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Open Quantum Systems Decoherence
A New Perspective on the Average Mixing Matrix
arXiv
Authors: Gabriel Coutinho, Chris Godsil, Krystal Guo, Hanmeng Zhan
Year
2017
Paper ID
7553
Status
Preprint
Abstract Read
~2 min
Abstract Words
87
Citations
N/A
Abstract
We consider the continuous-time quantum walk defined on the adjacency matrix of a graph. At each instant, the walk defines a mixing matrix which is doubly-stochastic. The average of the mixing matrices contains relevant information about the quantum walk and about the graph. We show that it is the matrix of transformation of the orthogonal projection onto the commutant algebra of the adjacency matrix, restricted to diagonal matrices. Using this formulation of the average mixing matrix, we find connections between its rank and automorphisms of the graph.
Why This Paper Matters
- This paper contributes to the Open Quantum Systems & Decoherence research area in the Quantum Articles archive.
- It adds a 2017 reference point for readers tracking recent quantum research.
- We consider the continuous-time quantum walk defined on the adjacency matrix of a graph.
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