Uncertainty over complementarity?

Wiseman, Howard Mark; Harrison, F. E.

doi:10.1038/377584a0

Cited by 87 publications

(88 citation statements)

References 5 publications

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“…However, ref. 37 did not remark that their experiment actually tested a relation different from equation (1), namely, they tested a special case of equation (16).…”

Section: Discussionmentioning

confidence: 99%

“…It has been debated, particularly around the mid-1990s [14][15][16] , whether the WPD principle, closely related to Bohr's complementarity principle 17 , is equivalent to another fundamental quantum idea with no classical analogue: Heisenberg's uncertainty principle 18 . The latter states that there are certain pairs of observables, such as position and momentum or two orthogonal components of spin angular momentum, which cannot simultaneously be known or jointly measured.…”

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confidence: 99%

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Equivalence of wave–particle duality to entropic uncertainty

2014

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Interferometers capture a basic mystery of quantum mechanics: a single particle can exhibit wave behaviour, yet that wave behaviour disappears when one tries to determine the particle's path inside the interferometer. This idea has been formulated quantitatively as an inequality, for example, by Englert and Jaeger, Shimony and Vaidman, which upper bounds the sum of the interference visibility and the path distinguishability. Such wave-particle duality relations (WPDRs) are often thought to be conceptually inequivalent to Heisenberg's uncertainty principle, although this has been debated. Here we show that WPDRs correspond precisely to a modern formulation of the uncertainty principle in terms of entropies, namely, the min-and max-entropies. This observation unifies two fundamental concepts in quantum mechanics. Furthermore, it leads to a robust framework for deriving novel WPDRs by applying entropic uncertainty relations to interferometric models. As an illustration, we derive a novel relation that captures the coherence in a quantum beam splitter.

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“…However, ref. 37 did not remark that their experiment actually tested a relation different from equation (1), namely, they tested a special case of equation (16).…”

Section: Discussionmentioning

confidence: 99%

mentioning

confidence: 99%

Equivalence of wave–particle duality to entropic uncertainty

2014

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“…The question about uncertainty relations in measurements again became crucial after the long interesting discussion in the literature [8,[14][15][16][17][18][19][20]. It was suggested in the course of this discussion that the uncertainty relation is completely wrong in interferometric experiments with atoms [20].…”

Section: Introductionmentioning

confidence: 98%

Heisenberg’s uncertainty relation may be violated in a single measurement

Mensky

Lebedev²

2006

J Russ Laser Res

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The well-known Heisenberg's uncertainty relation is an inequality between uncertainties of canonically conjugate observables in a given state. In this interpretation, the Heisenberg's uncertainty relation is a rigorous mathematical theorem and is, therefore, always valid. However, the same inequality is often applied in the situation of measurement, where it is illustrated in a quite different way. The uncertainty relation is then an inequality connecting the precision (resolution) of the measurement of one observable and the uncertainty of the conjugate observable in the state arising after the measurement. It turns out that in such an interpretation the Heisenberg's inequality may be violated for some measurement readouts that emerge with small but finite probabilities. Making use of the uncertainties averaged in a special way over all possible measurement readouts, one may formulate an inequality of the type of Heisenberg's inequality but valid for any measurement.

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“…Recently some new qualitative statements about complementarity have been proposed [3][4][5][6][7][8][9][10][11][12], and subsequently the question has been raised whether there exist any relations between these new expressions and the Schrödinger-Robertson and the Arthurs-Kelley uncertainty principles [8,9,11,13,14]. In addition, the fundamental physical mechanism that enforces complementarity has been debated [14][15][16][17]. The superposition principle also leads to nonlocality.…”

Section: Introductionmentioning

confidence: 99%

Comprehensive experimental test of quantum erasure

Trifonov

Björk

Söderholm

et al. 2002

The European Physical Journal D - Atomic, Molecular and Optical

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In an interferometer, path information and interference visibility are incompatible quantities. Complete determination of the path will exclude any possibility of interference, rendering the visibility zero. However, if the composite object and probe state is pure, it is, under certain conditions, possible to trade the path information for improved (conditioned) visibility. Such a procedure is called quantum erasure.We have performed such experiments with polarization entangled photon pairs. Using a partial polarizer we could vary the degree of entanglement between object and probe. We could also vary the interferometer splitting ratio and thereby vary the a priori path predictability. We have tested quantum erasure under a number of different experimental conditions and found good agreement between experiments and theory.

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Uncertainty over complementarity?

Cited by 87 publications

References 5 publications

Equivalence of wave–particle duality to entropic uncertainty

Equivalence of wave–particle duality to entropic uncertainty

Heisenberg’s uncertainty relation may be violated in a single measurement

Comprehensive experimental test of quantum erasure

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