Better Late than Never: Information Retrieval from Black Holes

Phys. Rev. Lett. 110, 101301 – Published 5 March 2013
Samuel L. Braunstein, Stefano Pirandola, and Karol Życzkowski


We show that, in order to preserve the equivalence principle until late times in unitarily evaporating black holes, the thermodynamic entropy of a black hole must be primarily entropy of entanglement across the event horizon. For such black holes, we show that the information entering a black hole becomes encoded in correlations within a tripartite quantum state, the quantum analogue of a one-time pad, and is only decoded into the outgoing radiation very late in the evaporation. This behavior generically describes the unitary evaporation of highly entangled black holes and requires no specially designed evolution. Our work suggests the existence of a matter-field sum rule for any fundamental theory.


  • Received 17 April 2012
  • Published 5 March 2013

Published by the American Physical Society under the terms of the Creative Commons Attribution 3.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

Published by the American Physical Society

Authors & Affiliations

Samuel L. Braunstein and Stefano Pirandola

  • Department of Computer Science, University of York, York YO10 5GH, United Kingdom

Karol Życzkowski

  • Institute of Physics, Jagiellonian University, 30-059 Krakow, Poland and Center for Theoretical Physics, Polish Academy of Science, 02-668 Warszawa, Poland

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