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A QFT information protocol for charged black holes

Paolo Palumbo

TL;DR

The paper extends algebraic quantum information tasks from type $\mathrm{II}$ to type $\mathrm{III}$ von Neumann factors to better reflect quantum field theory, where local algebras are typically type $\mathrm{III}$. It develops a quantum information retrieval protocol framed by inclusions $\mathcal{N} \subset \mathcal{M}$, relative commutants $\mathcal{A}=\mathcal{N}'\cap\mathcal{M}$, and the canonical shift $\Gamma$, with the Jones index $[\mathcal{M}:\mathcal{N}]$ governing information transfer between Alice and Bob. The Kosaki-Longo generalization to type $\mathrm{III}$ factors replaces finite-index intuition with operator-valued weights and modular theory, enabling a spacetime-compatible formulation. Applying this framework to adiabatically evaporating charged black holes within DHR superselection theory yields an index-based bound on charge emission and a relation between the statistical dimension $d(\rho)$ and information transfer, suggesting a quantization mechanism for Hawking radiation linked to parastatistics and quantum gravity effects. The work provides a rigorous algebraic route to understanding information retrieval in QFT and the fundamental limits imposed by superselection sectors on black hole radiation.

Abstract

A generalization for the quantum information retrieval protocol recently illustrated by Verlinde and van der Heijden for evaporating black holes is provided to inclusions of type III von Neumann factors. The physical interest of such scenario arises in Quantum Field Theory, where local algebras are type III von Neumann algebras. The formula obtained can be easily interpreted in terms of the statistical dimension of superselection sectors in the case of black holes undergoing charge evaporation, thanks to the index-statistics theorem, leading to a thermodynamic interpretation. A constraint on the values of the index leads to a final remark about the quantization of the charge emitted by the black hole during the evaporation process.

A QFT information protocol for charged black holes

TL;DR

The paper extends algebraic quantum information tasks from type to type von Neumann factors to better reflect quantum field theory, where local algebras are typically type . It develops a quantum information retrieval protocol framed by inclusions , relative commutants , and the canonical shift , with the Jones index governing information transfer between Alice and Bob. The Kosaki-Longo generalization to type factors replaces finite-index intuition with operator-valued weights and modular theory, enabling a spacetime-compatible formulation. Applying this framework to adiabatically evaporating charged black holes within DHR superselection theory yields an index-based bound on charge emission and a relation between the statistical dimension and information transfer, suggesting a quantization mechanism for Hawking radiation linked to parastatistics and quantum gravity effects. The work provides a rigorous algebraic route to understanding information retrieval in QFT and the fundamental limits imposed by superselection sectors on black hole radiation.

Abstract

A generalization for the quantum information retrieval protocol recently illustrated by Verlinde and van der Heijden for evaporating black holes is provided to inclusions of type III von Neumann factors. The physical interest of such scenario arises in Quantum Field Theory, where local algebras are type III von Neumann algebras. The formula obtained can be easily interpreted in terms of the statistical dimension of superselection sectors in the case of black holes undergoing charge evaporation, thanks to the index-statistics theorem, leading to a thermodynamic interpretation. A constraint on the values of the index leads to a final remark about the quantization of the charge emitted by the black hole during the evaporation process.
Paper Structure (23 sections, 15 theorems, 89 equations, 1 figure)

This paper contains 23 sections, 15 theorems, 89 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Quantum Teleportation
  3. Quantum teleportation for qubits
  4. Heisenberg picture of the teleportation scheme
  5. Jones Index and the protocol
  6. The algebras of Alice and Bob
  7. Conditional expectations and Jones basic construction
  8. The information retrieval protocol
  9. Jones Index for type III factors
  10. Towards a spacetime picture
  11. Kosaki-Longo index
  12. The protocol for charged black holes
  13. Physical setup
  14. Type $\mathrm{III}$ version of the protocol
  15. DHR superselection sectors
  16. ...and 8 more sections

Key Result

Proposition 4.2.1

If $I \in \mathrm{Dom}(\mathcal{E}^{-1})$, then $\mathcal{E}^{-1}(I) \in \mathcal{M} \cap \mathcal{M}' = \mathbb{C} I$.

Figures (1)

  • Figure 1: Visualization of the algebras introduced above. The picture is to be taken as a reference and does not represent the true picture.

Theorems & Definitions (30)

  • Definition 4.2.1
  • Proposition 4.2.1
  • proof
  • Definition 4.2.2
  • Definition 4.2.3
  • Proposition 4.2.2
  • proof
  • Proposition 4.2.3
  • proof
  • Proposition 4.2.4
  • ...and 20 more