dc.creator | Bausch, Johannes | |
dc.creator | Cubitt, Toby | |
dc.date.accessioned | 2018-11-24T23:18:48Z | |
dc.date.available | 2016-04-08T14:40:33Z | |
dc.date.available | 2018-11-24T23:18:48Z | |
dc.date.issued | 2016-04-08 | |
dc.identifier | https://www.repository.cam.ac.uk/handle/1810/254895 | |
dc.identifier.uri | http://repository.aust.edu.ng/xmlui/handle/123456789/3343 | |
dc.description.abstract | We address two sets of long-standing open questions in linear algebra and probability theory, from a computational complexity perspective: stochastic matrix divisibility, and divisibility and decomposability of probability distributions. We prove that finite divisibility of stochastic matrices is an NP-complete problem, and extend this result to nonnegative matrices, and completely-positive trace-preserving maps, i.e. the quantum analogue of stochastic matrices. We further prove a complexity hierarchy for the divisibility and decomposability of probability distributions, showing that finite distribution divisibility is in P, but decomposability is NP-hard. For the former, we give an explicit polynomial-time algorithm. All results on distributions extend to weak-membership formulations, proving that the complexity of these problems is robust to perturbations. | |
dc.language | en | |
dc.publisher | Elsevier | |
dc.publisher | Linear Algebra and its Applications | |
dc.rights | http://creativecommons.org/licenses/by/4.0/ | |
dc.rights | Attribution 4.0 International | |
dc.subject | stochastic matrices | |
dc.subject | cptp maps | |
dc.subject | probability distributions | |
dc.subject | divisibility | |
dc.subject | decomposability | |
dc.subject | complexity theory | |
dc.title | The Complexity of Divisibility | |
dc.type | Article | |