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arXiv:2108.01170 · Physical Review A

Optimal qubit circuits for quantum-enhanced telescopes

Robert Czupryniak, John Steinmetz, Paul G. Kwiat, Andrew N. Jordan

Published Nov 8, 2023• 14 citations
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Abstract

The authors propose two optimal phase-estimation schemes that can be used for quantum-enhanced long-baseline interferometry where distributed entanglement eliminates the loss of stellar photons during transmission over the baselines. The schemes can lead to a reduction of both the number of ancilla qubits and the number of gate operations by a factor of two.

DOI
10.1103/physreva.108.052408

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The authors propose two optimal phase-estimation schemes that can be used for quantum-enhanced long-baseline interferometry where distributed entanglement eliminates the loss of stellar photons during transmission over the baselines. The schemes can lead to a reduction of both the number of ancilla qubits and the number of gate operations by a factor of two.
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Long baseline optical interferometry, by combining the lights from widely-distributed telescopes, is shown to afford pronounced improvement in the imaging resolution in comparison with a single telescope. However, the noise and photon loss in the transmission between the telescopes would limit the length of baseline of interferometer to a few hundred meters. Here, we present a scheme for enhancement of long baseline optical interferometer by using quantum resources- noiseless linear amplifier (NLA) and displacement operation at the photon transmission channels. We exhibit this enhancement quantitatively by calculating higher fisher information compared with those of conventional optical interferometer.
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We give a detailed discussion of optimal quantum states for optical two-mode interferometry in the presence of photon losses. We derive analytical formulae for the precision of phase estimation obtainable using quantum states of light with a definite photon number and prove that maximization of the precision is a convex optimization problem. The corresponding optimal precision, i.e., the lowest possible uncertainty, is shown to beat the standard quantum limit thus outperforming classical interferometry. Furthermore, we discuss more general inputs: states with indefinite photon number and states with photons distributed between distinguishable time bins. We prove that neither of these is helpful in improving phase estimation precision.
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.