Why the Tsirelson Bound? Bub's Question and Fuchs' Desideratum
William Stuckey1, Michael Silberstein2,3, Timothy McDevitt4
1Department of Physics, Elizabethtown College, Elizabethtown, PA 17022, USA.
Entropy (Basel, Switzerland)
|December 3, 2020
Summary
The Tsirelson bound, crucial for quantum information theory, arises from conservation principles related to no preferred reference frame (NPRF). This explains why the world is quantum, not classical or superquantum.
Area of Science:
- Quantum Information Theory
- Foundations of Quantum Mechanics
- Quantum Correlations
Background:
- Explaining the quantum nature of the universe is a fundamental question in physics.
- The Tsirelson bound sets a limit on correlations in quantum systems, distinguishing them from classical and hypothetical superquantum systems.
Purpose of the Study:
- To provide a principle-based explanation for the Tsirelson bound within quantum information theory.
- To address the question of why the world is quantum rather than classical or superquantum.
Main Methods:
- Deriving quantum states and correlations corresponding to Bell basis states from conservation per no preferred reference frame (NPRF).
- Defining reference frames analogously to the light postulate in special relativity.
Main Results:
- The unique production of the Tsirelson bound for the Clauser-Horne-Shimony-Holt (CHSH) quantity is shown to be derivable from conservation per NPRF.
- Quantum correlations and states leading to the Tsirelson bound are linked to this fundamental conservation principle.
Conclusions:
- The Tsirelson bound is fundamentally based on the principle of no preferred reference frame (NPRF).
- This provides a constraint-based, principle-driven answer to foundational questions about quantum theory's structure, akin to special relativity.
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