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arXiv:1806.09881

Quantum process tomography with Heisenberg scaling based on Gaussian state and binary detection

Jiandong Zhang, Zijing Zhang, Longzhu Cen, Yuan Zhe Zhao

Published Jun 26, 2018• 0 citations
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Abstract

We propose a quantum process tomography scheme that utilizes two-mode squeezed vacuum to realize the parameter estimation with Heisenberg scaling. The objective is to estimate a rotating angle of polarization and parity detection is used as the detection strategy. With the help of symplectic matrix theory, we discuss the estimation visibility and sensitivity of output signal in lossless situation, the quantum Fisher information is also given via calculation. Finally, the impacts of two realistic factors on both visibility and sensitivity are also considered, including photon loss during the input generation, and photon loss along with thermal noise during the output detection.

DOI
10.48550/arxiv.1806.09881

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We propose a quantum process tomography scheme that utilizes two-mode squeezed vacuum to realize the parameter estimation with Heisenberg scaling. The objective is to estimate a rotating angle of polarization and parity detection is used as the detection strategy. With the help of symplectic matrix theory, we discuss the estimation visibility and sensitivity of output signal in lossless situation, the quantum Fisher information is also given via calculation. Finally, the impacts of two realistic factors on both visibility and sensitivity are also considered, including photon loss during the input generation, and photon loss along with thermal noise during the output detection.
Abstract Quantum phase estimation based on Gaussian states plays a crucial role in many application fields. In this paper, we study the precision bound for the scheme using two-mode squeezed Gaussian states. The quantum Fisher information is calculated and its maximization is used to determine the optimal parameters. We find that two single-mode squeezed vacuum states are the optimal Gaussian inputs for a fixed two-mode squeezing process. The corresponding precision bound is sub-Heisenberg-limited and scales as N −1/2. For practical purposes, we consider the effects originating from photon loss. The precision bound can still outperform the shot-noise limit when the lossy rate is below 0.4. Our work may demonstrate a significant and promising step towards practical quantum metrology.
It has been demonstrated that using two-mode squeezed vacuum state for phase estimation can break the Heisenberg limit. Our results reveal that the two-mode squeezed vacuum state is also applied to the optical rotation angle measurement. In our scheme, the resolution and sensitivity of the optical rotation angle signal are the same as the case of phase estimation. For the parameter estimation, phase or rotation angle, we discuss the influences of several imperfect factors on the resolution and sensitivity. First, the effect that the upper limit of photon-number resolving has on the maximum amount of available quantum Fisher information has been analyzed. Then, we have also studied the impacts of both the transmission efficiency in the transmission process and the detection efficiency on the detection results. Finally, conditions where all of the above imperfect elements are taken into account at the same time have also been explored. Additionally, other imperfect factors such as squeezing efficiency and dark counts are briefly discussed.
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We report on an orbital-angular-momentum-enhanced scheme for angular displacement estimation based on two-mode squeezed vacuum and parity detection. The sub-Heisenberg-limited sensitivity for angular displacement estimation is obtained in an ideal situation. Several realistic factors are also considered, including photon loss, dark counts, response-time delay, and thermal photon noise. Our results indicate that the effects of realistic factors on the sensitivity can be offset by raising orbital angular momentum quantum number ℓ. This implies that the robustness and the practicability of the system can be improved via raising ℓ without changing mean photon number N.
We investigate quantum advantages in loss sensing when the two-mode squeezed vacuum state is used as a probe. Following an experimental demonstration in PRX 4, 011049, we consider a quantum scheme in which the signal mode is passed through the target and a thermal noise is introduced to the idler mode before they are measured. We consider two detection strategies of practical relevance: coincidence-counting and intensity-difference measurement, which are widely used in quantum sensing and imaging experiments. By computing the signal-to-noise ratio, we verify that quantum advantages persist even under strong thermal background noise, in comparison with the classical scheme which uses a single-mode coherent state that directly suffers from the thermal noise. Such robustness comes from the fact that the signal mode suffers from the thermal noise in the classical scheme, while in the quantum scheme, the idler mode does. For a fairer comparison, we further investigate a different setup in which the thermal noise is introduced to the signal mode in the quantum schemes. In this new setup, we show that the quantum advantages are significantly reduced. Remarkably, however, under an optimum measurement scheme associated with the quantum Fisher information, we show that the two-mode squeezed vacuum state does exhibit a quantum advantage over the entire range of the environmental noise and loss. We expect this work to serve as a guide for experimental demonstrations of quantum advantages in loss parameter sensing, which is subject to lossy and noisy environment.