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Infinite-Dimensional Quantum Entropy: The Unified Entropy Case
Roman Gielerak1, Joanna Wiśniewska2, Marek Sawerwain1
1Institute of Control & Computation Engineering, University of Zielona Góra, Licealna 9, 65-417 Zielona Góra, Poland.
Entropy (Basel, Switzerland)
|January 8, 2025
Summary
This study extends unified quantum entropy to infinite-dimensional systems, enabling entropy calculations for quantum computation models. This advancement is crucial for understanding complex quantum states and developing new quantum technologies.
Area of Science:
- Quantum Information Theory
- Quantum Computation
Background:
- Infinite-dimensional systems are vital for continuous-variable quantum computation.
- Calculating entropy for infinite-dimensional quantum states is challenging.
Purpose of the Study:
- To extend the unified quantum entropy concept to infinite-dimensional systems.
- To develop a method for computing entropy in these complex systems.
Main Methods:
- Utilized Fredholm determinant theory to generalize unified quantum entropy.
- Extended known finite-dimensional entropy properties to infinite dimensions.
Main Results:
- Successfully extended the unified quantum entropy to infinite-dimensional systems.
- Demonstrated the computation of entropy for infinite Hilbert spaces through numerical examples.
Conclusions:
- The proposed method provides a framework for calculating quantum entropy in infinite-dimensional systems.
- This work facilitates a deeper understanding of continuous-variable quantum computation.
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