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This paper presents a significant theoretical advance by providing the first randomized polynomial-time algorithm for determining quantum separability with a fixed constant gap, resolving a long-standing complexity question in this domain. The result is strictly relevant to researchers working on foundational problems in quantum information theory and computational physics where efficient verification of state properties is critical. It does not address practical hardware implementation or current commercial applications but rather establishes new boundaries for what can be efficiently computed regarding bipartite density matrices.

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Quantum Separability in Polynomial Time

arXiv28 iulie 20261 min de cititArticolul și perspectiva sunt în engleză.

arXiv:2607.23773v1 Announce Type: new Abstract: The quantum separability problem asks whether a bipartite density matrix is separable or is $\eta$-far from every separable state. We give a randomized polynomial-time algorithm for this problem for every fixed constant gap $\eta>0$, when distance is measured in the Euclidean norm.

Abstract:The quantum separability problem asks whether a bipartite density matrix is separable or is $\eta$-far from every separable state. We give a randomized polynomial-time algorithm for this problem for every fixed constant gap $\eta>0$, when distance is measured in the Euclidean norm.

arXiv:2607.23773 [quant-ph]

(or arXiv:2607.23773v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2607.23773 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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