Distinguishing multi-partite states by local measurements

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.

18 pages, 6 figures, 1 unreferenced reference

References in corpus (2)

• Evenly distributed unitaries: on the structure of unitary designs
• Some applications of hypercontractive inequalities in quantum information theory

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