Using the framework of quantum multiparameter estimation, we study the problem of separating independent thermal optical sources mixed by an unknown passive linear transformation, which is known as blind source separation in signal processing. We propose a sensing-assisted method that iteratively estimates and suppresses optical correlations directly within the unit cells of a programmable interferometer. We show that collective quantum measurements exhibit a substantial advantage over conventional detection methods by constructing collective measurements that asymptotically achieve the Holevo Cramér--Rao bound in a unit cell of the interferometer for the respective sub-problem. By systematically arranging multiple such cells in a photonic mesh, our proposal implements an in situ Jacobi diagonalization of the input multimode correlation matrix. We contrast our method with a conventional approach where heterodyne detection is used to reconstruct the full covariance matrix and subsequently diagonalize it on a classical computer. A comparison with this heterodyne tomography approach shows that our sensing-based method is particularly advantageous in the weak-light regime.
Using the framework of quantum multiparameter estimation, we study the problem of separating independent thermal optical sources mixed by an unknown passive linear transformation, which is known as blind source separation in signal processing. We propose a sensing-assisted method that iteratively estimates and suppresses optical correlations directly within the unit cells of a programmable interferometer. We show that collective quantum measurements exhibit a substantial advantage over conventional detection methods by constructing collective measurements that asymptotically achieve the Holevo Cramér--Rao bound in a unit cell of the interferometer for the respective sub-problem. By systematically arranging multiple such cells in a photonic mesh, our proposal implements an in situ Jacobi diagonalization of the input multimode correlation matrix. We contrast our method with a conventional approach where heterodyne detection is used to reconstruct the full covariance matrix and subsequently diagonalize it on a classical computer. A comparison with this heterodyne tomography approach shows that our sensing-based method is particularly advantageous in the weak-light regime.
For more than a century, the diffraction limit has defined the resolution achievable by passive optical imaging systems. Although some resolution improvement can be gained through classical data processing of the image, it is limited by the noise arising from quantum nature of light. Minimizing the effect of this noise requires quantum treatment of optical imaging. By reformulating imaging as a problem of quantum measurement and estimation, it becomes possible to identify optimal detection strategies that recover spatial information previously thought inaccessible. This review summarizes the theoretical framework that underpins this development, from the formulation of quantum Cramer-Rao bounds and Chernoff bounds to the construction of receivers that attain them, such as those based on spatial-mode demultiplexing. We show how these methods can beat conventional imaging in the classification, localization, and imaging of sub-Rayleigh incoherent sources. We then discuss extensions to multiparameter and partially coherent scenarios, and highlight the unifying connections between estimation and discrimination tasks. Finally, we survey recent experimental demonstrations that approach quantum-limited resolution and outline emerging applications in microscopy, astronomy, and optical sensing.
Quantum superresolution promises to resolve closely spaced sources beyond the diffraction limit, but existing approaches generally rely on idealized source properties or require simultaneous estimation of multiple coupled parameters of realistic sources. Here we introduce a parameter-decoupled measurement that determines the separation of realistic passive sources without estimating their unknown brightness imbalance, mutual coherence, or relative phase. A complete four-parameter quantum Fisher information analysis identifies the separation information that remains accessible in the presence of these nuisance parameters. We then construct a directly measurable log-probability invariant from projection channels whose conditional statistics depend only on the separation. Broad classes of channel pairs satisfy the resulting decoupling condition. For a Gaussian point-spread function, the lowest-order implementation asymptotically attains the four-parameter quantum limit per incident signal in the sub-Rayleigh regime. This approach converts a realistic multiparameter imaging problem into an operationally single-parameter measurement, providing a practical route toward quantum-enhanced resolution of passive spatial, temporal, and spectral signals.
In astronomy, interferometry of light collected by separate telescopes is often performed by physically bringing the optical paths together in the form of Young's double-slit experiment. Optical loss severely limits the efficiency of this so-called direct detection method, motivating the fundamental question of whether one can achieve a comparable performance using separate optical measurements at the two telescopes before combining the measurement results. Using quantum mechanics and estimation theory, here I show that any such spatially local measurement scheme, such as heterodyne detection, is fundamentally inferior to coherently nonlocal measurements, such as direct detection, for estimating the mutual coherence of bipartite thermal light when the average photon flux is low. This surprising result reveals an overlooked signature of quantum nonlocality in a classic optics experiment.
Entanglement-assisted optical interferometry promises diffraction-limited imaging over baselines where light cannot be physically combined, but existing theory treats only a single visibility on one two-station baseline. This work formulates the multiparameter estimation problem for an M-station array imaging an extended scene. A reduction lemma shows that the multimode quantum Fisher information (QFI) equals the mean photon number times the QFI of a single delocalized photon, collapsing the problem to a finite-dimensional one. The local photon-number superselection rule (SSR) erases all phase information from the bare state, while shared entanglement restores a fraction f(r)=r/(1+r) of the QFI on a baseline supplied with r pairs -- a factor shown to be achievable, since the reduced two-mode state of any pair is exactly the two-station weak-thermal state. The QFI matrix and its mean Uhlmann curvature reveal numerically that a point source is measurement-compatible, whereas for every extended-source model examined it is incompatible, the Holevo bound exceeding the symmetric-logarithmic-derivative (SLD) bound by up to ~74%. An explicit collective receiver -- a global mode-sorting (quantum Fourier transform) measurement -- then attains a weighted variance within ~7% of the SLD bound and roughly an order of magnitude below an explicit pairwise receiver, and a noisy-resource advantage threshold gives the break-even baseline (~20 km for near-term parameters) beyond which repeater-distributed entanglement beats direct transmission. Finally, the optimal allocation of a finite entanglement budget is a convex program with a closed-form proportional (square-root-law) solution favoring low-visibility baselines. These results recast quantum aperture synthesis as collective multiparameter estimation and give concrete design targets, illustrated on the CHARA array.
Superresolution refers to the estimation of parameters of an image with an accuracy beyond standard classical techniques such as direct detection. In seminal work by Lu et al., a measurement to estimate the separation distance of two point sources (with a known centroid) was shown to achieve the quantum Cramer-Rao bound. This work made implicit use of reflection symmetry of the sources. Here we present a framework that uses more general symmetry in a constellation to construct a quantum measurement that achieves the quantum Cramer-Rao bound in estimation of parameters. We show how this technique can be used to estimate parameters simultaneously in symmetric point-source constellations with more than two point sources. In order to use symmetry explicitly, we make use discrete point spread functions in momentum space that maintain this symmetry. This framework allows us to use techniques from quantum computing such as Fourier transforms and linear optical circuits to implement the optimal measurement. To our knowledge, this is first work that shows for more than two point sources achievable quantum limits of estimation and modal transformations.
Classical, i.e. non-quantum, blind source separation (BSS) methods estimate unknown source signals by using only mixed signals obtained by transferring these source signals through a mixing transform, which typically has unknown parameter values. We developed quantum versions of BSS (called BQSS) and we extended them to the blind estimation of the unknown mixing/coupling parameters, thus achieving blind quantum process tomography (BQPT). In these investigations, the mixing parameter values remained fixed over time. We here analyze configurations where they vary. We show that the operation of our previous system may then be extended to handle BQPT and simple BQSS configurations. BQSS with rapidly evolving mixtures is more complex, because the fundamental quantum no-cloning theorem entails that each quantum state available at the output of our separating system cannot be copied so as to be used as the inputs of both (i) the subsequent quantum system which exploits it and (ii) the block of our separating system which continuously uses these states to update the separating system parameter values. We avoid this issue by introducing a quite different BQSS system, which is based on a master-slave structure and performs parallel adaptation and source state restoration. The proposed approach is thus based on spin electronics for implementing the considered quantum states, and on an original control loop in the proposed master-slave structure, which requires a specific measurement procedure, due to the quantum nature of the signals to be processed. This paper therefore bridges the gap between advanced information processing functions (especially self-learning algorithms) and the physical devices, defined at the atomic level, required for implementing such computations.