Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4950918 | Information Processing Letters | 2017 | 9 Pages |
Abstract
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 Q is NP-hard.
Related Topics
Physical Sciences and Engineering
Computer Science
Computational Theory and Mathematics
Authors
Stéphane Gaubert, Zheng Qu,