Some absolutely separable states can generate entanglement probabilistically via purity-non-generating operations, but completely absolutely separable states cannot; a new sufficient separability condition based only on largest and smallest eigenvalues and local dimension is derived.
Is absolute separability determined by the partial transpose?
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abstract
The absolute separability problem asks for a characterization of the quantum states $\rho \in M_m\otimes M_n$ with the property that $U\rho U^\dagger$ is separable for all unitary matrices $U$. We investigate whether or not it is the case that $\rho$ is absolutely separable if and only if $U\rho U^\dagger$ has positive partial transpose for all unitary matrices $U$. In particular, we develop an easy-to-use method for showing that an entanglement witness or positive map is unable to detect entanglement in any such state, and we apply our method to many well-known separability criteria, including the range criterion, the realignment criterion, the Choi map and its generalizations, and the Breuer-Hall map. We also show that these two properties coincide for the family of isotropic states, and several eigenvalue results for entanglement witnesses are proved along the way that are of independent interest.
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quant-ph 2years
2026 2verdicts
UNVERDICTED 2roles
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Introduces absolute Schmidt number for states invariant under global unitaries, with witness and moment-based detection methods plus resource measures, extended to covariant channels.
citing papers explorer
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Fundamental limitations on entanglement extraction from purity
Some absolutely separable states can generate entanglement probabilistically via purity-non-generating operations, but completely absolutely separable states cannot; a new sufficient separability condition based only on largest and smallest eigenvalues and local dimension is derived.
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Absolute Schmidt number: characterization, detection and resource-theoretic quantification
Introduces absolute Schmidt number for states invariant under global unitaries, with witness and moment-based detection methods plus resource measures, extended to covariant channels.