Quantum Entanglement & Purity Testing: A Graph Zeta Function Perspective

• URL: http://arxiv.org/abs/2307.03321v2
• Date: Tue, 11 Jul 2023 12:52:33 GMT
• Title: Quantum Entanglement & Purity Testing: A Graph Zeta Function Perspective
• Authors: Zachary P. Bradshaw and Margarite L. LaBorde
• Abstract summary: We show that a recently developed pure state separability algorithm based on the symmetric group is equivalent to the condition that the coefficients in the exponential expansion of this zeta function are unity. There is a one-to-one correspondence between the nonzero eigenvalues of a density matrix and the singularities of its zeta function.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We assign an arbitrary density matrix to a weighted graph and associate to it a graph zeta function that is both a generalization of the Ihara zeta function and a special case of the edge zeta function. We show that a recently developed bipartite pure state separability algorithm based on the symmetric group is equivalent to the condition that the coefficients in the exponential expansion of this zeta function are unity. Moreover, there is a one-to-one correspondence between the nonzero eigenvalues of a density matrix and the singularities of its zeta function. Several examples are given to illustrate these findings.

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