On the complexity of approximating the diamond norm

Avraham Ben-Aroya; Amnon Ta-Shma

doi:10.26421/qic10.1-2-6

On the complexity of approximating the diamond norm

Avraham Ben-Aroya^*
, Amnon Ta-Shma

^*Corresponding author for this work

School of Computer Science and AI

Research output: Contribution to journal › Article › peer-review

13 Scopus citations

Abstract

The diamond norm is a norm defined over the space of quantum transformations. This norm has a natural operational interpretation: it measures how well one can distinguish between two transformations by applying them to a state of arbitrarily large dimension. This interpretation makes this norm useful in the study of quantum interactive proof systems. In this note we exhibit an efficient algorithm for computing this norm using convex programming. Independently of us, Watrous [1] recently showed a different algorithm to compute this norm. An immediate corollary of this algorithm is a slight simplification of the argument of Kitaev and Watrous [2] that QIP ⊆ EXP.

Original language	English
Pages (from-to)	77-86
Number of pages	10
Journal	Quantum Information and Computation
Volume	10
Issue number	1-2
DOIs	https://doi.org/10.26421/qic10.1-2-6
State	Published - 1 Jan 2010

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On the complexity of approximating the diamond norm

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