Relative Entropies in Conformal Field Theory

Abstract

Relative entropy is a measure of distinguishability for quantum states, and plays a central role in quantum information theory. The family of Renyi entropies generalizes to Renyi relative entropies that include as special cases most entropy measures used in quantum information theory. We construct a Euclidean path-integral approach to Renyi relative entropies in conformal field theory, then compute the fidelity and the relative entropy of states in one spatial dimension at zero and finite temperature using a replica trick. In contrast to the entanglement entropy, the relative entropy is free of ultraviolet divergences, and is obtained as a limit of certain correlation functions. The relative entropy of two states provides an upper bound on their trace distance.

References in corpus (1)

• Thermodynamical Property of Entanglement Entropy for Excited States

Cited by in corpus (9)

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• More on the rainbow chain: entanglement, space-time geometry and thermal states
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• Subsystem distance after a local operator quench
• The Holographic Dual of the Entanglement Wedge Symplectic Form
• Numerical calculations on the relative entanglement entropy in critical spin chains
• Relative entropy in higher spin holography
• Quantum Information Approaches to Quantum Gravity