Aspects of universally valid Heisenberg uncertainty relation

Fujikawa, Kazuo; Umetsu, Koichiro

doi:10.1093/ptep/pts065

Cited by 8 publications

(6 citation statements)

References 25 publications

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“…Since the inequalities ( 4) and ( 7) are saturated for any single-qubit pure state, then we focus on the performance of the inequality (5) comparing with the RUR or SUR. We notice that reformulation by normalization turns out to be a relatively reasonable way to compare different types of uncertainty relations, e.g., dividing both sides of the inequalities by their own lower bound [45][46][47]. According to this line of thought, we can define the following two functionals…”

Section: Qubit System As An Illustrationmentioning

confidence: 99%

Implications and applications of the variance-based uncertainty equalities

et al. 2015

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In quantum mechanics, the variance-based Heisenberg-type uncertainty relations are a series of mathematical inequalities posing the fundamental limits on the achievable accuracy of the state preparations. In contrast, we construct and formulate two quantum uncertainty equalities, which hold for all pairs of incompatible observables and indicate the new uncertainty relations recently introduced by L. Maccone and A. K. Pati [Phys. Rev. Lett. 113, 260401 (2014)]. Furthermore, we present an explicit interpretation lying behind the derivations and relate these relations to the so-called intelligent states. As an illustration, we investigate the properties of these uncertainty inequalities in the qubit system and a state-independent bound is obtained for the sum of variances. Finally, we apply these inequalities to the spin squeezing scenario and its implication in interferometric sensitivity is also discussed.

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Section: Qubit System As An Illustrationmentioning

confidence: 99%

Implications and applications of the variance-based uncertainty equalities

et al. 2015

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“…Unfortunately, when X is a continuous spectrum, there's no generalization of von Neumann's formula (2) for the change in the state, due to the measurement. Indeed, no formula is possible until we introduce the notion of a finite detector resolution.…”

Section: Pvms and Observablesmentioning

confidence: 99%

“…In [1] Ozawa proposed an inequality to be satisfied in the case of successive measurements. This proposal remains controversial, as can be seen from the recent papers [2,3]. Lund and Wiseman [4] proposed an experimental test of Ozawa's ideas and Rozema et al [5] recently performed the experiment.…”

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confidence: 99%

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Uncertainties in successive measurements

Distler

Paban

2013

Phys. Rev. A

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When you measure an observable, A, in Quantum Mechanics, the state of the system changes. This, in turn, affects the quantum-mechanical uncertainty in some non-commuting observable, B. The standard Uncertainty Relation puts a lower bound on the uncertainty of B in the initial state. What is relevant for a subsequent measurement of B, however, is the uncertainty of B in the post-measurement state. We re-examine this problem, both in the case where A has a pure point spectrum and in the case where A has a continuous spectrum. In the latter case, the need to include a finite detector resolution, as part of what it means to measure such an observable, has dramatic implications for the result of successive measurements. Ozawa [1] proposed an inequality satisfied in the case of successive measurements. Among our results, we show that his inequality is ineffective (can never come close to being saturated). For the cases of interest, we compute a sharper lower bound.

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“…Therefore Eq. (33) is "universally valid" [29,32,34] whenever In contrast, the common interpretation of Heisenberg's original writings [36] suggests an uncertainty relation which reads [14,15,29,32,34]…”

Section: Uncertainty Relations: Theorymentioning

confidence: 99%

Discrete-event simulation of uncertainty in single-neutron experiments

Raedt

Michielsen

2014

Front. Physics

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A discrete-event simulation approach which provides a cause-and-effect description of many experiments with photons and neutrons exhibiting interference and entanglement is applied to a recent single-neutron experiment that tests (generalizations of) Heisenberg's uncertainty relation. The event-based simulation algorithm reproduces the results of the quantum theoretical description of the experiment but does not require the knowledge of the solution of a wave equation nor does it rely on concepts of quantum theory. In particular, the data satisfies uncertainty relations derived in the context of quantum theory.

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Aspects of universally valid Heisenberg uncertainty relation

Cited by 8 publications

References 25 publications

Implications and applications of the variance-based uncertainty equalities

Implications and applications of the variance-based uncertainty equalities

Uncertainties in successive measurements

Discrete-event simulation of uncertainty in single-neutron experiments

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