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arXiv:2602.21471 · Physics Letters A

On fully entangled fraction of arbitrary $d\otimes d$ quantum states

Xue-Na Zhu, Gui Bao, Ming Li, Ming-Jing Zhao, Shao-Ming Fei

quant-phSubmitted Feb 25, 2026• Announced Feb 26, 2026• 0 citations
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Abstract

We study the fully entangled fraction of quantum states based on the Bloch representation of density matrices. Analytical upper bounds on the fully entangled fraction are obtained for arbitrary $d\otimes d$ bipartite systems. The fully entangled fractions for classes of $d\otimes d$ quantum states are analytically derived. Detailed examples are given to illustrate the advantages of our results.

Journal reference
Physics Letters A 572 (2026) 131324
DOI
10.1016/j.physleta.2026.131324
Comments
9 pages,2 figures

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On fully entangled fraction of arbitrary d⊗dd\otimes dd⊗d quantum states
We study the fully entangled fraction of quantum states based on the Bloch representation of density matrices. Analytical upper bounds on the fully entangled fraction are obtained for arbitrary d⊗dd\otimes dd⊗d bipartite systems. The fully entangled fractions for classes of d⊗dd\otimes dd⊗d quantum states are analytically derived. Detailed examples are given to illustrate the advantages of our results.
We study the separability of bipartite quantum systems in arbitrary dimensions using the Bloch representation of their density matrix. This approach enables us to find an alternative characterization of the separability problem, from which we derive a necessary condition and sufficient conditions for separability. For a certain class of states the necessary condition and a sufficient condition turn out to be equivalent, therefore yielding a necessary and sufficient condition. The proofs of the sufficient conditions are constructive, thus providing decompositions in pure product states for the states that satisfy them. We provide examples that show the ability of these conditions to detect entanglement. In particular, the necessary condition is proved to be strong enough to detect bound entangled states.
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