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  • Open Access

Horizons and soft quantum information

Daine L. Danielson1,2,3,* and Gautam Satishchandran4,†

  • *Contact author: daine@mit.edu
  • †Contact author: gautam93@mit.edu
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Phys. Rev. D 114, 085003 – Published 6 October, 2026

DOI: https://doi.org/10.1103/mk9b-3qzz

Abstract

It was recently shown that black holes decohere any quantum superpositions in their vicinity. This decoherence is mediated by soft radiation through the horizon, and can be understood as the result of the fact that quantum states in the exterior source distinguishable states of long-range fields in the interior. To study this phenomenon and others, we extend Tomita-Takesaki theory to accommodate states of soft radiation such as arise in the electromagnetic and gravitational memory effects, and provide a general framework for computing the distinguishability of general coherent states. Applying these tools, we use the methods of unambiguous state discrimination and approximate quantum error correction to prove some new relations regarding the distinguishability of quantum states, and the quantum information content of soft radiation, and thereby show that a black hole (or, under the conditions stated below, any causal horizon) decoheres its environment as though its interior were full of optimal observers.

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Phys. Rev. D 114, 085003– Published 6 October, 2026
  • Received 26 February 2026
  • Accepted 17 June 2026
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