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arXiv:2210.16551

Strong entanglement criteria for mixed states, based on uncertainty relations

Manju Maan, Asoka Biswas, Shubhrangshu Dasgupta

Published Oct 29, 2022• 0 citations
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Abstract

We propose an entanglement criterion, specially designed for mixed states, based on uncertainty relation and the Wigner-Yanase skew information. The variances in this uncertainty relation does not involve any classical mixing uncertainty, and thus turns out to be purely of quantum mechanical nature. We show that any mixed entangled state can be characterized by our criterion. We demonstrate its utility for several generalized mixed entangled state including Werner states and it turns out to be stronger than any other known criterion in identifying the correct domain of relevant parameters for entanglement. The proposed criterion reduces to the Schrodinger-Robertson inequality for pure states.

DOI
10.48550/arxiv.2210.16551

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We formulate an entanglement criterion using Peres-Horodecki positive partial transpose operations combined with the Schr\"odinger-Robertson uncertainty relation. We show that any pure entangled bipartite and tripartite state can be detected by experimentally measuring mean values and variances of specific observables. Those observables must satisfy a specific condition in order to be used, and we show their general form in the $2\ifmmode\times\else\texttimes\fi{}2$ (two qubits) dimension case. The criterion is applied on a variety of physical systems including bipartite and multipartite mixed states and reveals itself to be stronger than the Bell inequalities and other criteria. The criterion also work on continuous variable cat states and angular momentum states of the radiation field.
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Quantum entanglement plays a critical role in many quantum applications, but detecting entanglement, especially in multipartite or high-dimensional quantum systems, remains a challenge. In this paper, we propose several families of entanglement criteria for detecting entanglement in multipartite or high-dimensional quantum states by the generalized Wigner-Yanase skew information Is(ρ,X)I^s(ρ,X)Is(ρ,X) for −1≤s≤0-1\leq s\leq0−1≤s≤0 and variance. We also reveal a complementary character between the criteria based on the generalized Wigner-Yanase skew information and an alternative one based on variance through specific examples. We illustrate the merits of these criteria and show that the combination of the entanglement criteria has a stronger detection capability, as it is capable of detecting entangled states that remain unrecognized by other criteria.
Abstract Quantum entanglement plays a critical role in many quantum applications, but detecting entanglement, especially in multipartite or high-dimensional quantum systems, remains a challenge. In this paper, we propose several families of entanglement criteria for detecting entanglement in multipartite or high-dimensional quantum states by the generalized Wigner–Yanase skew information I s ( ρ , X ) for − 1 ⩽ s ⩽ 0 and variance. We also reveal a complementary character between the criteria based on the generalized Wigner–Yanase skew information and an alternative one based on variance through specific examples. We illustrate the merits of these criteria and show that the combination of the entanglement criteria has a stronger detection capability, as it is capable of detecting entangled states that remain unrecognized by other criteria.