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Rényi Mutual Information in Quantum Field Theory
1School of Natural Sciences, Institute for Advanced Study, Princeton, New Jersey 08540, USA and Princeton Center for Theoretical Science, Princeton University, Princeton, New Jersey 08544, USA.
Physical Review Letters
|January 27, 2023
Summary
We introduce a new definition of Rényi mutual information (RMI) in quantum field theory that accurately measures subsystem correlations. This novel RMI is non-negative, UV finite, and bounds correlation functions, validated in conformal field theory.
Area of Science:
- Quantum Information Theory
- Quantum Field Theory
- Statistical Mechanics
Background:
- Standard definitions of mutual information in quantum field theory lack rigorous properties.
- A precise measure of quantum correlations is crucial for understanding complex quantum systems.
Purpose of the Study:
- To define and compute Rényi mutual information (RMI) rigorously in quantum field theory.
- To establish RMI as a genuine measure of quantum correlations, ensuring desirable properties like non-negativity and monotonicity.
- To develop a computational framework for RMI in continuum quantum field theories.
Main Methods:
- Utilized the Petz Rényi relative entropy for a proper definition of RMI.
- Developed a replica path integral approach for calculating RMI in quantum field theories.
- Evaluated RMI explicitly in 1+1D conformal field theory using twist fields.
Main Results:
- The proposed RMI is non-negative and monotonic under local operations, confirming it as a true correlation measure.
- RMI is UV finite and well-defined in the continuum limit, overcoming limitations of previous approaches.
- Proved that RMI bounds connected correlation functions.
- Validated results against exact numerics in the massless free fermion theory.
Conclusions:
- The Petz Rényi relative entropy provides a robust definition for RMI in quantum field theory.
- This new RMI serves as a reliable tool for quantifying quantum correlations in field theories.
- The replica path integral method offers a practical approach for computing RMI, with applications in various quantum field theories.
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