Entanglement of Purification in Random Tensor Networks

Chris Akers; Thomas Faulkner; Simon Lin; Pratik Rath

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arXiv · 2306.06163

Entanglement of Purification in Random Tensor Networks

Chris Akers·Thomas Faulkner·Simon Lin·Pratik Rath

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Abstract

The entanglement of purification $E_P(A\colon B)$ is a powerful correlation measure, but it is notoriously difficult to compute because it involves an optimization over all possible purifications. In this paper, we prove a new inequality: $E_P(A\colon B)\geq \frac{1}{2}S_R^{(2)}(A\colon B)$, where $S_R^{(n)}(A\colon B)$ is the Renyi reflected entropy. Using this, we compute $E_P(A\colon B)$ for a large class of random tensor networks at large bond dimension and show that it is equal to the entanglement wedge cross section $EW(A\colon B)$, proving a previous conjecture motivated from AdS/CFT.

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hep-th cond-mat.stat-mech gr-qc quant-ph

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Chris Akers, Thomas Faulkner, Simon Lin, Pratik Rath. 2023-06-09. Entanglement of Purification in Random Tensor Networks. https://arxiv.org/abs/2306.06163

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