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Article Dans Une Revue Information Processing Letters Année : 2017

Checking the strict positivity of Kraus maps is NP-hard

Vérifier la positivité stricte d'une application de Kraus est NP-dur

Résumé

Basic properties in Perron-Frobenius theory are positivity, primitivity, and irreducibility. Whereas these properties can be checked in polynomial time for stochastic matrices, we show that for Kraus maps - the noncommutative generalization of stochastic matrices - checking positivity is NP-hard. This is in contrast with irreducibility and primitivity, which we show to be checkable in strongly polynomial time for completely positive maps - the noncommutative generalization of nonpositive matrices. As an intermediate result, we get that the bilinear feasibility problem over $\mathbb{Q}$ is NP-hard.

Dates et versions

hal-01097942 , version 1 (22-12-2014)

Identifiants

Citer

Stéphane Gaubert, Zheng Qu. Checking the strict positivity of Kraus maps is NP-hard. Information Processing Letters, 2017, 118, pp.35--43. ⟨10.1016/j.ipl.2016.09.008⟩. ⟨hal-01097942⟩
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