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arXiv:1809.10706 · Physical Review A

Single-phase and correlated-phase estimation with multiphoton annihilated squeezed vacuum states: An energy-balancing scenario

N. Samantaray, Ivano Ruo Berchera, Ivo Pietro Degiovanni

Published Jun 4, 2020• 5 citations
arXivHTMLPDF

Abstract

In recent years, several works have demonstrated the advantage of photon-subtracted Gaussian states for various quantum optics and information protocols. In most of these works, the relation between the advantages and the usual increasing energy of the quantum state related to photon subtraction was not clearly investigated. In this paper, we study the performance of an interferometer injected with multiphoton-annihilated squeezed vacuum states mixed with coherent states for both single- and correlated-phase estimations. For single-phase estimation, although the use of multiphoton-annihilated squeezed vacuum states at low mean photons per mode provides an advantage compared to classical strategy, when the total input energy is held fixed, the advantage due to photon subtraction is completely lost. However, for the correlated case in the analogous scenario, some advantage appears to come from both the energy rise and improvement in photon statistics. In particular quantum enhanced sensitivity with photon-subtracted states appears more robust to losses, showing an advantage of about $30%$ with respect to the squeezed vacuum state in the case of a realistic value of the detection efficiency.

DOI
10.1103/physreva.101.063810

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In recent years, several works have demonstrated the advantage of photon-subtracted Gaussian states for various quantum optics and information protocols. In most of these works, the relation between the advantages and the usual increasing energy of the quantum state related to photon subtraction was not clearly investigated. In this paper, we study the performance of an interferometer injected with multiphoton-annihilated squeezed vacuum states mixed with coherent states for both single- and correlated-phase estimations. For single-phase estimation, although the use of multiphoton-annihilated squeezed vacuum states at low mean photons per mode provides an advantage compared to classical strategy, when the total input energy is held fixed, the advantage due to photon subtraction is completely lost. However, for the correlated case in the analogous scenario, some advantage appears to come from both the energy rise and improvement in photon statistics. In particular quantum enhanced sensitivity with photon-subtracted states appears more robust to losses, showing an advantage of about 3030%30 with respect to the squeezed vacuum state in the case of a realistic value of the detection efficiency.
We present the case of a Gottesman-Kitaev-Preskill (GKP) state-enhanced optical interferometry with detailed analysis of the phase sensitivity for both the SU(2) and SU(1,1) interferometers. The conventional quantum-enhanced SU(2) interferometer, employing coherent light at one input port and squeezed light at the other, is compared with a modified configuration using coherent light and a GKP state. While it is known that the squeezed vacuum state is the optimal Gaussian resource input mode when paired with the coherent state, we show that the finite-energy GKP state with sufficiently broad envelope outperforms the squeezed vacuum injection, irrespective of the presence of optical losses. This can be attributed to the enhanced robustness coming from the availability of multiple squeezed peaks in the GKP case. However, because lowering the mean photon number reduces the GKP envelope width, the squeezed vacuum input performs better when compared with a GKP state of equal or lower mean photon number. We also observe that optical losses tend to diminish the relative advantage of either input state, since both states approach the (unsqueezed) vacuum state asymptotically. Our work demonstrates the direct application of finite-energy GKP states in optical interferometry along with a methodology for estimating the quantum Fisher information (QFI) and presents a phase estimation procedure using non-Gaussian resources in comparison with conventional Gaussian states.
The phase sensitivity of SU(1,1) interferometer is investigated using a coherent state and an m-coherent superposition squeezed vacuum states as inputs and the intensity detection. Photon-subtraction, photon-addition and photon superposition are three special cases. Both ideal and realistic cases are considered. It is shown that the coefficient s of coherent superposition can modulate the performance of phase sensitivity, especially in a small squeezing region. Even in the presence of photon losses, the three-kind of non-Gaussian operations can achieve the improvement of measure precision, and the photon addition presents the best robustness compared to the photon subtraction and coherent superposition. For small squeezing, the first-order non-Gaussian operation may be the most preferred in improving phase sensitivity if considering the limitations of experimental conditions. Our results may be helpful for the practical application of quantum information.
The research focused on enhancing the measurement accuracy through the use of non-Gaussian states has garnered increasing attention. In this study, we propose a scheme to input the coherent state mixed with a photon-catalyzed squeezed vacuum state into the Mach-Zender interferometer to enhance phase measurement accuracy. The findings demonstrate that photon catalysis, particularly multi-photon catalysis, can effectively improve the phase sensitivity of parity detection and the quantum Fisher information. Moreover, the situation of photon losses in practical measurement was studied. The results indicate that external dissipation has a greater influence on phase sensitivity than the internal dissipation. Compared to input coherent state mixed with squeezed vacuum state, the utilization of coherent state mixed photon-catalyzed squeezed vacuum state, particularly the mixed multi-photon catalyzed squeezed vacuum state as input, can enhance the phase sensitivity and quantum Fisher information. Furthermore, the phase measurement accuracy can exceed the standard quantum limit, and even surpass the Heisenberg limit. This research is expected to significantly contribute to quantum precision measurement.
The research focused on enhancing the measurement accuracy through the use of non-Gaussian states has garnered increasing attention. In this study, we propose a scheme to input the coherent state mixed with photon-catalyzed squeezed vacuum state into the Mach-Zender interferometer to enhance phase measurement accuracy. The findings demonstrate that photon catalysis, particularly multi-photon catalysis, can effectively improve the phase sensitivity of parity detection and the quantum Fisher information. Moreover, the situation of photon losses in practical measurement was studied. The results indicate that external dissipation has a greater influence on phase sensitivity than the internal dissipation. Compared to input coherent state mixed with squeezed vacuum state, the utilization of coherent state mixed photon-catalyzed squeezed vacuum state, particularly the mixed multi-photon catalyzed squeezed vacuum state as input, can enhance the phase sensitivity and quantum Fisher information. Furthermore, the phase measurement accuracy can exceed the standard quantum limit, and even surpass the Heisenberg limit. This research is expected to significantly contribute to quantum precision measurement.
Abstract We address the performance of an interferometric setup in which a squeezed single photon interferes at a beam splitter with a coherent state. Our analysis in based on both the quantum Fisher information and the sensitivity when a Mach-Zehnder setup is considered and the difference photocurrent is detected at the output. We compare our results with those obtained feeding the interferometer with a squeezed vacuum (with the same squeezing parameter of the squeezed single photon) and a coherent state in order to have the same total number of photons circulating in the interferometer. We find that for fixed squeezing parameter and total number of photons there is a threshold of the coherent amplitude interfering with the squeezed single photon above which the squeezed single photons outperform the performance of squeezed vacuum (showing the highest quantum Fisher information). When the difference photocurrent measurement is considered, we can always find a threshold of the squeezing parameter (given the total number of photons and the coherent amplitude) above which squeezed single photons can be exploited to reach a better sensitivity with respect to the use of squeezed vacuum states also in the presence of non unit quantum efficiency.
Quantum metrology aims to achieve measurement precision that surpasses classical limits in the estimation of physical parameters. In realistic conditions, however, its advantage can be diminished by interactions between a quantum system and its environment. This necessitates careful design of quantum resources that can sustain enhanced performance even under noise. Here, we investigate how a quantum non-Gaussian operation can provide an advantage in noisy quantum metrology. Specifically, we examine the effect of single-photon subtraction applied to a two-mode squeezed vacuum state in the task of phase estimation using a Mach–Zehnder interferometer under photon loss. The single-photon subtraction can be implemented either before or after the first beam splitter in the interferometer. By evaluating the quantum Fisher information for both the original and the photon-subtracted states, we assess the potential enhancement in sensing precision. We show that the enhancement occurs when photon subtraction is performed before the first beam splitter, provided that loss acts only on the signal mode. Our findings shed light on the role of non-Gaussian operations in noisy quantum metrology, clarifying when photon subtraction can yield a genuine advantage over Gaussian resources.