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Logical Entropy: Introduction to Classical and Quantum Logical Information Theory.
1Department of Philosophy, University of California Riverside, Riverside, CA 92521, USA.
Entropy (Basel, Switzerland)
|December 3, 2020
Summary
Quantum logical information theory quantifies distinctions in quantum states using "qudits". It connects quantum logical entropy increases during measurement to the distinguishing of quantum eigenstates, offering a natural information measure for quantum systems.
Area of Science:
- Quantum Information Theory
- Mathematical Physics
- Information Theory
Background:
- Logical information theory quantifies distinctions using partitions and 'dits'.
- Shannon information theory's entropy definitions are derived from logical entropy.
- Classical logical entropy interprets as 'two-draw' probabilities for distinctions.
Purpose of the Study:
- To generalize logical information theory to the quantum domain.
- To introduce quantum logical information theory focusing on observable-distinguished eigenstates (qudits).
- To establish a quantitative link between quantum logical entropy and projective measurements.
Main Methods:
- Formalizing quantum logical information using distinctions (qudits) of observables.
- Deriving quantum logical entropy definitions analogous to classical counterparts.
- Developing the fundamental theorem for quantum logical entropy and measurement.
Main Results:
- Quantum logical entropy is defined based on distinguished eigenstates (qudits).
- The fundamental theorem quantifies the entropy increase from projective measurements.
- This increase is directly related to the measurement-distinguished eigenstates.
Conclusions:
- Quantum logical entropy provides a direct, quantitative link between measurement and state distinguishability.
- It offers a simple interpretation as 'two-draw' probabilities for quantum distinctions.
- Quantum logical entropy is presented as a natural information measure for quantum information theory.
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