Exact analytical relation between the entropies and the dominant eigenvalue of random reduced density matrices

• URL: http://arxiv.org/abs/2204.01754v4
• Date: Wed, 16 Nov 2022 13:52:36 GMT
• Title: Exact analytical relation between the entropies and the dominant eigenvalue of random reduced density matrices
• Authors: Ruge Lin
• Abstract summary: In this paper, we show how the entropy (including the von Neumann entropy) obtained by tracing across various sizes of subsystems is related to their dominant eigenvalue. The correlation between our study and entanglement generated by quantum computing is provided with various examples.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In this paper, we show how the entropy (including the von Neumann entropy obtained by tracing across various sizes of subsystems, the entanglement gap, as well as different degrees of R\'{e}nyi entropy) of the random reduced density matrices are related to their dominant eigenvalue. Analytical results are deduced from Random Matrix Theory (RMT) for decentralized Wishart matrices and backed up by computer simulations. The correlation between our study and entanglement generated by quantum computing is provided with various examples.

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