Tsirelson Bound

 https://www.nobelprize.org/prizes/physics/2022/popular-information/

Perplexity:

The Tsirelson bound is a crucial concept in the study of quantum mechanics and its implications for Bell's inequalities. It represents the upper limit on the strength of correlations that can be achieved through quantum entanglement, specifically in the context of the CHSH (Clauser-Horne-Shimony-Holt) inequality.

Significance of the Tsirelson Bound

Upper Limit on Quantum Correlations: The Tsirelson bound quantifies the maximum violation of Bell's inequalities that can be achieved using quantum mechanics. For the CHSH inequality, this bound is≈2.828. This indicates that while quantum mechanics allows for stronger correlations than classical theories, there is still a limit to how strong these correlations can be.

Distinction from Classical Theories: Classical local hidden variable theories can achieve a maximum correlation of 2, while quantum mechanics can exceed this limit, but only up to the Tsirelson bound. This distinction is significant because it shows that quantum mechanics does not allow for "superquantum" correlations that could violate the Tsirelson bound, thereby preserving certain foundational principles such as causality and locality.

Implications for Quantum Information Theory: The Tsirelson bound has profound implications for quantum information theory, particularly in understanding the limits of quantum communication and computation. It serves as a boundary for what can be achieved with entangled states, influencing protocols in quantum cryptography and teleportation.

Physical Principles Underlying the Bound: Various physical principles have been proposed to explain why the Tsirelson bound exists. These include no-signaling conditions (which prevent faster-than-light communication) and conservation principles related to information. These principles suggest that the Tsirelson bound is not merely a mathematical artifact but has deep physical significance.

Experimental Verification: The Tsirelson bound has been confirmed through numerous experiments that demonstrate quantum correlations. These experiments not only validate the predictions of quantum mechanics but also reinforce the notion that local hidden variable theories are insufficient to explain the observed phenomena.

Conclusion

The Tsirelson bound is a fundamental limit on the correlations that can be observed in quantum mechanics, distinguishing it from classical theories. It encapsulates the essence of quantum entanglement and its implications for information theory, while also providing a framework for understanding the constraints imposed by physical principles. This bound has been pivotal in both theoretical explorations and experimental validations of quantum mechanics, marking a significant milestone in our understanding of the quantum world.

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After much tinkering, managed to create a circuit that subtracts 2 from 3. It

uses 2's complement addition, and the most significant bit at the end is simply

not measured...