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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)
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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.

Keywords:
Heisenberg modelLieb–Robinson boundentanglement entropylocal order parameterpredictive complexityspin wave

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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.