Frequentist and Bayesian Quantum Phase Estimation

Frequentist and Bayesian phase estimation strategies lead to conceptually different results on the state of knowledge about the true value of an unknown parameter. We compare the two frameworks and their sensitivity bounds to the estimation of an interferometric phase shift limited by quantum noise, considering both the cases of a fixed and a fluctuating parameter. We point out that frequentist precision bounds, such as the Cramér–Rao bound, for instance, do not apply to Bayesian strategies and vice versa. In particular, we show that the Bayesian variance can overcome the frequentist Cramér–Rao bound, which appears to be a paradoxical result if the conceptual difference between the two approaches are overlooked. Similarly, bounds for fluctuating parameters make no statement about the estimation of a fixed parameter.

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Quantum phase estimation with arbitrary constant-precision phase shift operators

Quantum Information and Computation ◽

10.26421/qic12.9-10-9 ◽

2012 ◽

Vol 12 (9&10) ◽

pp. 864-875

Author(s):

Hamed Ahmadi ◽

Chen-Fu Chiang

Keyword(s):

Phase Shift ◽

Arbitrary Constant ◽

Quantum Algorithms ◽

Quantum Algorithm ◽

Quantum Phase ◽

Phase Estimation ◽

Shift Operators ◽

Physical Implementation ◽

Alternative Approach ◽

Original Approach

While Quantum phase estimation (QPE) is at the core of many quantum algorithms known to date, its physical implementation (algorithms based on quantum Fourier transform (QFT) ) is highly constrained by the requirement of high-precision controlled phase shift operators, which remain difficult to realize. In this paper, we introduce an alternative approach to approximately implement QPE with arbitrary constant-precision controlled phase shift operators. The new quantum algorithm bridges the gap between QPE algorithms based on QFT and Kitaev's original approach. For approximating the eigenphase precise to the nth bit, Kitaev's original approach does not require any controlled phase shift operator. In contrast, QPE algorithms based on QFT or approximate QFT require controlled phase shift operators with precision of at least Pi/2n. The new approach fills the gap and requires only arbitrary constant-precision controlled phase shift operators. From a physical implementation viewpoint, the new algorithm outperforms Kitaev's approach.

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An Absolute Phase Estimation Method for Interferometry Imagery

Journal of Engineering Technology and Applied Physics ◽

10.33093/jetap.2019.1.2.4 ◽

2019 ◽

Vol 1 (2) ◽

pp. 14-19

Author(s):

Sui Ping Lee ◽

Yee Kit Chan ◽

Tien Sze Lim

Keyword(s):

Noise Suppression ◽

Estimation Method ◽

Phase Image ◽

Phase Estimation ◽

Phase Reconstruction ◽

Estimation Algorithms ◽

Absolute Phase ◽

Filtering Rate ◽

Interferometric Phase ◽

Image Performance

Accurate interpretation of interferometric image requires an extremely challenging task based on actual phase reconstruction for incomplete noise observation. In spite of the establishment of comprehensive solutions, until now, a guaranteed means of solution method is yet to exist. The initially observed interferometric image is formed by 2π-periodic phase image that wrapped within (-π, π]. Such inverse problem is further corrupted by noise distortion and leads to the degradation of interferometric image. In order to overcome this, an effective algorithm that enables noise suppression and absolute phase reconstruction of interferometric phase image is proposed. The proposed method incorporates an improved order statistical filter that is able to adjust or vary on its filtering rate by adapting to phase noise level of relevant interferometric image. Performance of proposed method is evaluated and compared with other existing phase estimation algorithms. The comparison is based on a series of computer simulated and real interferometric data images. The experiment results illustrate the effectiveness and competency of the proposed method.

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Quantum phase estimation using a multi-headed cat state

Journal of the Optical Society of America B ◽

10.1364/josab.32.001186 ◽

2015 ◽

Vol 32 (6) ◽

pp. 1186 ◽

Cited By ~ 17

Author(s):

Su-Yong Lee ◽

Chang-Woo Lee ◽

Hyunchul Nha ◽

Dagomir Kaszlikowski

Keyword(s):

Quantum Phase ◽

Phase Estimation

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INTERFEROMETRIC PHASE SHIFT TECHNIQUE FOR MEASURING SHORT FLUORESCENT LIFETIMES

Applied Physics Letters ◽

10.1063/1.1753950 ◽

1964 ◽

Vol 4 (2) ◽

pp. 32-34 ◽

Cited By ~ 23

Author(s):

R. J. Carbone ◽

P. R. Longaker

Keyword(s):

Phase Shift ◽

Interferometric Phase ◽

Shift Technique

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Upper bounds on the performance of differential-phase-shift quantum key distribution

Quantum Information and Computation ◽

10.26421/qic9.1-2-4 ◽

2009 ◽

Vol 9 (1&2) ◽

pp. 62-80

Author(s):

H. Gomez-Sousa ◽

M. Curty

Keyword(s):

Phase Shift ◽

Quantum Key Distribution ◽

Key Distribution ◽

Upper Bounds ◽

The State ◽

Differential Phase Shift ◽

Differential Phase ◽

Unambiguous Discrimination

In this paper, we investigate limitations imposed by sequential attacks on the performance of a differential-phase-shift (DPS) quantum key distribution (QKD) protocol with weak coherent pulses. Specifically, we analyze a sequential attack based on optimal unambiguous discrimination of the relative phases between consecutive signal states emitted by the source. We show that this attack can provide tighter upper bounds for the security of a DPS QKD scheme than those derived from sequential attacks where the eavesdropper aims to identify the state of each signal emitted by the source unambiguously.

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