Free fermionic black holes as polarised mirrors

Abstract

Understanding the speed with which various classes of quantum systems can scramble information is a key goal of quantum information theory, with relevance to both fundamental physics and the study of the efficiency of quantum algorithms. Famously, such understanding enabled Hayden and Preskill to show that, under the assumption that black hole dynamics may be modelled by a Haar-random unitary, old black holes act as ''mirrors'', reflecting infalling quantum information back out again effectively instantaneously. In this work, we investigate which aspects of this mirror behaviour survive beyond the Haar-random setting by considering a random free fermionic model of black hole dynamics. We find that the rate of information release is governed by the underlying representation-theoretic structure; such a black hole acts as a ''polarised mirror'', retaining information encoded in low fermionic-degree irreps while reflecting information encoded in high fermionic-degree irreps much more rapidly. As a result of the retention of low-degree information, we show that faithful recovery of the infalling quantum information is impossible until all but a vanishing fraction of the black hole has evaporated. However, augmenting the dynamics with a fixed Clifford unitary can restore their reflective behaviour, even though the ensemble's frame potential remains unchanged and far above its Haar value. Remarkably, we find that such black holes can outperform their fully Haar-random counterparts: in the high-fidelity limit, recovering a single-qubit message requires asymptotically approximately 37% fewer emitted qubits.

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Cite

BibTeX RIS

BibTeX

@misc{krumtunger2026free,
  title = {{Free fermionic black holes as polarised mirrors}},
  author = {Maureen Krumtünger and Maxwell West},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.03304},
  eprint = {2610.03304},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.03304},
  note = {CC BY 4.0},
}

RIS

TY  - UNPB
TI  - Free fermionic black holes as polarised mirrors
AU  - Maureen Krumtünger
AU  - Maxwell West
PY  - 2026
DA  - 2026/10/02
PB  - arXiv
DO  - 10.48550/arxiv.2610.03304
UR  - https://arxiv.org/abs/2610.03304
AB  - Understanding the speed with which various classes of quantum systems can scramble information is a key goal of quantum information theory, with relevance to both fundamental physics and the study of the efficiency of quantum algorithms. Famously, such understanding enabled Hayden and Preskill to show that, under the assumption that black hole dynamics may be modelled by a Haar-random unitary, old black holes act as ''mirrors'', reflecting infalling quantum information back out again effectively instantaneously. In this work, we investigate which aspects of this mirror behaviour survive beyond the Haar-random setting by considering a random free fermionic model of black hole dynamics. We find that the rate of information release is governed by the underlying representation-theoretic structure; such a black hole acts as a ''polarised mirror'', retaining information encoded in low fermionic-degree irreps while reflecting information encoded in high fermionic-degree irreps much more rapidly. As a result of the retention of low-degree information, we show that faithful recovery of the infalling quantum information is impossible until all but a vanishing fraction of the black hole has evaporated. However, augmenting the dynamics with a fixed Clifford unitary can restore their reflective behaviour, even though the ensemble's frame potential remains unchanged and far above its Haar value. Remarkably, we find that such black holes can outperform their fully Haar-random counterparts: in the high-fidelity limit, recovering a single-qubit message requires asymptotically approximately 37% fewer emitted qubits.
ER  -

Abstract

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