PIRSA:18020084 Scientific Series Quantum Fields and Strings

DOI10.48660/18020084

Series: Quantum Fields and Strings

Bao, N. (2018). Conditional entanglement of purification . Perimeter Institute. https://pirsa.org/18020084

Bao, Ning. Conditional entanglement of purification . Perimeter Institute, Feb. 20, 2018, https://pirsa.org/18020084 

@misc{ pirsa_PIRSA:18020084,
  doi = {10.48660/18020084},
  url = {https://pirsa.org/18020084},
  author = {Bao, Ning},
  keywords = {Quantum Fields and Strings},
  language = {en},
  title = {Conditional entanglement of purification },
  publisher = {Perimeter Institute},
  year = {2018},
  month = {feb},
  note = {PIRSA:18020084 see, \url{https://pirsa.org}}
}

Abstract

We study the conjectured holographic duality between entanglement of purification and the entanglement wedge cross-section. We generalize both quantities and prove several information theoretic inequalities involving them. These include upper bounds on conditional mutual information and tripartite information, as well as a lower bound for tripartite information. These inequalities are proven both holographically and for general quantum states. In addition, we use the cyclic entropy inequalities to derive a new holographic inequality for the entanglement wedge cross-section, and provide numerical evidence that the corresponding inequality for the entanglement of purification may be true in general. Finally, we use intuition from bit threads to extend the conjecture to holographic duals of suboptimal purifications.

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