Entanglement detection under coherent noise: Greenberger-Horne-Zeilinger-like states

Zhou, Y.

doi:10.1103/physreva.101.012301

Cited by 12 publications

(6 citation statements)

References 42 publications

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“…Another interesting point is to replace identity operator by arbitrary N -separable operator X acting on (cf. 61 ). We postpone these issues for the future research.…”

Section: Discussionmentioning

confidence: 99%

On the structure of mirrored operators obtained from optimal entanglement witnesses

Bera

Bae

Hiesmayr

et al. 2023

Sci Rep

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Entanglement witnesses (EWs) are a versatile tool in the verification of entangled states. The framework of mirrored EW doubles the power of a given EW by introducing its twin—a mirrored EW—whereby two EWs related by mirroring can bound the set of separable states more efficiently. In this work, we investigate the relation between the EWs and its mirrored ones, and present a conjecture which claims that the mirrored operator obtained from an optimal EW is either a positive operator or a decomposable EW, which implies that positive-partial-transpose entangled states, also known as the bound entangled states, cannot be detected. This conjecture is reached by studying numerous known examples of optimal EWs. However, the mirrored EWs obtained from the non-optimal ones can be non-decomposable as well. We also show that mirrored operators obtained from the extremal decomposable witnesses are positive semi-definite. Interestingly, the witnesses that violate the well known conjecture of Structural Physical Approximation, do satisfy our conjecture. The intricate relation between these two conjectures is discussed and it reveals a novel structure of the separability problem.

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“…Another interesting point is to replace identity operator by arbitrary N -separable operator X acting on (cf. 61 ). We postpone these issues for the future research.…”

Section: Discussionmentioning

confidence: 99%

On the structure of mirrored operators obtained from optimal entanglement witnesses

Bera

Bae

Hiesmayr

et al. 2023

Sci Rep

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show abstract

“…These witnesses are typically tailored for specific classes of states (e.g. [23,24]) and are generally ineffective when applied to states without the preparation information [25][26][27].…”

Section: Definitionmentioning

confidence: 99%

Characterizing correlation within multipartite quantum systems via local randomized measurements

et al. 2022

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Given a quantum system on many qubits split into a few different parties, how many total correlations are there between these parties? Such a quantity, aimed to measure the deviation of the global quantum state from an uncorrelated state with the same local statistics, plays an important role in understanding multipartite correlations within complex networks of quantum states. Yet, the experimental access of this quantity remains challenging as it tends to be non-linear, and hence often requires tomography which becomes quickly intractable as dimensions of relevant quantum systems scale. Here, we introduce a much more experimentally accessible quantifier of total correlations, which can be estimated using only single-qubit measurements. It requires far fewer measurements than state tomography, and obviates the need to coherently interfere multiple copies of a given state. Thus we provide a tool for proving multipartite correlations that can be applied to near-term quantum devices.

show abstract

“…These witnesses are typically tailored for specific classes of states (e.g. [22,23]) and are generally ineffective when apply to states without the preparation information [24][25][26].…”

Section: Definitionmentioning

confidence: 99%

Characterizing correlation within multipartite quantum systems via local randomized measurements

Liu,

Zeng,

Zhou

et al. 2021

Preprint

Self Cite

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Given a quantum system on many qubits split into a few different parties, how much total correlations are there between these parties? Such a quantity -aimed to measure the deviation of the global quantum state from an uncorrelated state with the same local statistics -plays an important role in understanding multi-partite correlations within complex networks of quantum states. Yet, the experimental access of this quantity remains challenging as it tends to be non-linear, and hence often requires tomography which becomes quickly intractable as dimensions of relevant quantum systems scale. Here, we introduce a much more experimentally accessible quantifier of total correlations, which can be estimated using only single-qubit measurements. It requires far fewer measurements than state tomography, and obviates the need to coherently interfere multiple copies of a given state. Thus we provide a tool for proving multi-partite correlations that can be applied to near-term quantum devices.

show abstract

Entanglement detection under coherent noise: Greenberger-Horne-Zeilinger-like states

Cited by 12 publications

References 42 publications

On the structure of mirrored operators obtained from optimal entanglement witnesses

On the structure of mirrored operators obtained from optimal entanglement witnesses

Characterizing correlation within multipartite quantum systems via local randomized measurements

Characterizing correlation within multipartite quantum systems via local randomized measurements

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