Simultaneous Measurement of Noncommuting Observables

She, C. Y.; Heffner, Hubert C.

doi:10.1103/physrev.152.1103

Cited by 93 publications

(76 citation statements)

References 4 publications

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“…This relation was proven mathematically [6][7][8][9] under the joint unbiasedness condition requiring that the (experimental) mean values of the outcome x of the A measurement and the outcome y of the B measurement should coincide with the (theoretical) mean values of observables A and B, respectively, on any input state ψ. It is a common opinion that currently available measuring devices satisfy this relation [10][11][12].…”

mentioning

confidence: 96%

Universally valid reformulation of the Heisenberg uncertainty principle on noise and disturbance in measurement

2003

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The Heisenberg uncertainty principle [1] states that the product of the noise in a position measurement and the momentum disturbance caused by that measurement should be no less than the limit set by Planck's constant,h/2, as demonstrated by Heisenberg's thought experiment using a γ-ray microscope [2]. Here I show that this common assumption is false: a universally valid trade-off relation between the noise and the disturbance has an additional correlation term, which is redundant when the intervention brought by the measurement is independent of the measured object, but which allows the noise-disturbance product much below Planck's constant when the intervention is dependent. A model of measuring interaction with dependent intervention shows that Heisenberg's lower bound for the noise-disturbance product is violated even by a nearly nondisturbing, precise position measuring instrument. An experimental implementation is also proposed to realize the above model in the context of optical quadrature measurement with currently available linear optical devices.

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confidence: 96%

Universally valid reformulation of the Heisenberg uncertainty principle on noise and disturbance in measurement

2003

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“…A salient feature of this relation is that the lefthand side contains only the standard deviations of measuring apparatus, and the lower bound is twice of the common relation [8,9,10,11,12].…”

Section: Arthurs-kelly Relationmentioning

confidence: 99%

Heisenberg Uncertainty Relation Revisited — Universality of Robertson's Relation

Fujikawa

2014

Int. J. Mod. Phys. A

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It is shown that all the known uncertainty relations are the secondary consequences of Robertson's relation. The basic idea is to use the Heisenberg picture so that the time development of quantum mechanical operators incorporate the effects of the measurement interaction. A suitable use of triangle inequalities then gives rise to various forms of uncertainty relations. The assumptions of unbiased measurement and unbiased disturbance are important to simplify the resulting uncertainty relations and to give the familiar uncertainty relations such as a naive Heisenberg error-disturbance relation. These simplified uncertainty relations are however valid only conditionally. Quite independently of uncertainty relations, it is shown that the notion of precise measurement is incompatible with the assumptions of unbiased measurement and unbiased disturbance. We can thus naturally understand the failure of the naive Heisenberg's error-disturbance relation, as was demonstrated by the recent spin-measurement by J. Erhart, et al..

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“…[2], was studied from a more general viewpoint in Ref. [17] by assuming that the statistics are fully determined by the observed values and the associated spreads. From this hypothesis a Gaussian function was constructed according to the principle of maximum entropy [18].…”

Section: Introductionmentioning

confidence: 99%

Strong correspondence principle for joint measurement of conjugate observables

Lorenzo¹

2011

Phys. Rev. A

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It is demonstrated that the statistics for a joint measurement of two conjugate variables in quantum mechanics are expressed through an equation identical to the classical one, provided that joint classical probabilities are replaced by Wigner functions and that the interaction between the system and the detectors is accounted for. This constitutes an extension of Ehrenfest's correspondence principle and is thereby dubbed the strong correspondence principle. Furthermore, it is proved that the detectors provide an additive term to all the cumulants and that if they are prepared in a Gaussian state they contribute only to the first and second cumulants.

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Simultaneous Measurement of Noncommuting Observables

Cited by 93 publications

References 4 publications

Universally valid reformulation of the Heisenberg uncertainty principle on noise and disturbance in measurement

Universally valid reformulation of the Heisenberg uncertainty principle on noise and disturbance in measurement

Heisenberg Uncertainty Relation Revisited — Universality of Robertson's Relation

Strong correspondence principle for joint measurement of conjugate observables

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