Journal
JOURNAL OF MATHEMATICAL PHYSICS
Volume 57, Issue 9, Pages -Publisher
AMER INST PHYSICS
DOI: 10.1063/1.4962339
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Funding
- Spanish MINECO Project [FIS2013-40627-P]
- Generalitat de Catalunya CIRIT Project [2014 SGR 966]
- ERC (Advanced Grant IRQUAT) [ERC-267386]
- Austrian Science Fund (FWF) through START Project [Y879-N27]
- Swiss National Science Foundation [AMBIZIONE PZ00P2_161351]
- FEDER funds
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We introduce a 3-parameter class of maps (1) acting on a bipartite system which are a natural generalisation of the depolarizing channel (and include it as a special case). Then, we find the exact regions of the parameter space that alternatively determine a positive, completely positive, entanglement-breaking, or entanglement-annihilating map. This model displays a much richer behaviour than the one shown by a simple depolarizing channel, yet it stays exactly solvable. As an example of this richness, positive partial transposition but not entanglement-breaking maps is found in Theorem 2. A simple example of a positive yet indecomposable map is provided (see the Remark at the end of Section IV). The study of the entanglement-annihilating property is fully addressed by Theorem 7. Finally, we apply our results to solve the problem of the entanglement annihilation caused in a bipartite system by a tensor product of local depolarizing channels. In this context, a conjecture posed in the work of Filippov [J. Russ. Laser Res. 35, 484 (2014)] is affirmatively answered, and the gaps that the imperfect bounds of Filippov and Ziman [Phys. Rev. A 88, 032316 (2013)] left open are closed. To arrive at this result, we furthermore show how the Hadamard product between quantum states can be implemented via local operations. Published by AIP Publishing.
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