Certifying Einstein-Podolsky-Rosen steering via the local uncertainty principle

Zhen, Yi-Zheng; Zheng, Yulin; Cao, Wenfei; Li, Li; Chen, Zeng-Bing; Liu, Nai-Le; Chen, Kai

doi:10.1103/physreva.93.012108

Cited by 57 publications

(47 citation statements)

References 43 publications

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“…Also, for these values of q, they can be connected to the variance criteria from Refs. [57,58]. To see this, consider an observable A with eigenvalues ±1 and corresponding outcome probabilities p ± .…”

Section: Optimal Values Of Q and R For Steering Detectionmentioning

confidence: 99%

Entropic Steering Criteria: Applications to Bipartite and Tripartite Systems

Costa

Uola

Gühne

2018

Entropy

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The effect of quantum steering describes a possible action at a distance via local measurements. Whereas many attempts on characterizing steerability have been pursued, answering the question as to whether a given state is steerable or not remains a difficult task. Here, we investigate the applicability of a recently proposed method for building steering criteria from generalized entropic uncertainty relations. This method works for any entropy which satisfy the properties of (i) (pseudo-) additivity for independent distributions; (ii) state independent entropic uncertainty relation (EUR); and (iii) joint convexity of a corresponding relative entropy. Our study extends the former analysis to Tsallis and Rényi entropies on bipartite and tripartite systems. As examples, we investigate the steerability of the three-qubit GHZ and W states.

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Section: Optimal Values Of Q and R For Steering Detectionmentioning

confidence: 99%

Entropic Steering Criteria: Applications to Bipartite and Tripartite Systems

Costa

Uola

Gühne

2018

Entropy

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show abstract

“…The uncertainty relation keeps on being one of the core issues concerned in quantum theory, due to its profound and broad influence in many aspects, e.g. in entanglement detection 6,7 , quantum cryptography 8,9 , quantum nonlocality 10,11 , quantum steering 12,13 , quantum coherence 14,15 , and so on. Further research on the uncertainty relation may bring more potentially beneficial applications of quantum physics.…”

Section: Introductionmentioning

confidence: 99%

Tight N-observable uncertainty relations and their experimental demonstrations

Chen

Wang

et al. 2019

Sci Rep

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The uncertainty relation, as one of the fundamental principles of quantum physics, captures the incompatibility of noncommuting observables in the preparation of quantum states. In this work, we derive two strong and universal uncertainty relations for N ( N ≥ 2) observables with discrete and bounded spectra, one in multiplicative form and the other in additive form. To verify their validity, for illustration, we implement in the spin-1/2 system an experiment with single-photon measurement. The experimental results exhibit the validity and robustness of these uncertainty relations, and indicate the existence of stringent lower bounds.

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“…It comes as no surprise that fully entangled states can achieve quantum steering [28]. The operational symmetries of fully entangled states allow one party's local measurements to be remotely affected by another's local operations, negating the possibility for the former party to assign a local hidden state model to explain their measurement results.…”

mentioning

confidence: 99%

Operational symmetries of entangled states

Tzitrin¹,

Goldberg²,

Cresswell³

2020

J. Phys. A: Math. Theor.

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Quantum entanglement obscures the notion of local operations; there exist quantum states for which all local actions on one subsystem can be equivalently realized by actions on another. We characterize the states for which this fundamental property of entanglement does and does not hold, including multipartite and mixed states. Our results lead to a method for quantifying entanglement based on operational symmetries and has connections to quantum steering, envariance, the Reeh-Schlieder theorem, and classical entanglement.

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Certifying Einstein-Podolsky-Rosen steering via the local uncertainty principle

Cited by 57 publications

References 43 publications

Entropic Steering Criteria: Applications to Bipartite and Tripartite Systems

Entropic Steering Criteria: Applications to Bipartite and Tripartite Systems

Tight N-observable uncertainty relations and their experimental demonstrations

Operational symmetries of entangled states

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