Quantum Max-flow/Min-cut release_rfgyouvolvdqvctuww3pjqfady

by Shawn X. Cui, Michael H. Freedman, Or Sattath, Richard Stong, Greg Minton

Released as a article .

2016  

Abstract

The classical max-flow min-cut theorem describes transport through certain idealized classical networks. We consider the quantum analog for tensor networks. By associating an integral capacity to each edge and a tensor to each vertex in a flow network, we can also interpret it as a tensor network, and more specifically, as a linear map from the input space to the output space. The quantum max flow is defined to be the maximal rank of this linear map over all choices of tensors. The quantum min cut is defined to be the minimum product of the capacities of edges over all cuts of the tensor network. We show that unlike the classical case, the quantum max-flow=min-cut conjecture is not true in general. Under certain conditions, e.g., when the capacity on each edge is some power of a fixed integer, the quantum max-flow is proved to equal the quantum min-cut. However, concrete examples are also provided where the equality does not hold. We also found connections of quantum max-flow/min-cut with entropy of entanglement and the quantum satisfiability problem. We speculate that the phenomena revealed may be of interest both in spin systems in condensed matter and in quantum gravity.
In text/plain format

Archived Files and Locations

application/pdf  302.6 kB
file_aboah7sr2vezfgm2exwwsqyyly
arxiv.org (repository)
web.archive.org (webarchive)
Read Archived PDF
Preserved and Accessible
Type  article
Stage   accepted
Date   2016-06-30
Version   v3
Language   en ?
arXiv  1508.04644v3
Work Entity
access all versions, variants, and formats of this works (eg, pre-prints)
Catalog Record
Revision: 3d4da2f4-d9b1-45e8-965e-0d98ce988b47
API URL: JSON