Distinguishing multi-partite states by local measurements

TL;DR

This paper investigates the distinguishability norm for multi-partite quantum states under local measurements, revealing its relation to a multi-party Hilbert-Schmidt norm and implications for LOCC measurement schemes.

Contribution

It demonstrates that the local measurement distinguishability norm is essentially equivalent to a multi-party Hilbert-Schmidt norm, with constants depending only on the number of parties.

Findings

Norms are equivalent up to constants depending only on the number of parties.

Implications for LOCC measurement schemes and data hiding are discussed.

Results suggest optimality bounds for multi-party data hiding schemes.

Abstract

We analyze the distinguishability norm on the states of a multi-partite system, defined by local measurements. Concretely, we show that the norm associated to a tensor product of sufficiently symmetric measurements is essentially equivalent to a multi-partite generalisation of the non-commutative 2-norm (aka Hilbert-Schmidt norm): in comparing the two, the constants of domination depend only on the number of parties but not on the Hilbert spaces dimensions. We discuss implications of this result on the corresponding norms for the class of all measurements implementable by local operations and classical communication (LOCC), and in particular on the leading order optimality of multi-party data hiding schemes.