Local approximation of multipartite quantum measurements

Abstract

We provide a necessary condition that a quantum measurement can be implemented by the class of protocols known as Local Operations and Classical Communication, or LOCC, including when an error is allowed but must vanish in the limit of an infinite number of rounds, a case referred to as asymptotic LOCC. Our condition unifies, extends, and provides an intuitive, geometric justification for previous results on asymptotic LOCC. We use our condition to answer a variety of long-standing, unsolved problems, including for distinguishability of certain sets of states by LOCC. These include various classes of unextendible product bases, for which we prove they cannot be distinguished by LOCC even when infinite resources are available and asymptotically vanishing error is allowed.

Comments welcome. Latest (close to published) version has a new title and is greatly expanded by inclusion of many examples of applications illustrating the power of our main result, Theorem $1$. One of the referee's on the paper noted that Theorem $1$ "constitutes a major breakthrough in the field of asymptotic LOCC" . . . in case that piques anyone's interest. :)

References in corpus (7)

• Supplementary information for "Quantum supremacy using a programmable superconducting processor"
• Quantum cryptography: Public key distribution and coin tossing
• Quantum Resource Theories
• Quantum teleportation in high dimensions
• Experimental high-dimensional quantum teleportation
• Understanding entanglement as resource: locally distinguishing unextendible product bases
• A class of unambiguous state discrimination problems achievable by separable measurements but impossible by local operations and classical communication

Cited by in corpus (2)

• Local approximation for perfect discrimination of quantum states
• Graph theoretic quantum contextuality and unextendible Product Bases