General approach to quantum channel impossibility by local operations and classical communication

Abstract

We describe a general approach to proving the impossibility of implementing a quantum channel by local operations and classical communication (LOCC), even with an infinite number of rounds, and find that this can often be demonstrated by solving a set of linear equations. The method also allows one to design an LOCC protocol to implement the channel whenever such a protocol exists in any finite number of rounds. Perhaps surprisingly, the computational expense for analyzing LOCC channels is not much greater than that for LOCC measurements. We apply the method to several examples, two of which provide numerical evidence that the set of quantum channels that are not LOCC is not closed and that there exist channels that can be implemented by LOCC either in one round or in three rounds that are on the boundary of the set of all LOCC channels. Although every LOCC protocol must implement a separable quantum channel, it is a very difficult task to determine whether or not a given channel is separable. Fortunately, prior knowledge that the channel is separable is not required for application of our method.

To appear in Physical Review Letters. Version 2 is very close to what will be published, except no matlab code included here (arXiv didn't like mcode package). Note: semidefinite programming is no longer used in this version

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Cited by in corpus (8)

• Transformations among Pure Multipartite Entangled States via Local Operations Are Almost Never Possible
• Entanglement manipulation of multipartite pure states with finite rounds of classical communication
• LOCC protocols with bounded width per round optimize convex functions
• The Round Complexity of Local Operations and Classical Communication (LOCC) in Random-Party Entanglement Distillation
• Vector Representations of Graphs and Distinguishing Quantum Product States with One-way LOCC
• Transformations in quantum networks via local operations assisted by finitely many rounds of classical communication
• Strong bounds on required resources for quantum channels by local operations and classical communication
• Global versus Local Discrimination of Locally Implementable Multipartite Unitaries