Why the Quantum

To answer Wheeler's question "Why the quantum?" via quantum information theory according to Bub, one must explain both why the world is quantum rather than classical and why the world is quantum rather than superquantum, i.e., "Why the Tsirelson bound?" We show that the quantum correlations resulting from spin one-half states, i.e., the spin singlet state and 'Mermin photon state', which uniquely produce the Tsirelson bound for the Clauser-Horne-Shimony-Holt (CHSH) quantity, can be derived from the conservation of angular momentum (on average) for the quantum exchange of momentum. This explanation of the Tsirelson bound does not require hidden variables or 'causal influences', local or nonlocal. Since superquantum correlations exceed quantum correlations, we know that they would also violate conservation of angular momentum and we show how this happens using the Popescu-Rohrlich (PR) correlations. Thus, quantum correlations responsible for the Tsirelson bound satisfy conservation of angular momentum for the quantum exchange of momentum while both classical and superquantum correlations can fail to satisfy this constraint. We generalize the result to conservation per any measurement associated with a Bell basis state. While this constraint is not surprising per se, the details on how it obtains evidence a deeper principle at work in Nature, i.e., no preferred reference frame.

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