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arXiv:2606.31010

Estimating the concurrence for quantum states via symmetric measurements

Hao-Fan Wang, Wen Zhou, Lin Chen, Li Xu, Shao-Ming Fei

quant-phSubmitted Jun 30, 2026• Announced Jul 1, 2026• 0 citations
v1 · Jun 30, 2026v2 · Jul 2, 2026v3 · Oct 17, 2026
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Abstract

We derive improved lower bounds of concurrence induced by symmetric measurements, which retains experimental feasibility without state tomography. More importantly, we resolve a related inequality conjecture, which implies that numerous previous results based on symmetric measurements are strictly stronger than the one based on realignment. In addition, we also present a lower bound of genuine tripartite entanglement concurrence based on symmetric measurements.

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We derive improved lower bounds of concurrence induced by symmetric measurements, which retains experimental feasibility without state tomography. More importantly, we resolve a related inequality conjecture, which implies that numerous previous results based on symmetric measurements are strictly stronger than the one based on realignment. In addition, we also present a lower bound of genuine tripartite entanglement concurrence based on symmetric measurements.
The detection and estimation of quantum entanglement are the essential issues in the theory of quantum entanglement. We construct matrices based on the realignment of density matrices and the vectorization of the reduced density matrices, from which a family of separability criteria are presented for both bipartite and multipartite systems. Moreover, tighter lower bounds of concurrence and convex-roof extended negativity are derived. Criteria are also given to detect the genuine tripartite entanglement. Lower bounds of the concurrence of genuine tripartite entanglement are presented. By detailed examples we show that our results are better than the corresponding ones in identifying and estimating quantum entanglement as well as genuine multipartite entanglement.
We present a lower bound of concurrence for arbitrary-dimensional bipartite quantum states. This lower bound may be used to improve all the known lower bounds of concurrence. Moreover, the lower bound gives rise to an operational sufficient criterion of distillability of quantum entanglement. The significance of our result is illustrated by quantitative evaluation of entanglement for entangled states that fail to be identified by the usual concurrence estimation method and by showing the distillability of mixed states that cannot be recognized by other distillability criteria.