Average mutual information for random fermionic Gaussian quantum states

• URL: http://arxiv.org/abs/2412.20244v1
• Date: Sat, 28 Dec 2024 19:11:21 GMT
• Title: Average mutual information for random fermionic Gaussian quantum states
• Authors: Lucas Hackl, Mario Kieburg, Joel Maldonado,
• Abstract summary: We compute the typical mutual information in a bipartite system averaged over the ensemble of mixed Gaussian states with a fixed spectrum. We evaluate the average von Neumann entropy in a subsystem based on the level density and the average mutual information.
• Score: 0.43695508295565777
• License:
• Abstract: Studying the typical entanglement entropy of a bipartite system when averaging over different ensembles of pure quantum states has been instrumental in different areas of physics, ranging from many-body quantum chaos to black hole evaporation. We extend such analysis to open quantum systems and mixed states, where we compute the typical mutual information in a bipartite system averaged over the ensemble of mixed Gaussian states with a fixed spectrum. Tools from random matrix theory and determinantal point processes allow us to compute arbitrary k-point correlation functions of the singular values of the corresponding complex structure in a subsystem for a given spectrum in the full system. In particular, we evaluate the average von Neumann entropy in a subsystem based on the level density and the average mutual information. Those results are given for finite system size as well as in the thermodynamic limit.

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