States in Quantum Mechanics

L. D. Faddeev, O. Yakubovskiĭ

Ciann‐Dong Yang, Hung-Jen Weng

This paper proposes a new mixed quantum mechanics (QM)-molecular mechanics (MM) approach, where MM is replaced by quantum Hamilton mechanics (QHM), which inherits the modeling capability of MM, while preserving the state-dependent nature of QM. QHM, a single mechanics playing the roles of QM and MM simultaneously, will be employed here to derive the three-dimensional quantum dynamics of diatomic molecules. The resulting state-dependent molecular dynamics including vibration, rotation and spin are shown to completely agree with the QM description and well match the experimental vibration-rotation spectrum. QHM can be incorporated into the framework of a mixed quantum-classical Bohmian method to enable a trajectory interpretation of orbital-spin interaction and spin entanglement in molecular dynamics.

Lorenzo Catani, Dan E. Browne, Nadish de Silva

Spekkens’ toy model (SM) is a non-contextual hidden-variable model made to support the epistemic view of quantum theory, where quantum states are states of partial knowledge about a deeper underlying reality. Despite being a classical model, it has reproduced many features of quantum theory (entanglement, teleportation, . . .): (almost) everything but contextuality, which therefore seems to be the inherent quantum feature. In addition to the importance in foundation of quantum theory, the notion of contextuality seems to be a crucial resource for quantum computation. In particular it has been proven that, in the case of odd prime discrete dimensional systems, contextuality is necessary for universal quantum computation in state-injection schemes of computation based on stabilizer quantum mechanics (SQM). The latter is a subtheory of quantum mechanics which is very popular in the field of quantum computation and quantum error correction. State-injection schemes consist of a classically-simulable part (like SQM) and a resource state that boosts the computation to a quantum improvement. In the odd-dimensional case, SM is operationally equivalent to SQM. In the even-dimensional case, the equivalence only holds in terms of structure, not in terms of statistical predictions. This because qubit-SQM shows contextuality, while qudit(odd dimensions)-SQM does not. We believe that SM can be a valid tool to study contextuality as a resource in the field of quantum computation. Restricted versions of SM compatible with quantum mechanics (QM) can be used as the non-contextual classically-simulable part of state-injection schemes thus opening other scenarios where studying if contextuality is necessary for quantum computational speed-up.

John Forge

Franz Schwabl

Michel Ghins

Back in 1964, Richard Feynman famously stated that "Nobody understands quantum mechanics."Indeed, despite its impressive empirical success, quantum mechanics (QM) remains the most perplexing and mind-boggling theory ever produced by humans.In his clear and thought-provoking book, Jean Bricmont advocates the merits of "the de Broglie-Bohm theory" and forcefully argues that it provides an intelligible picture of the quantum world out there.Being aware, however, that the de Broglie-Bohm theory is not immune from difficulties, the author acknowledges that understanding QM is an "unfinished story" (292). AQ1After a short introductory chapter, Bricmont discusses in Chapter 2 what he calls the "first mystery" of quantum mechanics, namely "interference and superpositions."Spin measurements with Mach -Zehnder interferometers ( § 2.2) show that the quantum state is a superposition of two incompatible states (spin up and spin down).When a measurement is takenperformed, the quantum state instantly collapses into one of the two states.Schrödinger's celebrated cat thought experiment was meant to show that believing in the existence of a superposition of states "cat alive" and "cat dead" before opening the box, simply is absurd (38).According to standard QM the evolution of 1✉ 1 Page 1 sur 5 e.