Trade-off relation between information and disturbance in quantum measurement

Shitara, Tomohiro; Kuramochi, Yui; Ueda, Masahito

doi:10.1103/physreva.93.032134

Cited by 24 publications

(27 citation statements)

References 31 publications

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“…Results of this type can be seen as hybrid preparation-measurement uncertainty relations, as they describe a trade off between the accuracy of a measured quantity, namely, the estimator for the desired parameter; and the variance of the operator generating translations in that parameter, a quantity pertaining to the preparation. Quantum parameter estimation has been also used to formulate joint measurement uncertainty relations [37,38] and error-disturbance relations [39].…”

mentioning

confidence: 99%

Uncertainty and trade-offs in quantum multiparameter estimation

Kull¹,

Guérin²,

Verstraete³

2020

J. Phys. A: Math. Theor.

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Uncertainty relations in quantum mechanics express bounds on our ability to simultaneously obtain knowledge about expectation values of non-commuting observables of a quantum system. They quantify trade-offs in accuracy between complementary pieces of information about the system. In Quantum multiparameter estimation, such trade-offs occur for the precision achievable for different parameters characterizing a density matrix: an uncertainty relation emerges between the achievable variances of the different estimators. This is in contrast to classical multiparameter estimation, where simultaneous optimal precision is attainable in the asymptotic limit. We study trade-off relations that follow from known tight bounds in quantum multiparameter estimation. We compute trade-off curves and surfaces from Cramér-Rao type bounds which provide a compelling graphical representation of the information encoded in such bounds, and argue that bounds on simultaneously achievable precision in quantum multiparameter estimation should be regarded as measurement uncertainty relations. From the state-dependent bounds on the expected cost in parameter estimation, we derive a state independent uncertainty relation between the parameters of a qubit system.Ever since its first formulation, the uncertainty principle has seen many refinements and clarifications. As quantum theory developed, its state-of-the-art concepts and mathematical tools were used to formulate in precise terms the ideas which were put forward in Heisenberg's 1927 paper [1]. As a result, our current understanding of the uncertainties inherent in quantum mechanics is spelled out in a collection of theorems pertaining to well defined operational tasks.Soon after Heisenberg's paper, rigorous proofs of his uncertainty relations were formulated [2][3][4]. Those are usually referred to as preparation uncertainty relations. Most well known is the relation due to Weyl and Robertson arXiv:2002.05961v1 [quant-ph]

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mentioning

confidence: 99%

Uncertainty and trade-offs in quantum multiparameter estimation

Kull¹,

Guérin²,

Verstraete³

2020

J. Phys. A: Math. Theor.

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“…The conditional evolution induced by the continuous measurement also allows the possibility to perform a traditional strong measurement on the final conditional state and therefore we have to take into account the QFI of the conditional states. The correct figure of merit for this setting was introduced in [14] and dubbed effective QFI (see also [57][58][59][60] where analogous quantities are studied in different contexts). The effective QFI is defined as the classical FI for the continuous measurement plus the average QFI of the conditional states:…”

Section: Effective Qfimentioning

confidence: 99%

Quantum frequency estimation with conditional states of continuously monitored independent dephasing channels

Albarelli

Rossi

Genoni

2020

Int. J. Quantum Inform.

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We discuss the problem of estimating a frequency via N -qubit probes undergoing independent dephasing channels that can be continuously monitored via homodyne or photo-detection. We derive the corresponding analytical solutions for the conditional states, for generic initial states and for arbitrary efficiency of the continuous monitoring. For the detection strategies considered, we show that: i) in the case of perfect continuous detection, the quantum Fisher information (QFI) of the conditional states is equal to the one obtained in the noiseless dynamics; ii) for smaller detection efficiencies, the QFI of the conditional state is equal to the QFI of a state undergoing the (unconditional) dephasing dynamics, but with an effectively reduced noise parameter.

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“…In Ref. [44], it was proven in full generality that, for a parameter ξ and statistical model ρ ξ , F ξ and D…”

Section: The Information/∆-disturbance Trade-off -F β Vs D (∆) βmentioning

confidence: 99%

Trade-off between information and disturbance in qubit thermometry

Seveso

Paris

2018

Phys. Rev. A

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We address the trade-off between information and disturbance in qubit thermometry from the perspective of quantum estimation theory. Given a quantum measurement, we quantify information via the Fisher information of the measurement and disturbance via four different figures of merit, which capture different aspects (statistical, thermodynamical, geometrical) of the trade-off. For each disturbance measure, the efficient measurements, i.e. the measurements that introduce a disturbance not greater than any other measurement extracting the same amount of information, are determined explicitly. The family of efficient measurements varies with the choice of the disturbance measure. On the other hand, commutativity between the elements of the probability operatorvalued measure (POVM) and the equilibrium state of the thermometer is a necessary condition for efficiency with respect to any figure of disturbance. *

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Trade-off relation between information and disturbance in quantum measurement

Cited by 24 publications

References 31 publications

Uncertainty and trade-offs in quantum multiparameter estimation

Uncertainty and trade-offs in quantum multiparameter estimation

Quantum frequency estimation with conditional states of continuously monitored independent dephasing channels

Trade-off between information and disturbance in qubit thermometry

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