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Lossless quantum data compression with exponential penalization: an operational interpretation of the quantum Rényi
Guido Bellomo1, Gustavo M Bosyk2, Federico Holik3
1CONICET-Universidad de Buenos Aires, Instituto de Investigación en Ciencias de la Computación (ICC), Buenos Aires, Argentina.
Scientific Reports
|November 9, 2017
Summary
We introduce an operational interpretation for quantum Rényi entropies in lossless quantum data compression. This framework reveals their role in optimal quantum encoding schemes, analogous to von Neumann entropy.
Area of Science:
- Quantum Information Theory
- Quantum Computing
- Data Compression
Background:
- Lossless quantum data compression is a fundamental problem in quantum information.
- Quantum Rényi entropies are a generalization of quantum entropies with applications in various quantum information tasks.
- Existing frameworks primarily focus on von Neumann entropy for optimal quantum coding.
Purpose of the Study:
- To provide an operational interpretation for the family of quantum Rényi entropies.
- To establish a connection between quantum Rényi entropies and optimal quantum data compression schemes.
- To explore alternative cost functions beyond average codeword length in quantum encoding.
Main Methods:
- Development of a general quantum encoding scheme satisfying a quantum Kraft-McMillan inequality.
- Analysis of optimal encoding strategies under standard average length minimization.
- Investigation of encoding schemes with an exponential average length penalty.
Main Results:
- Reconstruction of known results where von Neumann entropy bounds the average length of optimal quantum codes.
- Demonstration that quantum Rényi entropies naturally emerge when considering exponential average length.
- Establishment of quantum Rényi entropies as key quantities relating optimal encoding to source description.
Conclusions:
- Quantum Rényi entropies offer a valuable perspective on quantum data compression beyond the standard average length.
- The operational interpretation extends the utility of quantum Rényi entropies in the context of quantum encoding.
- This work provides a more comprehensive understanding of the relationship between source properties and compression efficiency in quantum systems.
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