Quantum realization of arbitrary joint measurability structures

Kunjwal, Ravi; Heunen, Chris; Fritz, Tobias

doi:10.1103/physreva.89.052126

Cited by 55 publications

(104 citation statements)

References 17 publications

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“…Indeed, as later shown by the authors of Ref. [22] recently, quantum theory does admit all contextuality scenarios since it allows one to realize any conceivable set of (in)compatibility relations between a set of observables.…”

Section: Discussionmentioning

confidence: 89%

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Minimal state-dependent proof of measurement contextuality for a qubit

Kunjwal

Ghosh

2014

Phys. Rev. A

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We show that three unsharp binary qubit measurements are enough to violate a generalized noncontextuality inequality, the LSW inequality, in a state-dependent manner. For the case of trine spin axes we calculate the optimal quantum violation of this inequality. Besides, we show that unsharp qubit measurements do not allow a state-independent violation of this inequality. We thus provide a minimal state-dependent proof of measurement contextuality requiring one qubit and three unsharp measurements. Our result rules out generalized noncontextual models of these measurements which were previously conjectured to exist. More importantly, this class of generalized noncontextual models includes the traditional Kochen-Specker (KS) noncontextual models as a proper subset, so our result rules out a larger class of models than those ruled out by a violation of the corresponding KS-inequality in this scenario.Comment: 9 pages, 3 figure

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Section: Discussionmentioning

confidence: 89%

“…Whether, and to what extent, this is the case with more complicated contextuality scenarios realizable, for example, via the construction in Ref. [22] remains to be explored.…”

Section: Discussionmentioning

confidence: 99%

Minimal state-dependent proof of measurement contextuality for a qubit

Kunjwal

Ghosh

2014

Phys. Rev. A

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“…In recent years there is a surge of research activity dedicated to explore the notion of measurement incompatibility and its connection with the counter-intuitive quantum notions like non-locality, contextuality and nonmacrorealism [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23]. In particular, it is known that measurement incompatibility plays a key role in bringing to surface the violations of the so-called no-go theorems in the quantum world.…”

Section: Introductionmentioning

confidence: 99%

N-term pairwise-correlation inequalities, steering, and joint measurability

et al. 2017

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Chained inequalities involving pairwise correlations of qubit observables in the equatorial plane are constructed based on the positivity of a sequence of moment matrices. When a jointly measurable set of fuzzy POVMs is employed in first measurement of every pair of sequential measurements, the chained pairwise correlations do not violate the classical bound imposed by the moment matrix positivity. We identify that incompatibility of the set of POVMs employed in first measurements is only necessary, but not sufficient, in general, for the violation of the inequality. On the other hand, there exists a one-to-one equivalence between the degree of incompatibility (which quantifies the joint measurability) of the equatorial qubit POVMs and the optimal violation of a non-local steering inequality, proposed by Jones and Wiseman (Phys. Rev. A, 84, 012110 (2011)). To this end, we construct a local analogue of this steering inequality in a single qubit system and show that its violation is a mere reflection of measurement incompatibility of equatorial qubit POVMs, employed in first measurements in the sequential unsharp-sharp scheme.

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“…The joint probabilities p(x, x ′ ) (or p(z, z ′ )) of Alice's sharp outcome x (or z) and Bob's unsharp outcome x ′ (or z ′ ), are obtained (see (12)) to be,…”

Section: Beating Entropic Uncertainty Bound Using Incompatible Mmentioning

confidence: 99%

“…While sharp values for non-commuting observables can not be assigned jointly via their PV measurements, their unsharp joint values could be perceived when compatible POVMs are employed. Active research efforts are dedicated to investigate operationally significant criteria of joint measurability (compatibility) of two or more POVMs and also to develop a resource theory of measurement incompatibility [5][6][7][8][9][10][11][12][13][14][15][16][17] . In this paper, we review the notion of compatible POVMs in the generalized measurement setting.…”

Section: Introductionmentioning

confidence: 99%

Unsharp Measurements and Joint Measurability

2015

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We give an overview of joint unsharp measurements of non-commuting observables using positive operator valued measures (POVMs). We exemplify the role played by joint measurability of POVMs in entropic uncertainty relation for Alice's pair of non-commuting observables in the presence of Bob's entangled quantum memory. We show that Bob should record the outcomes of incompatible (non-jointly measurable) POVMs in his quantum memory so as to beat the entropic uncertainty bound. In other words, in addition to the presence of entangled Alice-Bob state, implementing incompatible POVMs at Bob's end is necessary to beat the uncertainty bound and hence, predict the outcomes of non-commuting observables with improved precision. We also explore the implications of joint measurability to validate a moment matrix constructed from average pairwise correlations of three dichotomic non-commuting qubit observables. We prove that a classically acceptable moment matrix -which ascertains the existence of a legitimate joint probability distribution for the outcomes of all the three dichotomic observables -could be realized if and only if compatible POVMs are employed.

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Quantum realization of arbitrary joint measurability structures

Cited by 55 publications

References 17 publications

Minimal state-dependent proof of measurement contextuality for a qubit

Minimal state-dependent proof of measurement contextuality for a qubit

N-term pairwise-correlation inequalities, steering, and joint measurability

Unsharp Measurements and Joint Measurability

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