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Entanglement of Purification in Random Tensor Networks
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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.
Forward citations
Cited by 2 Pith papers
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Optimal symmetry operators
The Araki cone α=0 purification uniquely attains the Uhlmann fidelity, defining an 'optimal symmetry operator' with maximal expectation value.
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R\'enyi Entanglement of Purification and Half R\'enyi Reflected Entropy in Free Scalar Theory
In a free scalar lattice model, numerical calculations show Rényi entanglement of purification is at least half the Rényi reflected entropy for 0 < n < 2 in the small subsystems tested.
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