When a quantum measurement can be implemented locally ... and when it cannot

Abstract

Local operations on subsystems and classical communication between parties (LOCC) constitute the most general protocols available on spatially separated quantum systems. Every LOCC protocol implements a separable generalized measurement -- a complete measurement for which every outcome corresponds to a tensor product of operators on individual subsystems -- but it is known that there exist separable measurements that cannot be implemented by LOCC. A longstanding problem in quantum information theory is to understand the difference between LOCC and the full set of separable measurements. In this paper, we show how to construct an LOCC protocol to implement an arbitrary separable measurement, except that with those measurements for which no LOCC protocol exists, the method shows explicitly that this is the case.

21 pages, 7 figures. Extensively revised to include details of all arguments, explicitly proving all results in full rigor. Version 3 has sections reordered and other restructuring, but otherwise contains the same discussion as version 2

References in corpus (2)

• Local Transformations Requiring Infinite Rounds of Classical Communication
• Separable Operations on Pure States

Cited by in corpus (10)

• Quantum causal modelling
• A framework for bounding nonlocality of state discrimination
• Difficulty of distinguishing product states locally
• General approach to quantum channel impossibility by local operations and classical communication
• Local quantum protocols for separable measurements with many parties
• 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
• Devising local protocols for multipartite quantum measurements
• Extended necessary condition for local operations and classical communication: Tight bound for all measurements
• Multi-partite subspaces containing no locally inaccessible information