Local quantum protocols for separable measurements with many parties

Abstract

In a recent paper \cite{mySEPvsLOCC}, we showed how to construct a quantum protocol for implementing a bipartite, separable quantum measurement using only local operations on subsystems and classical communication between parties (LOCC) within any fixed number of rounds of communication, whenever such a protocol exists. Here, we generalize that construction to one that applies for any number of parties. One important observation is that the construction automatically determines the ordering of the parties' measurements, overcoming a significant apparent difficulty in designing protocols for more than two parties. We also present various other results about LOCC, including showing that if, in any given measurement operator of the separable measurement under consideration, the local parts for two different parties are rank-1 operators that are not repeated in any other measurement operator of the measurement, then this separable measurement cannot be exactly implemented by LOCC in any finite number of rounds.

Comments welcome. 13 pages, 5 figures

References in corpus (4)

• Multipartite Nonlocality without Entanglement in Many Dimensions
• Separable Operations on Pure States
• Nonlocal Entanglement Transformations Achievable by Separable Operations
• Implementation of multipartite unitary operations with limited resources

Cited by in corpus (6)

• General approach to quantum channel impossibility by local operations and classical communication
• Necessary condition for local quantum operations and classical communication with extensive violation by separable operations
• Conditions for uniqueness of product representations for separable quantum channels and separable quantum states
• Truncated moment sequences and a solution to the channel separability problem
• Devising local protocols for multipartite quantum measurements
• Extended necessary condition for local operations and classical communication: Tight bound for all measurements