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Local Invariance of Divergence-Based Quantum Information Measures.
Christopher Popp1, Tobias C Sutter1, Beatrix C Hiesmayr1
1Faculty of Physics, University of Vienna, Währingerstraße 17, 1090 Vienna, Austria.
Entropy (Basel, Switzerland)
|October 28, 2025
Summary
Researchers proved that quantum information measures based on generalized divergences are invariant under local transformations. This invariance simplifies calculations and optimizes quantum protocols, enhancing the characterization of quantum systems.
Area of Science:
- Quantum Information Science
- Quantum Computing
- Quantum Information Theory
Background:
- Quantum information quantities like mutual information and entropies are crucial for understanding quantum systems.
- Characterizing these quantities is essential for advancing quantum information science and protocols.
Purpose of the Study:
- To identify and prove the invariance of information measures based on generalized divergences under local transformations.
- To establish a method for improving the computation and optimization of quantum information quantities.
Main Methods:
- Identifying information measures derived from generalized divergences.
- Proving invariance under local isometric or unitary transformations.
- Utilizing the reversal channel for local isometries and the data-processing inequality.
Main Results:
- Demonstrated that specific information measures are invariant under local isometric or unitary transformations.
- Established invariance for both asymptotic and one-shot regimes without depending on the divergence's functional form.
- Showcased the applicability of these invariances to enhance computations and optimize quantum protocols.
Conclusions:
- The proven invariances offer a powerful tool for characterizing and computing relevant information measures in quantum information processing.
- These findings contribute to a more robust understanding and application of quantum information theory.
- The results have broad implications for various fields within quantum information science.
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