Subsystem fidelity in two-dimensional conformal field theories

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.

21 pages, 2 figures; v2, 26 pages, 4 figures, published version

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