Quantum Incompatibility in Collective Measurements

Carmeli, Claudio; Heinosaari, Teiko; Reitzner, Daniel; Schultz, Jussi; Toigo, Alessandro

doi:10.3390/math4030054

Cited by 5 publications

(5 citation statements)

References 4 publications

(14 reference statements)

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“…It was proved in Ref. [25] that this triplet is 2-compatible if and only if 0 ≤ t ≤ √ 3 2;, hence we conclude that s min (X t , Y t , Z t ) = 2 for 1 √ 3 < t ≤ √ 3 2. From these results, we cannot conclude the minimal simulation number for values √ 3 2 < t < 1.…”

Section: Example 6 (Triplet Of Orthogonal Qubit Observables)supporting

confidence: 65%

“…, A (n) means that we can simultaneously implement their measurements using a single observable, even if only one input system is available. In the context of quantum observables, this notion has been recently generalized to the case where it is assumed that we have access to k copies [25]. We can then make a collective measurement on a state s ⊗k .…”

Section: B Connection To K-compatibilitymentioning

confidence: 99%

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Simulability of observables in general probabilistic theories

2018

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The existence of incompatibility is one of the most fundamental features of quantum theory, and can be found at the core of many of the theory's distinguishing features, such as Bell inequality violations and the no-broadcasting theorem. A scheme for obtaining new observables from existing ones via classical operations, the so-called simulation of observables, has led to an extension of the notion of compatibility for measurements. We consider the simulation of observables within the operational framework of general probabilistic theories and introduce the concept of simulation irreducibility. While a simulation irreducible observable can only be simulated by itself, we show that any observable can be simulated by simulation irreducible observables, which in the quantum case correspond to extreme rank-1 positive-operator-valued measures. We also consider cases where the set of simulators is restricted in one of two ways: in terms of either the number of simulating observables or their number of outcomes. The former is seen to be closely connected to compatibility and k-compatibility, whereas the latter leads to a partial characterization for dichotomic observables. In addition to the quantum case, we further demonstrate these concepts in state spaces described by regular polygons.

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Section: Example 6 (Triplet Of Orthogonal Qubit Observables)supporting

confidence: 65%

Section: B Connection To K-compatibilitymentioning

confidence: 99%

Simulability of observables in general probabilistic theories

2018

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“…Motivated by the strong connections between quantum measurement theory and quantum correlations presented in this section (see also Section V.D and Section V.H), it will be an interesting question for future research to isolate the measurement resources behind other quantum tasks. Conversely, it will be of interest to see if other concepts of incompatibility such as broadcastability , incompatibility on many copies (Carmeli et al, 2016), and measurement simulability (Oszmaniec et al, 2017) will find counterparts in the realm of quantum correlations. To conclude, we note that whereas further connections between measurement theory and correlations remain unknown, jointly measurable sets (Carmeli et al, 2019;Skrzypczyk et al, 2019), or more generally all convex subsets of measurements (Uola et al, 2019b), can be characterized through state discrimination tasks.…”

Section: E Further Topics On Incompatibilitymentioning

confidence: 99%

Quantum steering

et al. 2020

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Quantum correlations between two parties are essential for the argument of Einstein, Podolsky, and Rosen in favour of the incompleteness of quantum mechanics. Schrödinger noted that an essential point is the fact that one party can influence the wave function of the other party by performing suitable measurements. He called this phenomenon quantum steering and studied its properties, but only in the last years this kind of quantum correlation attracted significant interest in quantum information theory. In this paper we review the theory of quantum steering. We first present the basic concepts of steering and local hidden state models and their relation to entanglement and Bell nonlocality. Then, we describe the various criteria to characterize steerability and structural results on the phenomenon. A detailed discussion is given on the connections between steering and incompatibility of quantum measurements. Finally, we review applications of steering in quantum information processing and further related topics. 34 J. Quantum teleportation 34 K. Resource theory of steering 35 L. Post-quantum steering 36 M. Historical aspects of steering 36 1. Discussions between Schrödinger and Einstein 36 2. The two papers by Schrödinger 37 3. Impact of these papers 38 VI. Conclusion 38 References 39 arXiv:1903.06663v2 [quant-ph]

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“…Other works have investigated measurement (in)compatibility in subspaces [27][28][29], while Ref. [30] defined a concept of n-compatibility considering a scenario where a set of measurements is performed on n copies of a state. As far as we can say, these concepts are unrelated to n-dimensional simulability.…”

mentioning

confidence: 99%