Physics – Quantum Physics
Scientific paper
2011-07-16
Physics
Quantum Physics
10 pages. Comments are welcome
Scientific paper
In order to better understand the class of quantum operations that preserve the positivity of partial transpose (PPT operations) and its relation to the widely used class of local operations and classical communication (LOCC), we study the problem of distinguishing orthogonal maximally entangled states (MES) by PPT operations. Firstly, we outline a rather simple proof to show that the number of $d\otimes d$ PPT distinguishable MES is at most $d$, which slightly generalizes existing results on this problem. Secondly, we construct 4 MES in $4\otimes 4$ state space that cannot be distinguished by PPT operations. Before our work, it was unknown whether there exists $d$ MES in $d\otimes d$ state space that are locally indistinguishable. This example leads us to a novel phenomenon of "Entanglement Catalysis Discrimination". Moreover, we find there exists a set of locally indistinguishable states $K$ such that $K^{\otimes m}$ is locally distinguishable for some finite $m$. As an interesting application, we exhibit a quantum channel with one sender and two receivers, whose one-shot zero-error local capacity is not optimal, but multi-use would enhance the capacity to achieve the full output dimension even without entangled input. Finally, we consider the entanglement cost of distinguishing three Bell states and a $2\otimes 2$ entangled basis. In the former case a bipartite pure entangled state with the largest Schmidt coefficient at most 2/3 is necessary and sufficient, while in the latter case an additional Bell state, or one ebit, should be supplied.
Duan Runyao
Ying Mingsheng
Yu Nengkun
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