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Order Indices and Entanglement Production in Quantum Systems
1Bogolubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, Dubna 141980, Russia.
Entropy (Basel, Switzerland)
|December 8, 2020
Summary
This review explores order indices and entanglement production in many-body systems. It reveals a deep connection between these distinct concepts, applicable to finite systems and quantum operations.
Area of Science:
- Statistical Mechanics
- Quantum Information Theory
Background:
- Order indices classify order in statistical systems, applicable to finite systems.
- Order parameters typically describe long-range order in the thermodynamic limit.
- Entanglement production quantifies entanglement generated in many-partite quantum systems.
Purpose of the Study:
- To review order indices and entanglement production in many-body systems.
- To highlight the intimate relationship between these two quantities.
Main Methods:
- Review of theoretical concepts in statistical mechanics and quantum information.
- Analysis of the mathematical connections between order indices and entanglement measures.
Main Results:
- Order indices provide a comprehensive classification of order (long-range, mid-range, short-range) for finite systems.
- A significant, previously underemphasized, relationship exists between order indices and entanglement production.
- This connection unifies the understanding of order and entanglement in quantum systems.
Conclusions:
- The review emphasizes the profound link between order indices and entanglement production.
- Understanding this relationship offers new insights into the nature of many-body systems.
- This work bridges concepts from statistical mechanics and quantum information theory.
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