PIRSA:18080084 Scientific Series Quantum Information

DOI10.48660/18080084

Series: Perimeter Institute Quantum Discussions

Wilming, H. (2018). Single-shot interpretations of von Neumann entropy. Perimeter Institute. https://pirsa.org/18080084

Wilming, Henrik. Single-shot interpretations of von Neumann entropy. Perimeter Institute, Aug. 29, 2018, https://pirsa.org/18080084 

@misc{ pirsa_PIRSA:18080084,
  doi = {10.48660/18080084},
  url = {https://pirsa.org/18080084},
  author = {Wilming, Henrik},
  keywords = {Quantum Information},
  language = {en},
  title = {Single-shot interpretations of von Neumann entropy},
  publisher = {Perimeter Institute},
  year = {2018},
  month = {aug},
  note = {PIRSA:18080084 see, \url{https://pirsa.org}}
}

Abstract

In quanum physics, the von Neumann entropy usually arises in i.i.d settings, while single-shot settings are commonly characterized by smoothed min- or max-entropies. In this talk, I will discuss new results that give single-shot interpretations to the von Neumann entropy under appropriate conditions. I first present new results that give a single-shot interpretation to the Area Law of entanglement entropy in many-body physics in terms of compression of quantum information on the boundary of a region of space. Then I show that the von Neumann entropy governs single-shot transitions whenever one has access to arbitrary auxiliary systems, which have to remain invariant in a state-transition ("catalysts"), as well as a decohering environment. Getting rid of the decohering environment yields the "catalytic entropy conjecture", for which I present some supporting arguments.

If time permits, I also discuss some applications of these result to thermodynamics and speculate about consequences for quantum information theory and holography.

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