Entanglement Breaking Channels, Stochastic Matrices, and Primitivity

• URL: http://arxiv.org/abs/2109.01340v1
• Date: Fri, 3 Sep 2021 06:57:43 GMT
• Title: Entanglement Breaking Channels, Stochastic Matrices, and Primitivity
• Authors: Jennifer Ahiable, David W.Kribs, Jeremy Levick, Rajesh Pereira, and Mizanur Rahaman
• Abstract summary: We consider the important class of quantum operations called entanglement breaking channels. We show how every such channel induces matrix representations that have the same non-zero spectrum as the channel. We then use this to investigate when entanglement breaking channels are primitive, and prove this depends on primitivity of the matrix representations.
• Score: 3.9146761527401424
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We consider the important class of quantum operations (completely positive trace-preserving maps) called entanglement breaking channels. We show how every such channel induces stochastic matrix representations that have the same non-zero spectrum as the channel. We then use this to investigate when entanglement breaking channels are primitive, and prove this depends on primitivity of the matrix representations. This in turn leads to tight bounds on the primitivity index of entanglement breaking channels in terms of the primitivity index of the associated stochastic matrices. We also present examples and discuss open problems generated by the work.

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