Subsystem fidelity in two-dimensional conformal field theories

TL;DR

This paper develops a universal framework for analyzing subsystem fidelity in 2D conformal field theories, connecting quantum information measures with applications in quantum gravity and holography.

Contribution

It introduces a short-interval expansion method using OPE of twist operators, applicable to various 2D CFTs including holographic theories, with universal and specific results.

Findings

Universal contributions from quasiprimary operators derived

Excellent agreement with known analytical and numerical results

Method extended to holographic CFTs for black hole microstate analysis

Abstract

We investigate the short-interval expansion of the subsystem fidelity in two-dimensional conformal field theories (2D CFTs) using the operator product expansion (OPE) of twist operators. We obtain universal contributions from general quasiprimary operators valid for arbitrary 2D CFTs, along with specific results in free massless boson and fermion theories. The analytical predictions demonstrate excellent agreement with established analytical results in field theories and numerical calculations in integrable models. Furthermore, we extend the method to holographic CFTs, where subsystem fidelity serves to analyze the distinguishability of black hole microstates through the AdS/CFT correspondence. This work establishes a unified framework for quantifying quantum state distinguishability across various 2D CFTs, bridging quantum information techniques with applications in quantum gravity.