Unified Quantum Entropy for Infinite-Dimensional Systems
Author Information
Author(s): Gielerak Roman, Wiśniewska Joanna, Sawerwain Marek
Primary Institution: University of Zielona Góra
Hypothesis
How can we calculate the value of entropy for quantum states described by a continuous Hilbert space?
Conclusion
The study successfully extends the concept of unified quantum entropy to infinite-dimensional systems using Fredholm determinants, allowing for the calculation of entropy values that may otherwise be infinite.
Supporting Evidence
- The study extends known properties of quantum entropies to infinite-dimensional cases.
- Numerical examples demonstrate the application of the proposed methods for calculating entropy.
- The approach provides better numerical stability compared to traditional methods.
Takeaway
This study helps us understand how to measure randomness in quantum systems that are very complex, like those with infinite dimensions, by using special math tools.
Methodology
The study uses Fredholm determinant theory to extend the notion of unified quantum entropy to infinite-dimensional systems and provides numerical examples for calculating entropy values.
Limitations
The study does not address which properties of the renormalised entropy remain true for certain parameter ranges.
Digital Object Identifier (DOI)
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