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arXiv:2304.05249 · Physical Review A

All multipartite entanglements are quantum coherences in locally distinguishable bases

Ahana Ghoshal, Swati Choudhary, Ujjwal Sen

Published Sep 2, 2025• 4 citations
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Abstract

We find that the m-separability and k-partite entanglement of a multipartite quantum system is correlated with quantum coherence of the same with respect to complete orthonormal bases, distinguishable under local operations and classical communication in certain partitions. In particular, we show that the geometric measure of m-inseparable entanglement of a multipartite quantum state is equal to the square of minimum fidelity-based quantum coherence of the state with respect to complete orthonormal bases, that are locally distinguishable in a partition into m-parties.

DOI
10.1103/3pxs-vpst

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Abstract Entanglement is a defining feature of quantum mechanics, producing correlations between the results of spacelike-separated measurements which cannot be explained by any local, single-world theory of nature. In this paper we employ a rigorous mathematical approach to explore the classification of bases for quantum systems by their entanglement properties. For bipartite systems, a basis is said to have type if it contains p entangled states and q separable states. Our main result is to prove a long-standing conjecture of Eakins and Jaroszkiewicz stating that no type orthonormal (o.n.) basis exists: an o.n. basis containing an entangled state is guaranteed to contain at least one other. Furthermore, we prove that o.n. bases of all other types do exist, before moving on to discuss the multipartite case. Our results show that there are fundamental constraints on the emergence of nonlocality in general orthogonal measurement.
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