Information amplification via postselection: A parameter-estimation perspective

Tanaka, Saki; Yamamoto, Naoki

doi:10.1103/physreva.88.042116

Cited by 115 publications

(118 citation statements)

References 35 publications

(61 reference statements)

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“…Especially for the latter, a post-selection of the measurement results is involved and the role played by post-selection in quantum metrology has attracted a lot of attention recently [68][69][70][71][72]. Mixed-state cloning or broadcasting would be also very interesting in terms of QFI [20].…”

Section: Discussionmentioning

confidence: 99%

Multiple phase estimation in quantum cloning machines

Yao

Xing

et al. 2014

Phys. Rev. A

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Since the initial discovery of the Wootters-Zurek no-cloning theorem, a wide variety of quantum cloning machines have been proposed aiming at imperfect but optimal cloning of quantum states within its own context. Remarkably, most previous studies have employed the Bures fidelity or the Hilbert-Schmidt norm as the figure of merit to characterize the quality of the corresponding cloning scenarios. However, in many situations, what we truly care about is the relevant information about certain parameters encoded in quantum states. In this work, we investigate the multiple phase estimation problem in the framework of quantum cloning machines, from the perspective of quantum Fisher information matrix (QFIM). Focusing on the generalized d-dimensional equatorial states, we obtain the analytical formulas of QFIM for both universal quantum cloning machine (UQCM) and phase-covariant quantum cloning machine (PQCM), and prove that PQCM indeed performs better than UQCM in terms of QFIM. We highlight that our method can be generalized to arbitrary cloning schemes where the fidelity between the single-copy input and output states is input-state independent. Furthermore, the attainability of the quantum Cramér-Rao bound is also explicitly discussed.

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Section: Discussionmentioning

confidence: 99%

Multiple phase estimation in quantum cloning machines

Yao

Xing

et al. 2014

Phys. Rev. A

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“…To each of these N outcomes, inequality (15) holds with the lower bound of the probability (22). Thus, the average probability that the measurement yields outcomes within the quantum uncertainty κ is given by the sum over all possible N ,…”

Section: Uncertainty Of Weak Measurementmentioning

confidence: 99%

“…The other approach is based on estimation theory, and addresses the question whether the technique of postselection can be statistically superior to the conventional one, both in the case where an ideal 'noiseless' experiment can be performed [15], and in the presence of certain types of statistical 'noise' [16][17][18]. Utilising the standard estimation theory [19][20][21], they examine the feasibility of improving parameter estimation of the coupling constant g by weak measurement.…”

Section: Introductionmentioning

confidence: 99%

Merit of amplification by weak measurement in view of measurement uncertainty

Lee¹,

Tsutsui²

2014

Quantum Stud.: Math. Found.

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Aharonov's weak value is a physical quantity obtainable by weak measurement, which admits amplification through state selections. The amplification is expected to be useful for precision measurement, but it is achieved at the expense of statistical deterioration due to the selections, which brings the question as to whether it can provide a truly superior means over the conventional measurement. We approach this problem by taking measurement uncertainty into account, and present a probabilistic evaluation of its impact to the final result of the measurement in weak measurement. By examining the significance condition for detecting the coupling g, we show that the trade-off relation between the amplification effect and the statistical deterioration does permit a finite range of usable amplification where the superiority is ensured. Apart from the Gaussian state models employed for demonstration, our argument is mathematically rigorous and general; it is free from approximation and valid for arbitrary observables A and couplings g.

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“…We will not focus so much here on what combination of initial and final states, coupling parameters and meter states are necessary to approach equality in Eqs. (18)(19)(20), save to note that ifÂ 2 = I then | f =Â|i will saturate the second condition and implies a real weak value. The question has been considered outside of the linear regime we consider [19,38].…”

Section: Optimal Protocolsmentioning

confidence: 99%

“…Other impressive experiments include the estimation of the angular tilt of a mirror in a Sagnac interferometer to a precision of a few hundred femtoradians [16]. From 2013 onwards, however, theoretical treatments of the weak value technique called into doubt whether there was any true advantage over standard strategies [17][18][19][20], especially from the point of view of parameter estimation. There were also a slew of theoretical [21,22] and experimental [23] papers arguing for the merits of weak value techniques.…”

Section: Introductionmentioning

confidence: 99%

Seeing opportunity in every difficulty: protecting information with weak value techniques

Knee

Briggs

2018

Quantum Stud.: Math. Found.

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A weak value is an effective description of the influence of a pre and post-selected 'principal' system on another 'meter' system to which it is weakly coupled. Weak values can describe anomalously large deflections of the meter, and deflections in otherwise unperturbed variables: this motivates investigation of the potential benefits of the protocol in precision metrology. We present a visual interpretation of weak value experiments in phase space, enabling an evaluation of the effects of three types of detector noise as 'Fisher information efficiency' functions. These functions depend on the marginal distribution of the Wigner function of the 'meter', and give a unified view of the weak value protocol as a way of protecting Fisher information from detector imperfections. This approach explains why weak value techniques are more effective for avoiding detector saturation than for mitigating detector jitter or pixelation.

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Information amplification via postselection: A parameter-estimation perspective

Cited by 115 publications

References 35 publications

Multiple phase estimation in quantum cloning machines

Multiple phase estimation in quantum cloning machines

Merit of amplification by weak measurement in view of measurement uncertainty

Seeing opportunity in every difficulty: protecting information with weak value techniques

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