Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

From state distinguishability to effective bulk locality

Nima Lashkari, Joan Simon

TL;DR

The paper tackles how unitarity can coexist with an emergent bulk locality in black hole physics by analyzing a microcanonical subspace ${\cal H}_E$ of dimension $d_E$ and the maximally mixed state $\Omega_E=\mathbb{I}_E/d_E$. It introduces a quantitative framework based on quantum information theory to identify observables ${\cal A}$ that can distinguish microstates, showing that distinguishability $D_{\mathcal{A}}$ is exponentially suppressed unless the observable has about $N({\cal A})\sim\sqrt{d_E}$ outcomes, and that achieving such resolution requires either exponentially long times or large energies. This implies that bulk locality emerges only after coarse-graining to low-energy observables ${\cal A}_{low}$, providing a quantitative link between typicality, concentration of measure, and holographic locality, and connecting with black hole complementarity and interior constructions like Papadodimas–Raju. The results argue that EFT breakdown is inevitable for microstate-resolving measurements, while low-energy bulk physics remains effectively local and compatible with a geometric interior in the appropriate observable regime. Overall, the work clarifies the conditions under which locality is an emergent, coarse-grained feature of quantum gravity and how it coexists with unitary black hole evolution.

Abstract

We provide quantitative evidence that the emergence of an effective notion of spacetime locality in black hole physics is due to restricting to the subset of observables that are unable to resolve black hole microstates from the maxi- mally entangled state. We identify the subset of observables in the full quantum theory that can distinguish microstates, and argue that any measurement of such observables involves either long times or large energies, both signaling the breaking down of effective field theory where locality is manifest. We discuss some of the implications of our results for black hole complementarity and the existence of black hole interiors.

From state distinguishability to effective bulk locality

TL;DR

The paper tackles how unitarity can coexist with an emergent bulk locality in black hole physics by analyzing a microcanonical subspace of dimension and the maximally mixed state . It introduces a quantitative framework based on quantum information theory to identify observables that can distinguish microstates, showing that distinguishability is exponentially suppressed unless the observable has about outcomes, and that achieving such resolution requires either exponentially long times or large energies. This implies that bulk locality emerges only after coarse-graining to low-energy observables , providing a quantitative link between typicality, concentration of measure, and holographic locality, and connecting with black hole complementarity and interior constructions like Papadodimas–Raju. The results argue that EFT breakdown is inevitable for microstate-resolving measurements, while low-energy bulk physics remains effectively local and compatible with a geometric interior in the appropriate observable regime. Overall, the work clarifies the conditions under which locality is an emergent, coarse-grained feature of quantum gravity and how it coexists with unitary black hole evolution.

Abstract

We provide quantitative evidence that the emergence of an effective notion of spacetime locality in black hole physics is due to restricting to the subset of observables that are unable to resolve black hole microstates from the maxi- mally entangled state. We identify the subset of observables in the full quantum theory that can distinguish microstates, and argue that any measurement of such observables involves either long times or large energies, both signaling the breaking down of effective field theory where locality is manifest. We discuss some of the implications of our results for black hole complementarity and the existence of black hole interiors.

Paper Structure

This paper contains 26 sections, 3 theorems, 82 equations.

Table of Contents

  1. Introduction
  2. Black holes vs Quantum Statistical Mechanics
  3. Distinguishing quantum states
  4. Expectation value of operators
  5. Ensemble average:
  6. Time average:
  7. Ensemble vs time averages:
  8. Ensemble vs time averages:
  9. The use of typicality on expectation values
  10. Ensemble average:
  11. Time average:
  12. Ensemble vs time averages:
  13. Measure of distinguishability
  14. Coarse-grained observables
  15. Relation to coarse-grained observables :
  16. ...and 11 more sections

Key Result

Lemma 3.1

Levy's lemma: Given a bounded function $f(\psi)$ defined over the set of pure states $\psi \in {\cal H}_E$, for any such random state $\psi$ and any $\epsilon > 0$ where $c=(18\pi^3)^{-1}$, $d_E$ is the dimension of $\mathcal{H}_E$, and $\lambda=\sup|\nabla f|$ is the Lipschitz constant of the function $f(\psi)$.

Theorems & Definitions (3)

  • Lemma 3.1
  • Theorem 3.2
  • Theorem 3.3