Certifying entangled measurements in known Hilbert spaces

TL;DR

This paper investigates conditions under which joint measurements in known Hilbert spaces can be certified as entangled, demonstrating that outcome statistics can reveal the measurement's nature when system dimensions are known.

Contribution

It establishes criteria for certifying entangled measurements in known Hilbert spaces based on outcome statistics and system dimensionality assumptions.

Findings

Outcome statistics can certify entangled measurements when system dimensions are known.

Certain measurement scenarios cannot be simulated by local operations and classical communication.

The approach provides a method to verify measurement entanglement in quantum systems.

Abstract

We study under which conditions it is possible to assert that a joint demolition measurement cannot be simulated by Local Operations and Classical Communication. More concretely, we consider a scenario where two parties, Alice and Bob, send each an unknown state to a third party, Charlie, who in turn interacts with the states in some undisclosed way and then announces an outcome. We show that, under the assumption that Alice and Bob know the dimensionality of their systems, there exist situations where the statistics of the outcomes reveals the nature of Charlie's measurement.