Parity detection achieves the Heisenberg limit in interferometry with coherent mixed with squeezed vacuum light

Seshadreesan, Kaushik P.; Anisimov, Petr M.; Lee, Hwang; Dowling, Jonathan P.

doi:10.1088/1367-2630/13/8/083026

Cited by 91 publications

(91 citation statements)

References 27 publications

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“…This optimal condition for SU(1,1) interferometers is similar to the SU(2) case [16,17]. For a Mach-Zehnder Interferometer (MZI) injected by coherent and squeezed vacuum light, the phase sensitivity with parity detection is 1/ |α| 2 e 2r + sinh 2 r. When a coherent state and squeezed vacuum state are in roughly equal intensities, |α| 2 ≃ sinh 2 r, the phase sensitivity reaches the HL.…”

Section: Introductionmentioning

confidence: 79%

Phase sensitivity at the Heisenberg limit in an SU(1,1) interferometer via parity detection

et al. 2016

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We theoretically investigate the phase sensitivity with parity detection on an SU(1,1) interferometer with a coherent state combined with a squeezed vacuum state. This interferometer is formed with two parametric amplifiers for beam splitting and recombination instead of beam splitters. We show that the sensitivity of estimation phase approaches Heisenberg limit and give the corresponding optimal condition. Moreover, we derive the quantum Cramér-Rao bound of the SU(1,1) interferometer.

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Section: Introductionmentioning

confidence: 79%

Phase sensitivity at the Heisenberg limit in an SU(1,1) interferometer via parity detection

et al. 2016

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“…Schemes for phase measurement often consider N00N states, or equal photon numbers in both input ports for an interferometer [1,13,28,37]. The states that are most commonly produced experimentally are the TMSV states.…”

Section: Discussionmentioning

confidence: 99%

“…This parity measurement can be implemented with photon-number-resolving detectors or homodyne detection [28,29]. Using balanced homodyne detection and detectors with 99% quantum efficiency, phase estimation precision above the shot noise limit has been experimentally demonstrated with squeezed vacuum [16].…”

Section: Modelmentioning

confidence: 99%

“…Squeezed vacuum, which is the brightest experimentally available nonclassical light, has received much attention. In particular, the two-mode squeezed-vacuum (TMSV) which is the simplest two-mode state that contains strong photon-number entanglement, offers a notable improvement in phase estimation precision when compared to coherent states [4][5][6][7].…”

Section: Introductionmentioning

confidence: 99%

“…In previous schemes considered [4,6,7], it was unclear as to how an unambiguous estimate could be made, given that the parity of the output is symmetric around BS BS   F IG. 1.…”

Section: Introductionmentioning

confidence: 99%

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Adaptive phase estimation with two-mode squeezed vacuum and parity measurement

et al. 2017

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A proposed phase-estimation protocol based on measuring the parity of a two-mode squeezedvacuum state at the output of a Mach-Zehnder interferometer shows that the Cramér-Rao sensitivity is sub-Heisenberg [Phys. Rev. Lett. 104, 103602 (2010)]. However, these measurements are problematic, making it unclear if this sensitivity can be obtained with a finite number of measurements. This sensitivity is only for phase near zero, and in this region there is a problem with ambiguity because measurements cannot distinguish the sign of the phase. Here, we consider a finite number of parity measurements, and show that an adaptive technique gives a highly accurate phase estimate regardless of the phase. We show that the Heisenberg limit is reachable, where the number of trials needed for mean photon numbern = 1 is approximately one hundred. We show that the Cramér-Rao sensitivity can be achieved approximately, and the estimation is unambiguous in the interval (−π/2, π/2).

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Enhanced Phase Estimation in Parity‐Detection‐Based Mach–Zehnder Interferometer using Non‐Gaussian Two‐Mode Squeezed Thermal Input State

2023

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While the quantum metrological advantages of performing non‐Gaussian operations on two‐mode squeezed vacuum (TMSV) states have been extensively explored, similar studies in the context of two‐mode squeezed thermal (TMST) states are severely lacking. This paper explores the potential advantages of performing non‐Gaussian operations on TMST state for phase estimation using parity detection‐based Mach–Zehnder interferometry and compares it with the TMSV case. To this end, a realistic photon subtraction, addition, and catalysis model is considered. A unified Wigner function of the photon subtracted, photon added, and photon catalyzed TMST state is derived, which is used to obtain the expression for the phase sensitivity. The results show that performing non‐Gaussian operations on TMST states can enhance the phase sensitivity for significant squeezing and transmissivity parameter ranges. Because of the probabilistic nature of these operations, it is of utmost importance to consider their success probability. When the success probability is considered, the photon catalysis operation performed using a high transmissivity beam splitter is the optimal non‐Gaussian operation. This contrasts with the TMSV case, where photon addition is observed as the most optimal. Further, the derived Wigner function of the non‐Gaussian TMST states will be useful for state characterization and various quantum protocols.

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Parity detection achieves the Heisenberg limit in interferometry with coherent mixed with squeezed vacuum light

Cited by 91 publications

References 27 publications

Phase sensitivity at the Heisenberg limit in an SU(1,1) interferometer via parity detection

Phase sensitivity at the Heisenberg limit in an SU(1,1) interferometer via parity detection

Adaptive phase estimation with two-mode squeezed vacuum and parity measurement

Enhanced Phase Estimation in Parity‐Detection‐Based Mach–Zehnder Interferometer using Non‐Gaussian Two‐Mode Squeezed Thermal Input State

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