Antidistinguishability of pure quantum states

Heinosaari, Teiko; Kerppo, Oskari

doi:10.1088/1751-8121/aad1fc

Cited by 31 publications

(28 citation statements)

References 11 publications

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“…coexistence, broadcastability, and non-disturbance (Busch et al, 2016;Heinosaari and Wolf, 2010), see also Section IV.E. Typically all the incompatibility related extensions of non-commutativity (on a single system) coincide with non-commutativity for projective measurements, but for the case of POVMs they form a strict hierarchy (Heinosaari and Wolf, 2010). It is worth mentioning that in the process matrix formulation of POVMs, even commuting process POVMs can be incompatible (Sedlák et al, 2016).…”

Section: A Measurement Incompatibilitymentioning

confidence: 99%

“…Clearly commutativity implies non-disturbance by the use of the Lüders rule and nondisturbance implies joint measurability by defining for a non-disturbing scenario G a,b = I † a (B b ), where the dagger refers to the Heisenberg picture. For a proof that the implications can not be reversed in general, and for more detailed analysis on when the implications are reversible, we refer to (Heinosaari and Wolf, 2010).…”

Section: E Further Topics On Incompatibilitymentioning

confidence: 99%

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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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Section: A Measurement Incompatibilitymentioning

confidence: 99%

Section: E Further Topics On Incompatibilitymentioning

confidence: 99%

Quantum steering

et al. 2020

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“…Ref. [6] shows that if any triple of the states is antidistinguishable, then it follows that the set of d states is antidistinguishable. On the other hand, it does not follow that if the set of d states is antidistinguishable, then any triple must be antidistinguishable.…”

Section: Appendix A: Multiplicative Error Samplingmentioning

confidence: 99%

Simple communication complexity separation from quantum state antidistinguishability

Havlíček

Barrett

2020

Phys. Rev. Research

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A set of n pure quantum states is called antidististinguishable if there exists an n-outcome measurement that never outputs the outcome 'k' on the k-th quantum state. We describe sets of quantum states for which any subset of three states is antidistinguishable and use this to produce a two-player communication task that can be solved with log d qubits, but requires one-way communication of at least log(4/3)(d − 1) − 1 ≈ 0.415(d − 1) − 1 classical bits. The advantages of the approach are that the proof is simple and self-contained -not needing, for example, to rely on hard-to-establish prior results in combinatorics -and that with slight modifications, non-trivial bounds can be established in any dimension ≥ 3. The task can be framed in terms of the separated parties solving a relation, and the separation is also robust to multiplicative error in the output probabilities. We show, however, that for this particular task, the separation disappears if two-way classical communication is allowed. Finally, we state a conjecture regarding antidistinguishability of sets of states, and provide some supporting numerical evidence. If the conjecture holds, then there is a two-player communication task that can be solved with log d qubits, but requires one-way communication of Ω(d log d) classical bits.

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“…This means if Monty opens a goat door, then the contestant's probability of winning is the same whether the contestant chooses to switch the door or not. ψ-ontic Monty Hall game: Antidistinguishability [32,46,47], where there is a measurement for which each outcome identifies that a specific member of a set of quantum states was definitely not prepared, is highlighted in the PBR proof by | Φ i |Ψ i | 2 = 0 for all i. We will exploit this to construct our game, which can be thought of as a quantum Ignorant Monty Hall game.…”

Section: But In This Game Monty Doesn't Know What Lies Behind Any Ofmentioning

confidence: 99%

Quantum PBR Theorem as a Monty Hall Game

Rajan

Visser

2019

Quantum Reports

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The quantum Pusey-Barrett-Rudolph (PBR) theorem addresses the question of whether the quantum state corresponds to a ψ-ontic model (system's physical state) or to a ψ-epistemic model (observer's knowledge about the system). We reformulate the PBR theorem as a Monty Hall game, and show that winning probabilities, for switching doors in the game, depend whether it is a ψ-ontic or ψ-epistemic game. For certain cases of the latter, switching doors provides no advantage. We also apply the concepts involved to quantum teleportation, in particular for improving reliability.

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Antidistinguishability of pure quantum states

Cited by 31 publications

References 11 publications

Quantum steering

Quantum steering

Simple communication complexity separation from quantum state antidistinguishability

Quantum PBR Theorem as a Monty Hall Game

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