Bit threads and holographic entanglement of purification

DOI10.1007/JHEP08(2019)140zbMATH Open1421.83099arXiv1904.06871WikidataQ125903186 ScholiaQ125903186MaRDI QIDQ5970974

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Publication date: 23 September 2019

Published in: (Search for Journal in Brave)

Abstract: The entanglement of purification (EoP), which measures the classical correlations and entanglement of a given mixed state, has been conjectured to be dual to the area of the minimal cross section of the entanglement wedge in holography. Using the surface-state correspondence, we propose a `bit thread' formulation of the EoP. With this formulation, proofs of some known properties of the EoP are performed. Moreover, we show that the quantum advantage of dense code (QAoDC), which reflects the increase in the rate of classical information transmission through quantum channel due to entanglement, also admits a flow interpretation. In this picture, we can prove the monogamy relation of QAoDC with the EoP for tripartite states. We also derive a new lower bound for $S(AB)$ in terms of QAoDC, which is tighter than the one given by the Araki-Lieb inequality.

Full work available at URL: https://arxiv.org/abs/1904.06871

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