It has been shown that shared entanglement between two telescope sites can in principle be used to localize a point source by mimicking the standard phase-scanning interferometer, but without physically bringing the light from the distant telescopes together. In this paper, we show that a receiver that employs spatial-mode sorting at each telescope site, combined with pre-shared entanglement and local quantum operations can be used to mimic the most general multimode interferometer acting on light collected from the telescopes. As an example application to a quantitative passive-imaging problem, we show that the quantum-limited precision of estimating the angular separation between two stars can be attained by an instantiation of the aforesaid entanglement based receiver. We discuss how this entanglement assisted strategy can be used to achieve the quantum-limited precision of any complex quantitative imaging task involving any number of telescopes. We provide a blueprint of this general receiver that involves quantum transduction of starlight into quantum memory banks and spatial mode sorters deployed at each telescope site, and measurements that include optical detection as well as qubit gates and measurements on the quantum memories. We discuss the relative Fisher-information contributions of local mode sorting at telescope sites vis-a-vis distributed entanglement-assisted interferometry, to the overall quantum-limited information about the scene, based on the ratio of the baseline distance to the individual telescope diameter.
It has been shown that shared entanglement between two telescope sites can in principle be used to localize a point source by mimicking the standard phase-scanning interferometer, but without physically bringing the light from the distant telescopes together. In this paper, we show that a receiver that employs spatial-mode sorting at each telescope site, combined with pre-shared entanglement and local quantum operations can be used to mimic the most general multimode interferometer acting on light collected from the telescopes. As an example application to a quantitative passive-imaging problem, we show that the quantum-limited precision of estimating the angular separation between two stars can be attained by an instantiation of the aforesaid entanglement based receiver. We discuss how this entanglement assisted strategy can be used to achieve the quantum-limited precision of any complex quantitative imaging task involving any number of telescopes. We provide a blueprint of this general receiver that involves quantum transduction of starlight into quantum memory banks and spatial mode sorters deployed at each telescope site, and measurements that include optical detection as well as qubit gates and measurements on the quantum memories. We discuss the relative Fisher-information contributions of local mode sorting at telescope sites vis-a-vis distributed entanglement-assisted interferometry, to the overall quantum-limited information about the scene, based on the ratio of the baseline distance to the individual telescope diameter.
Long-baseline interferometry will be possible using preshared entanglement between two telescope sites to mimic the standard phase-scanning interferometer, but without physical beam combination. We show that spatial-mode sorting at each telescope, along with preshared entanglement, can be used to realize the most general multimode interferometry on light collected by any number of telescopes, enabling achieving quantitative-imaging performance at the ultimate limit pursuant to the baseline as afforded by quantum theory. We work out an explicit example involving two telescopes imaging two point sources.
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.
Telescope systems with distributed apertures are a well-established approach for boosting resolution in astronomical imaging. However, theoretical limits on quantitative imaging precision, and the fundamentally best possible mode-sorting, beam-combining, and detection schemes to use with such arrays, remain largely unexplored. Using mathematical tools of the quantum and classical Crámer-Rao bounds, we perform analyses showing the fundamental origins of the enhancement provided by distributed imaging systems, over and above a single monolithic telescope, and consider the precision with which one can estimate any desired parameter embedded in a scene's incoherent radiation with a multi-aperture imaging system. We show how quantum-optimal measurements can be realized via beam-combination strategies of two classes: (1) , where light from different apertures is directed to a common focal plane, e.g., of a segmented-aperture telescope; and (2) , where light collected at each aperture, e.g., telescope sites of a long-baseline array, is routed to an optical interferometer. As an example, we show an explicit calculation of the quantum Fisher information (QFI) for estimating the angular separation between two-point emitters using two identical apertures separated by a baseline distance. We show that this QFI splits instructively into additive contributions from the single apertures and from the baseline. We quantify the relative benefits of intratelescope (e.g., spatial-mode) optical processing and intertelescope beam combination. We show how both receiver designs can be used to capture both sources of information and discuss how similar methods could be extended to more general imaging tasks. We discuss translating QFI-attaining measurements to explicit receiver designs, and the use of preshared entanglement to achieve the QFI when it is impractical to colocate and combine light collected by the apertures. Published by the American Physical Society 2024
Conventional stellar interferometry reconstructs incoherent sources from pairwise mutual coherences between telescopes. Are such pairwise measurements sufficient for quantum-limited subdiffraction imaging with a telescope array? We show that for generic image-moment estimation, they are not. We consider weak incoherent light from a generic extended source observed by an array of telescopes, each supporting a single optical mode. For an N-telescope array, we derive the quantum Fisher information (QFI) scaling of image moments up to the cutoff 2N-2 and prove that arbitrary measurements restricted to telescope pairs attain the full-array QFI scaling only up to second order. Thus, estimating higher-order moments at the quantum limit requires genuinely multi-telescope interference. Inspired by spatial-mode demultiplexing (SPADE) from single-aperture subdiffraction imaging, we construct array-SPADE measurements that attain the optimal QFI scaling up to the finite-array cutoff. Finally, we show that these measurements can, in principle, be embedded in ancilla- and memory-assisted quantum-network architectures for long-baseline telescopy.
A quantum-enhanced telescope (interferometer) can have significant advantages in precisely measuring the angular position of remote objects through sending out ancillary quantum entanglement pairs alongside the large baselines of telescopes. In principle, the larger the baseline, the higher the expected measurement resolution. However, the well-known major problem of photon transmission loss would drastically undermine the practical application of all quantum-enhanced telescopes and optical interferometers that transmit photons along the baseline, especially for the large baselines required for high angular resolution. Here, we propose a photon-transmission-loss-independent quantum-enhanced interferometer that is robust to the transmission loss and keeps its advantages unchanged given whatever large baseline. This removes the well-known barrier to the practical application of quantum-enhanced telescopes. Moreover, in contrast to the previous results of quantum-entanglement-enhanced telescopes requesting sophisticated resources—perfect single-photon entanglement, photon-number-resolving detectors, or quantum memories—our method requires only threshold detectors and tunable coherent-state or two-mode squeezed-state sources, which are mature technologies nowadays, and it does not need any quantum memory. We demonstrate the high performance of our method using Fisher information. For the phase difference of weak light from a remote star, the high-quality result of Fisher information remains constant under arbitrarily large transmission loss, and hence all the advantageous results and the performance of our method are actually independent of transmission loss.
In this Letter, we show that by combining quantum metrology and networking tools, it is possible to extend the baseline of an interferometric optical telescope and thus improve diffraction-limited imaging of point source positions. The quantum interferometer is based on single-photon sources, linear optical circuits, and efficient photon number counters. Surprisingly, with thermal (stellar) sources of low photon number per mode and high transmission losses across the baseline, the detected photon probability distribution still retains a large amount of Fisher information about the source position, allowing for a significant improvement in the resolution of positioning point sources, on the order of 10 μas. Our proposal can be implemented with current technology. In particular, our proposal does not require experimental optical quantum memories.