arXiv:2405.11741 · Physical Review A

Quantum entanglement estimation via symmetric-measurement-based positive maps

Jiaxin Li, Hongmei Yao, Shao-Ming Fei, Zhaobing Fan, Haitao Ma

Published May 15, 2024• 11 citations

Abstract

We provide a class of positive and trace-preserving maps based on symmetric measurements. From these positive maps we present separability criteria, entanglement witnesses, and the lower bounds of concurrence. We show by detailed examples that our separability criteria, entanglement witnesses, and lower bounds can detect and estimate the quantum entanglement better than existing related results.

DOI: 10.1103/physreva.109.052426

Related papers

Symmetric measurement-induced lower bounds of concurrence

Hao‐Fan Wang, Shao-Ming Fei

We provide a class of lower bounds for concurrence based on symmetric measurements. We show that our lower bounds estimate the quantum entanglement better than some existing lower bounds by detailed examples. Moreover, our lower bounds can be experimentally identified without state tomography.

arXiv:2503.21177Physical Review AMar 26, 20257 citations

Indecomposable entanglement witnesses from symmetric measurements

Katarzyna Siudzińska

We propose a family of positive maps constructed from a recently introduced class of symmetric measurements. These maps are used to define entanglement witnesses, which include other popular approaches with mutually unbiased bases and mutually unbiased measurements. A particular interest is given to indecomposable witnesses that can be used to detect entanglement of quantum states with positive partial transposition. We present several examples for different number of measurements.

arXiv:2202.04046Feb 8, 20220 citations

Lower Bound of Concurrence Based on Generalized Positive Maps

秦慧慧, 费少明

We study the concurrence of arbitrary dimensional bipartite quantum systems. By using a positive but not completely positive map, we present an analytical lower bound of concurrence. Detailed examples are used to show that our bound can detect entanglement better and can improve the well known existing lower bounds.

Communications in Theoretical PhysicsJan 1, 20130 citations

Lower Bound of Concurrence Based on Generalized Positive Maps

Huihui Qin, Shao-Ming Fei

arXiv:1401.1624Communications in Theoretical PhysicsDec 1, 20132 citations

Quantum Separability Criteria Based on Symmetric Measurements

Yu Lu, Wen Zhou, Meng Su +3 more

We propose experimentally feasible separability criteria for bipartite systems based on local symmetric measurements. Through detailed examples, we demonstrate that our criteria can detect entanglement more effectively compared to existing counterparts. Furthermore,we demonstrate the potential for our results to be generalized to general multipartite systems.

quant-pharXiv:2512.10380Physical Review ADec 12, 20250 citations

Improved separability criteria via some classes of measurements

Shen, S., Li, M., Li-Jost, X. +1 more

The entanglement detection via local measurements can be experimentally implemented. Based on mutually unbiased measurements and general symmetric informationally complete positive-operator-valued measures, we present separability criteria for bipartite quantum states, which, by theoretical analysis, are stronger than the related existing criteria via these measurements. Two detailed examples are supplemented to show the efficiency of the presented separability criteria.

Jan 1, 201813 citations