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On Dynamical Measures of Quantum Information
James Fullwood1, Arthur J Parzygnat2
1School of Mathematics Statistics, Hainan University, 58 Renmin Avenue, Haikou 570228, China.
Entropy (Basel, Switzerland)
|April 26, 2025
Summary
This study introduces a new joint entropy for quantum systems evolving over time, generalizing von Neumann entropy to spacetime. This framework quantifies information dynamics and conservation in quantum processes.
Area of Science:
- Quantum Information Theory
- Quantum Thermodynamics
- Spacetime Physics
Background:
- The standard von Neumann entropy applies to static quantum states.
- Extending entropy measures to time-dependent quantum systems is crucial for understanding quantum dynamics.
Purpose of the Study:
- To define joint entropy for timelike-separated quantum systems.
- To develop a spacetime generalization of von Neumann entropy.
- To formulate dynamical extensions of quantum information measures.
Main Methods:
- Utilizing the theory of quantum states evolving over time.
- Defining joint entropy for timelike-separated systems with dual spacelike descriptions.
- Developing dynamical extensions for quantum joint entropy, conditional entropy, and mutual information.
Main Results:
- A novel joint entropy for timelike-separated quantum systems is established.
- This entropy generalizes von Neumann entropy and quantifies information dynamics.
- Information conservation in quantum processes is precisely formulated.
Conclusions:
- The proposed dynamical entropy offers a spacetime generalization of quantum information measures.
- It provides a framework for understanding information loss/gain during quantum evolution.
- The entropy has an operational interpretation in terms of state disturbance during measurements.
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