Necessary condition for local quantum operations and classical communication with extensive violation by separable operations

Abstract

We give a conceptually simple necessary condition such that a separable quantum operation can be implemented by local operations on subsystems and classical communication between parties (LOCC), a condition which follows from a novel approach to understanding LOCC. This necessary condition holds for any number of parties and any finite number of rounds of communication and as such, also provides a completely general sufficient condition that a given separable operation cannot be exactly implemented by LOCC. Furthermore, it demonstrates an extremely strong difference between separable operations and LOCC, in that there exist examples of the former for which the condition is extensively violated. More precisely, the violation by separable operations of our necessary condition for LOCC grows without limit as the number of parties increases.

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Cited by in corpus (5)

• A class of unambiguous state discrimination problems achievable by separable measurements but impossible by local operations and classical communication
• Conditions for uniqueness of product representations for separable quantum channels and separable quantum states
• Devising local protocols for multipartite quantum measurements
• Local approximation of multipartite quantum measurements
• Extended necessary condition for local operations and classical communication: Tight bound for all measurements