The absolute separability problem asks for a characterization of the quantum states ρ∈Mm⊗Mn with the property that UρU† is separable for all unitary matrices U. We investigate whether or not it is the case that ρ is absolutely separable if and only if UρU† 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.
Additional Metadata
THEME Null option (theme 11)
Publisher Rinton
Journal Quantum Information and Computation
Project Progress in quantum computing:Algorithms, communication, and applications
Grant This work was funded by the European Commission 7th Framework Programme; grant id erc/615307 - Progress in quantum computing: Algorithms, communication, and applications (QPROGRESS)
Citation
Arunachalam, S, Johnston, N, & Russo, V. (2015). Is absolute separability determined by the partial transpose?. Quantum Information and Computation, 15(7&8), 694–720.