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Published on: September 8, 2023
483
Predictive Complexity of Quantum Subsystems.
Curtis T Asplund1, Elisa Panciu2
1Department of Physics & Astronomy, San José State University, One Washington Square, San José, CA 95192-0106, USA.
Entropy (Basel, Switzerland)
|January 8, 2025
Summary
We introduce predictive complexity, a quantum measure generalizing entanglement entropy. This new complexity better identifies key quantum dynamics and distinguishes entanglement types in quantum systems.
Area of Science:
- Quantum Information Science
- Condensed Matter Physics
- Complex Systems Theory
Background:
- Entanglement entropy quantifies quantum correlations but may not fully capture system dynamics.
- Predictive state analysis in classical systems uses forecasting complexity to understand system behavior.
- Quantum systems exhibit complex dynamics crucial for computation and materials science.
Purpose of the Study:
- To define and introduce predictive states and predictive complexity for quantum systems.
- To establish predictive complexity as a generalization and potential improvement over entanglement entropy.
- To demonstrate the utility of predictive complexity in analyzing quantum dynamics and entanglement.
Main Methods:
- Defining predictive states as equivalence classes of state vectors predicting subsystem behavior.
- Formulating predictive complexity based on these predictive states.
- Applying the framework to an isotropic Heisenberg model spin chain.
Main Results:
- Predictive complexity is shown to be a generalization of entanglement entropy.
- Calculations on a spin chain reveal predictive complexity better highlights dynamic events like magnon collisions.
- Predictive complexity acts as a local order parameter distinguishing short and long-range entanglement.
Conclusions:
- Predictive complexity offers a novel approach to characterizing quantum systems.
- This measure provides deeper insights into quantum dynamics and entanglement properties.
- It holds potential for applications in quantum information processing and condensed matter studies.
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