, here I evaluate a quantum bound on the Fisher information that can be extracted by any far-field optical measurement about the moments of a subdiffraction object. The bound matches the performance of a spatial-mode-demultiplexing (SPADE) measurement scheme in terms of its scaling with the object size, indicating that SPADE is close to quantum-optimal. Coincidentally, the result is also applicable to the estimation of diffusion parameters with a quantum probe subject to random displacements.

quant-ph↗

arXiv2018

Comment on "Resurgence of Rayleigh's curse in the presence of partial coherence"

Larson and Saleh [Optica 5, 1382 (2018)] suggest that Rayeleigh's curse can recur and become unavoidable if the two sources are partially coherent. Here we show that their calculations and assertions have fundamental problems, and spatial-mode demultiplexing (SPADE) can overcome Rayleigh's curse even for partially coherent sources.

quant-ph↗

arXiv2018

Subdiffraction incoherent optical imaging via spatial-mode demultiplexing: semiclassical treatment

I present a semiclassical analysis of a spatial-mode demultiplexing (SPADE) measurement scheme for far-field incoherent optical imaging under the effects of diffraction and photon shot noise. Building on previous results that assume two point sources or the Gaussian point-spread function, I generalize SPADE for a larger class of point-spread functions and evaluate its errors in estimating the moments of an arbitrary subdiffraction object. Compared with the limits to direct imaging set by the Cramér-Rao bounds, the results show that SPADE can offer far superior accuracy in estimating the second and higher-order moments.

physics.optics↗

arXiv2017

Quantum limits on the time-bandwidth product of an optical resonator

A thought-provoking proposal by Tsakmakidis et al. [Science 356, 1260 (2017)] suggests that nonreciprocal optics can break a time-bandwidth limit to passive resonators. Here I quantize their resonator model and show that quantum mechanics does impose a limit, or requires extra noise to be added in the same fashion as amplified spontaneous emission in an active resonator. I also use thermodynamics to argue that extra dissipation or noise must be present in their proposed device.

quant-ph↗

arXiv2017

Fisher information for far-field linear optical superresolution via homodyne or heterodyne detection in a higher-order local oscillator mode

The distance between two point light sources is difficult to estimate if that distance is below the diffraction (Rayleigh's) resolution limit of the imaging device. A recently proposed technique enhances the precision of this estimation by exploiting the source-separation-dependent coupling of light into higher-order $\rm{TEM}$ modes, particularly the $\rm{TEM}_{01}$ mode of the image. We theoretically analyze the estimation of the source separation by means of homodyne or heterodyne detection with a local oscillator in the $\rm{TEM}_{01}$ mode, which is maximally sensitive to the separation in the sub-Rayleigh regime. We calculate the per-photon Fisher information associated with this estimation and compare it with direct imaging. For thermal sources, the per-photon Fisher information depends on the average photon number per thermal mode of the image; it surpasses the Fisher information for direct imaging (in the interesting sub-Rayleigh regime) when the average photon number exceeds two for homodyne detection and four for heterodyne detection.

physics.optics↗

arXiv2017

Quantum limit for two-dimensional resolution of two incoherent optical point sources

We obtain the multiple-parameter quantum Cramér-Rao bound for estimating the transverse Cartesian components of the centroid and separation of two incoherent optical point sources using an imaging system with finite spatial bandwidth. Under quite general and realistic assumptions on the point-spread function of the imaging system, and for weak source strengths, we show that the Cramér-Rao bounds for the $x$ and $y$ components of the separation are independent of the values of those components, which may be well below the conventional Rayleigh resolution limit. We also propose two linear optics-based measurement methods that approach the quantum bound for the estimation of the Cartesian components of the separation once the centroid has been located. One of the methods is an interferometric scheme that approaches the quantum bound for sub-Rayleigh separations. The other method using fiber coupling can in principle attain the bound regardless of the distance between the two sources.

quant-ph↗

arXiv2017

Conservative classical and quantum resolution limits for incoherent imaging

I propose classical and quantum limits to the statistical resolution of two incoherent optical point sources from the perspective of minimax parameter estimation. Unlike earlier results based on the Cramér-Rao bound, the limits proposed here, based on the worst-case error criterion and a Bayesian version of the Cramér-Rao bound, are valid for any biased or unbiased estimator and obey photon-number scalings that are consistent with the behaviors of actual estimators. These results prove that, from the minimax perspective, the spatial-mode demultiplexing (SPADE) measurement scheme recently proposed by Tsang, Nair, and Lu [Phys. Rev. X 6, 031033 (2016)] remains superior to direct imaging for sufficiently high photon numbers.

quant-ph↗

arXiv2017

Subdiffraction incoherent optical imaging via spatial-mode demultiplexing

I propose a spatial-mode demultiplexing (SPADE) measurement scheme for the far-field imaging of spatially incoherent optical sources. For any object too small to be resolved by direct imaging under the diffraction limit, I show that SPADE can estimate its second or higher moments much more precisely than direct imaging can fundamentally do in the presence of photon shot noise. I also prove that SPADE can approach the optimal precision allowed by quantum mechanics in estimating the location and scale parameters of a subdiffraction object. Realizable with far-field linear optics and photon counting, SPADE is expected to find applications in both fluorescence microscopy and astronomy.

physics.optics↗

arXiv2016

Far-field Superresolution of Thermal Electromagnetic Sources at the Quantum Limit

We obtain the ultimate quantum limit for estimating the transverse separation of two thermal point sources using a given imaging system with limited spatial bandwidth. We show via the quantum Cramér-Rao bound that, contrary to the Rayleigh limit in conventional direct imaging, quantum mechanics does notmandate any loss of precision in estimating even deep sub-Rayleigh separations. We propose two coherent measurement techniques, easily implementable using current linear-optics technology, that approach the quantum limit over an arbitrarily large range of separations. Our bound is valid for arbitrary source strengths, all regions of the electromagnetic spectrum, and for any imaging system with an inversion-symmetric point-spread function. The measurement schemes can be applied to microscopy, optical sensing, and astrometry at all wavelengths.

quant-ph↗

arXiv2016

Semiclassical Theory of Superresolution for Two Incoherent Optical Point Sources

Using a semiclassical model of photodetection with Poissonian noise and insights from quantum metrology, we prove that linear optics and photon counting can optimally estimate the separation between two incoherent point sources without regard to Rayleigh's criterion. The model is applicable to weak thermal or fluorescent sources as well as lasers.

quant-ph↗

arXiv2016

Quantum-optimal detection of one-versus-two incoherent sources with arbitrary separation

We analyze the fundamental resolution of incoherent optical point sources from the perspective of a quantum detection problem: deciding whether the optical field on the image plane is generated by one source or two weaker sources with arbitrary separation. We investigate the detection performances of two measurement methods recently proposed by us to enhance the estimation of the separation. For the detection problem, we show that the method of binary spatial-mode demultiplexing is quantum-optimal for all values of separations, while the method of image-inversion interferometry is near-optimal for sub-Rayleigh separations. Unlike the proposal by Helstrom, our schemes do not require the separation to be given and can offer that information as a bonus in the event of a successful detection. For comparison, we also demonstrate the supremacy of our schemes over direct imaging for sub-Rayleigh separations. These results demonstrate that simple linear optical measurements can offer supremal performances for both detection and estimation.

quant-ph↗

arXiv2016

Quantum Theory of Superresolution for Two Incoherent Optical Point Sources

Rayleigh's criterion for resolving two incoherent point sources has been the most influential measure of optical imaging resolution for over a century. In the context of statistical image processing, violation of the criterion is especially detrimental to the estimation of the separation between the sources, and modern farfield superresolution techniques rely on suppressing the emission of close sources to enhance the localization precision. Using quantum optics, quantum metrology, and statistical analysis, here we show that, even if two close incoherent sources emit simultaneously, measurements with linear optics and photon counting can estimate their separation from the far field almost as precisely as conventional methods do for isolated sources, rendering Rayleigh's criterion irrelevant to the problem. Our results demonstrate that superresolution can be achieved not only for fluorophores but also for stars.

quant-ph↗

arXiv2016

Quantum Weiss-Weinstein bounds for quantum metrology

Sensing and imaging are among the most important applications of quantum information science. To investigate their fundamental limits and the possibility of quantum enhancements, researchers have for decades relied on the quantum Cramér-Rao lower error bounds pioneered by Helstrom. Recent work, however, has called into question the tightness of those bounds for highly nonclassical states in the non-asymptotic regime, and better methods are now needed to assess the attainable quantum limits in reality. Here we propose a new class of quantum bounds called quantum Weiss-Weinstein bounds, which include Cramér-Rao-type inequalities as special cases but can also be significantly tighter to the attainable error. We demonstrate the superiority of our bounds through the derivation of a Heisenberg limit and phase-estimation examples.

quant-ph↗

arXiv2016

Spectrum analysis with quantum dynamical systems

Measuring the power spectral density of a stochastic process, such as a stochastic force or magnetic field, is a fundamental task in many sensing applications. Quantum noise is becoming a major limiting factor to such a task in future technology, especially in optomechanics for temperature, stochastic gravitational wave, and decoherence measurements. Motivated by this concern, here we prove a measurement-independent quantum limit to the accuracy of estimating the spectrum parameters of a classical stochastic process coupled to a quantum dynamical system. We demonstrate our results by analyzing the data from a continuous optical phase estimation experiment and showing that the experimental performance with homodyne detection is close to the quantum limit. We further propose a spectral photon counting method that can attain quantum-optimal performance for weak modulation and a coherent-state input, with an error scaling superior to that of homodyne detection at low signal-to-noise ratios.

quant-ph↗

arXiv2016

Multiparameter Heisenberg limit

Using a quantum version of the Bell-Ziv-Zakai bound, I derive a Heisenberg limit to multiparameter estimation for any Gaussian prior probability density. The mean-square error lower bound is shown to have a universal quadratic scaling with respect to a quantum resource, such as the average photon number in the case of optical phase estimation, suitably weighted by the prior covariance matrix.

quant-ph↗