Astronomical interferometry is a cornerstone technique for high-resolution stellar imaging and observational astrophysics, extracting spatial information from the coherence of light collected by separated telescopes. Since the degree of coherence is complex, a genuine imaging task requires the joint recovery of the modulus and the relative phase, instead of independent singleparameter estimations. We investigate the simultaneous estimation of both parameters based on direct interferometry scheme and continuou-svariable quantum teleportation scheme. We find that in simultaneous estimation the direct interferometry scheme consistently yields a lower quantum Cramér-Rao bound, demonstrating its superiority over the continuous-variable quantum teleportation scheme. Furthermore, we establish the conditions under which the classical Cramér-Rao bound for Gaussian measurements saturates the quantum Cramér-Rao bound, identifying heterodyne detection as a near-optimal measurement scheme in the large mean photon number regime. An analysis of transmission loss reveals that the direct interferometry scheme yields superior precision in the short-baseline regime, whereas the continuous-variable quantum teleportation scheme outperforms it at longer baselines.
Astronomical interferometry is a cornerstone technique for high-resolution stellar imaging and observational astrophysics, extracting spatial information from the coherence of light collected by separated telescopes. Since the degree of coherence is complex, a genuine imaging task requires the joint recovery of the modulus and the relative phase, instead of independent singleparameter estimations. We investigate the simultaneous estimation of both parameters based on direct interferometry scheme and continuou-svariable quantum teleportation scheme. We find that in simultaneous estimation the direct interferometry scheme consistently yields a lower quantum Cramér-Rao bound, demonstrating its superiority over the continuous-variable quantum teleportation scheme. Furthermore, we establish the conditions under which the classical Cramér-Rao bound for Gaussian measurements saturates the quantum Cramér-Rao bound, identifying heterodyne detection as a near-optimal measurement scheme in the large mean photon number regime. An analysis of transmission loss reveals that the direct interferometry scheme yields superior precision in the short-baseline regime, whereas the continuous-variable quantum teleportation scheme outperforms it at longer baselines.
We propose a method to build an astronomical interferometer using continuous-variable quantum teleportation to overcome transmission loss between distant telescopes. The scheme relies on two-mode squeezed states shared by distant telescopes as entanglement resources, which are distributed using continuous-variable quantum repeaters. We find the optimal measurement on the teleported states, which uses beam splitters and photon-number-resolved detection. Compared to prior proposals relying on discrete states, our scheme has the advantages of using linear optics to implement it without wasting stellar photons, and making use of multiphoton events, which are regarded as noise in previous discrete schemes. We also outline the parameter regimes in which our scheme outperforms the direct detection method, schemes utilizing distributed discrete-variable entangled states, and local heterodyne techniques.
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
Interferometry with quantum light is known to provide enhanced precision for estimating a single phase. However, depending on the parameters involved, the quantum limit for the simultaneous estimation of multiple parameters may not be attainable, leading to tradeoffs in the attainable precisions. Here we study the simultaneous estimation of two parameters related to optical interferometry: phase and loss, using a fixed number of photons. We derive a tradeoff in the estimation of these two parameters which shows that, in contrast to single-parameter estimation, it is impossible to design a strategy saturating the quantum Cram\'er-Rao bound for loss and phase estimation in a single setup simultaneously. We design optimal quantum states with a fixed number of photons achieving the best possible simultaneous precisions. Our results reveal general features about concurrently estimating Hamiltonian and dissipative parameters and have implications for sophisticated sensing scenarios such as quantum imaging.
Interferometry with quantum light is known to provide enhanced precision for estimating a single phase. However, depending on the parameters involved, the quantum limit for the simultaneous estimation of multiple parameters may not attainable, leading to trade-offs in the attainable precisions. Here we study the simultaneous estimation of two parameters related to optical interferometry: phase and loss, using a fixed number of photons. We derive a trade-off in the estimation of these two parameters which shows that, in contrast to single-parameter estimation, it is impossible to design a strategy saturating the quantum Cramer-Rao bound for loss and phase estimation in a single setup simultaneously. We design optimal quantum states with a fixed number of photons achieving the best possible simultaneous precisions. Our results reveal general features about concurrently estimating Hamiltonian and dissipative parameters, and has implications for sophisticated sensing scenarios such as quantum imaging.
Estimating nonlinear phase shifts is useful to analyze many dynamical processes. In this work, with respect to the second-order nonlinear phase shifts, we propose an estimation scheme with a coherent state as the input and balanced homodyne detection as the readout strategy. The measurement setup is a nonlinear-linear hybrid interferometer composed of an optical parametric amplifier and a beam splitter. We analyze the precision and determine the optimal parameters of our scheme. The precision is compared with the quantum Cramér–Rao bound as well as the precision of a conventional nonlinear interferometer. In view of the fact that photon loss is ubiquitous, the effects of transmission loss and detection loss on the precision are addressed. At low gain, our scheme is superior to the scheme using a conventional nonlinear interferometer, and the precision can saturate the quantum Cramér–Rao bound.
We investigate the ultimate precision achievable in Gaussian quantum metrology. We derive general analytical expressions for the quantum Fisher information matrix and for the measurement compatibility condition, ensuring asymptotic saturability of the quantum Cram\'er-Rao bound, for the estimation of multiple parameters encoded in multimode Gaussian states. We then apply our results to the joint estimation of a phase shift and two parameters characterizing Gaussian phase covariant noise in optical interferometry. In such a scheme, we show that two-mode displaced squeezed input probes with optimally tuned squeezing and displacement fulfill the measurement compatibility condition and enable the simultaneous estimation of all three parameters, with an advantage over individual estimation schemes that quickly rises with increasing mean energy of the probes.