Subsystem fidelity in two-dimensional conformal field theories

TL;DR

The paper develops a universal, operator-based framework to quantify state distinguishability via subsystem fidelity in 2D CFTs using twist-operator OPEs and the replica trick. It identifies universal contributions from quasiprimary families (e.g., $\mathcal X\mathcal X$, $\mathcal X\mathcal X\mathcal X$, and $T\mathcal X\mathcal X$) and validates them against exact results in free massless boson/fermion theories and numerical lattice models. The method is extended to 2D holographic CFTs, where fidelity between heavy microstates and thermal states illuminates bulk/reconstruction aspects in AdS$_3$/CFT$_2$. The work provides a cohesive approach to quantum state distinguishability across diverse 2D CFTs, linking quantum information techniques with holography and gravity.

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.

Figures (2)

• Figure 1: Comparison between CFT predictions (solid red lines) and XX spin chain results (symbols) for the subtracted fidelity $F_{(2)}-F$. The good agreement validates the short-interval expansion approach.
• Figure 2: Comparison between CFT predictions (solid red lines) and critical Ising chain results (symbols) for the subtracted fidelity $F_{(2)}-F$. The agreement demonstrates the applicability of our method to fermionic systems.