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Intrinsic and Measured Information in Separable Quantum Processes
David Gier1, James P Crutchfield1
1Complexity Sciences Center and Physics and Astronomy Department, University of California at Davis, One Shields Avenue, Davis, CA 95616, USA.
Entropy (Basel, Switzerland)
|June 26, 2025
Summary
Researchers developed methods to understand quantum information sources by analyzing their classical outputs. This allows for synchronization with the source
Area of Science:
- Quantum Information Science
- Quantum Thermodynamics
- Stochastic Processes
Background:
- Stationary quantum information sources generate sequences of correlated qudits, forming quantum stochastic processes.
- Measurements on these qudit sequences by an observer yield classical stochastic processes.
Purpose of the Study:
- To introduce quantum-information-theoretic properties for separable qudit sequences.
- To establish bounds on the classical information properties of measured processes.
- To develop methods for synchronizing with and reconstructing quantum information sources.
Main Methods:
- Defining quantum-information-theoretic properties for separable qudit sequences.
- Utilizing hidden Markov dynamics to describe observer synchronization.
- Employing specific positive operator-valued measures and adaptive measurement protocols for synchronization.
- Applying tomographic reconstruction for approximating information sources with classical models (i.i.d., Markov, etc.).
Main Results:
- Introduced quantum-information-theoretic properties that bound classical information properties.
- Demonstrated methods for observers to synchronize with the internal state of quantum sources.
- Developed a tomographic reconstruction technique to approximate quantum sources with classical models.
- Identified classes of separable processes based on quantum information properties and measurement complexity.
Conclusions:
- Quantum information-theoretic properties provide a framework for understanding and bounding classical information derived from quantum sources.
- Synchronization and reconstruction methods enable detailed analysis of quantum information sources, even those with hidden dynamics.
- The study classifies quantum processes and highlights the role of measurement complexity in their analysis.
Keywords:
Shannon entropy rateadaptive measurementclassical information theorycomputational mechanicsexcess entropyhidden Markov modelsinformation sourcemeasurementmutual informationnon-Markovian processpositive operator-valued measurequantum information theoryquantum process tomographyquantum stochastic processsynchronizationunifilarityvon Neumann entropy rate
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