Horizons and Soft Quantum Information

TL;DR

The paper addresses how horizons decohere nearby quantum superpositions through soft memory and memory-induced infrared effects. It develops an infrared extension of Tomita-Takesaki theory to treat soft modes, and introduces a rigorous information-decoherence framework for quantum channels with horizon environments, proving the exact equality $\mathcal{I}(\mathcal{N}^{c}) = D(\mathcal{N})$. It then derives explicit expressions for the Holevo fidelity, Uhlmann fidelity, and relative entropy for general coherent states with memory, and constructs an IR-complete horizon algebra that supports factorization across horizon cuts. The results reveal that horizons act as maximally entangling environments with linearly growing distinguishability of interior states over time, and they connect these insights to scattering theory and causal horizons, offering a principled, operational description of holographic-like horizon information flow in quantum gravity.

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 any horizon) decoheres its environment as though its interior were full of optimal observers.

Figures (2)

• Figure 1: Bob can perform any possible measurement in region $\mathscr{B}_c$, defined as the region on the $-z$ side of the horizon that lies to the past of the future light cone of the horizon cut $\mathscr{C}$
• Figure 2: A spatial component $A_\mu$, tangent to the horizon, of the electromagnetic potential is plotted as a function of affine time $V$ parameterizing a horizon generator at angle $x^B$. (a) depicts a field configuration in the "easy case" of Casini et al., while (b) depicts a field configuration in the "hard case." (c) shows the result of applying a specific asymptotic symmetry transformation to (b), resulting in a field configuration in the "easy case." In particular, the final field configuration can be written as a linear combination of two field configurations: one $\Pi_c A$ supported only to the past of the horizon cut $\mathscr{C}$, and another $\Pi'_c A$ supported only to the future. However, neither of the field configurations $\Pi_c A$ and $\Pi'_c A$ decay asymptotically in time---they exhibit electromagnetic memory Bieri_2013, and thus do not lie in the standard Hilbert space of scattering theory due to their soft radiation content.

Theorems & Definitions (2)

• Definition : Channel Decoherence
• Definition : Channel Information