arXiv:2405.07049 · Journal of the Optical Society of America B

Using non-Gaussian quantum states for detection of a given phase shift

Valentin L. Gorshenin, Farid Ya Khalili

Published May 16, 2025• 2 citations

Abstract

It is known that non-Gaussian and only non-Gaussian quantum states can be orthogonal to other quantum states. We show here that, due to this feature, using the non-Gaussian (Fock or Schrödinger cat) states of the probing light, it is possible to detect a given phase shift in optical interferometers with vanishing error probability. Squeezing of the probing non-Gaussian quantum state at the input of the interferometer and the proportional anti-squeezing at the output state allow for the improvement of the sensitivity proportionally to the squeeze factor. The optical losses, most notably the non-ideal quantum efficiency of the photodetection, degrade the sensitivity, introducing finite “false positive” and “false negative” detection errors. However, using state-of-the-art photon-number-resolving detectors, it is still possible to obtain smaller detection error probabilities than in the case of Gaussian quantum states.

DOI: 10.1364/josab.561267

Related papers

High-fidelity detection of a phase shift using non-Gaussian quantum states of light

F. Y. Khalili

We show that by injecting a light pulse prepared in a non-Gaussian quantum state into the dark port of a two-arm interferometer, it is possible to detect a given phase shift with the fidelity which is limited only by the optical losses and the photodetection inefficiency. The value of the phase shift is inversely proportional to the amplitude of the classical carrier light injected into another (bright) port of the interferometer. It can be reduced by using an additional degenerate parametric amplifier (squeezer) in the input dark port and the matching anti-squeezer in the output dark port. We show that using the modern high-efficiency photon number resolving detectors, it is possible to reduce the detection error by almost one order of magnitude in comparison with the ordinary (Gaussian-state) interferometry.

arXiv:1812.03727Dec 10, 20180 citations

Using anti-squeezed Schrödinger cat states for detection of a given phase shift

V. L. Gorshenin, K. D. Dyadkin, S. D. Chikalkin

We propose to use the antisqueezing-enhanced non-Gaussian Schrödinger cat quantum states of the probing light for the task of detection of a given phase shift in optical interferometers. We show that the antisqueezing allows to increase the robustness of the setup to optical losses. We find the optimal degrees of the antisqueezing for experimentally achievable values of the Schrödinger cat amplitude and the optical losses and compare the resulting sensitivity with the one provided by the Gaussian squeezed states.

quant-pharXiv:2603.02038Mar 3, 20260 citations

Using Schrödinger cat quantum state for detection of a given phase shift

Valentin L. Gorshenin

Abstract We show that injecting a light pulse prepared in the Shrödinger cat quantum state into the dark port of a two-arm interferometer, it is possible to detect a given phase shift unambiguously. The value of this phase shift is inversely proportional to the amplitudes of both the classical carrier light and the Shrödinger cat state. However, an unconventional detection procedure is required for this purpose. By measuring the number of photons at the output dark port, it is possible to detect the phase shift with a vanishing ‘false positive’ probability. The ‘false negative’ probability in this case decreases as the amplitude of the Schrödinger cat state increases and, for reasonable values of this amplitude, can be made less than about 0.1.

arXiv:2403.03787Laser Physics LettersApr 16, 20247 citations

Fock state interferometry for quantum enhanced phase discrimination

Reihaneh Shahrokhshahi, Saikat Guha, Olivier Pfister

We study Fock state interferometry, consisting of a Mach-Zehnder Interferometer with two Fock state inputs and photon-number-resolved detection at the two outputs. We show that it allows discrimination of a discrete number of apriori-known optical phase shifts with an error probability lower than what is feasible with classical techniques under a mean photon number constraint. We compare its performance with the optimal quantum probe for M-ary phase discrimination, which unlike our probe, is difficult to prepare. Our technique further allows discriminating a null phase shift from an increasingly small one at zero probability of error under ideal conditions, a feature impossible to attain using classical probe light. Finally, we describe one application to quantum reading with binary phase-encoded memory pixels.

arXiv:2102.05772Feb 10, 20210 citations

Optical enhanced interferometry with two-mode squeezed twin-Fock states and parity detection*

Li-Li Hou, Shuai Wang, Xuefen Xu

We theoretically investigate the quantum enhanced metrology using two-mode squeezed twin-Fock states and parity detection. Our results indicate that, for a given initial squeezing parameter, compared with the two-mode squeezed vacuum state, both phase sensitivity and resolution can be enhanced when the two-mode squeezed twin-Fock state is considered as an input state of a Mach–Zehnder interferometer. Within a constraint on the total photon number, although the two-mode squeezed vacuum state gives the better phase sensitivity when the phase shift φ to be estimated approaches to zero, the phase sensitivity offered by these non-Gaussian entangled Gaussian states is relatively stable with respect to the phase shift itself. When the phase shift slightly deviates from φ = 0, the phase sensitivity can be still enhanced by the two-mode squeezed twin-Fock state over a broad range of the total mean photon number where the phase uncertainty is still below the quantum standard noise limit. Finally, we numerically prove that the quantum Cramér–Rao bound can be approached with the parity detection.

Chinese Physics BJan 7, 202011 citations

Gaussian-state interferometry with passive and active elements

Carlo Sparaciari, Stefano Olivares, Matteo G. A. Paris

We address the precision of optical interferometers fed by quantum and semiclassical Gaussian states involving passive and/or active elements, such as beam splitters, photodetectors, and optical parametric amplifiers. We first address the ultimate bounds to precision by discussing the behavior of the quantum Fisher information. We then consider photodetection at the output and calculate the sensitivity of the interferometers taking into account the nonunit quantum efficiency of the detectors. Our results show that in the ideal case of photon number detectors with unit quantum efficiency the best configuration is the symmetric one, namely, a passive (active) interferometer with a passive (active) detection stage: in this case one may achieve Heisenberg scaling of sensitivity by suitably optimizing over Gaussian states at the input. On the other hand, in the realistic case of detectors with nonunit quantum efficiency, the performances of the passive scheme are unavoidably degraded, whereas detectors involving optical parametric amplifiers allow us to fully compensate for the presence of loss in the detection stage, thus restoring the Heisenberg scaling.

arXiv:1510.07716Physical Review AFeb 5, 201697 citations