Frontiers of quantum physics

Abstract:

The emergence of intrinsic probability is one of the central problems in quantum mechanics, and investigating the origin of the Born rule provides the most direct approach to this problem. Many derivations of the Born rule have been proposed based on different postulates and frameworks. Identifying which postulates are genuinely necessary is therefore essential for understanding the origin of quantum probability. Here we prove that two postulates commonly employed in derivations of the Born rule, additivity and noncontextuality, are not equivalent and thus cannot be unified into a single postulate. We further show that the additivity postulate is indispensable in five major derivations of the Born rule: Gleason's theorem, Busch's extension of Gleason's theorem, the Deutsch-Wallace theorem, Zurek's envariance derivation, and the Finkelstein-Hartle theorem. We demonstrate that these derivations rely either on explicit additivity assumptions or on implicit forms of additivity embedded in the original arguments and that removing or weakening additivity gives rise to significant problems in the derivations. Our results support the view that additional postulates with intrinsic probabilistic properties should be introduced to derive the Born rule.

Abstract:

The unification of quantum theory and the general theory of relativity, describing gravity, is one of the most important challenges in science. Einstein's general theory of relativity is based on the principle of equivalence and has been confirmed to great accuracy for large bodies. However, in the quantum domain, the equivalence principle has been predicted to take a unique form involving a gauge phase, which is equal, in the context of a measurement on Earth, to the quantum phase of a free-falling wave packet relative to its counterpart wave packet which is static in Earth's frame. To measure this phase, we realize a novel cold-atom interferometer in which one wave packet stays static in the laboratory frame while the other is in free fall. The observed relative phase of the wave packets confirms the predicted phase and shows that, in our low energy regime, the equivalence principle may be applied to the quantum domain. Our observation constitutes a fundamental test of the interface between quantum theory and gravity. The new interferometer also opens the door for further probing of the latter interface, as well as to searches for new physics.