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Relative entropies in conformal field theory
1Stanford Institute for Theoretical Physics and Department of Physics, Stanford University, Stanford, California 94305-4060, USA and Department of Physics and Astronomy, University of British Columbia, 6224 Agricultural Road, Vancouver, British Columbia V6T 1W9, Canada.
Physical Review Letters
|August 16, 2014
Summary
We developed a new method to calculate Renyi relative entropies in quantum systems. This approach avoids divergences, offering a more robust measure of state distinguishability in quantum information theory.
Area of Science:
- Quantum Information Theory
- Quantum Many-Body Physics
- Conformal Field Theory
Background:
- Relative entropy quantifies distinguishability between quantum states.
- Renyi relative entropies generalize common entropy measures in quantum information.
- Understanding these entropies is crucial for quantum information processing and condensed matter physics.
Purpose of the Study:
- To develop a Euclidean path-integral approach for Renyi relative entropies.
- To compute fidelity and relative entropy in one spatial dimension.
- To investigate the behavior of relative entropy at zero and finite temperatures.
Main Methods:
- Constructed a Euclidean path-integral formalism for Renyi relative entropies.
- Employed a replica trick to compute entropies in one spatial dimension.
- Analyzed states at both zero and finite temperatures.
Main Results:
- The relative entropy is free of ultraviolet divergences, unlike entanglement entropy.
- Relative entropy was computed as a limit of correlation functions.
- The relative entropy provides an upper bound for the trace distance between states.
Conclusions:
- The developed path-integral method offers a robust way to calculate Renyi relative entropies.
- The findings contribute to a deeper understanding of quantum state distinguishability.
- This work has implications for quantum information theory and the study of quantum phases of matter.
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