Position and quantum theory

Hans Laue

Shasanka Mohan Roy, Virendra Singh

Present quantum theory, which is statistical in nature, does not predict joint probability distribution of position and momentum because they are noncommuting. We propose a deterministic quantum theory which predicts a joint probability distribution such that the separate probability distributions for position and momentum agree with usual quantum theory. Unlike the Wigner distribution the suggested distribution is positive definite. The theory predicts a correlation between position and momentum in individual events.

Jaroslaw Wojciech Wawrzycki

We present a proof of positivity of an invariant kernel, which is of basic importance for the Staruszkiewicz theory of the quantum Coulomb field. Presented proof of positivity is independent of the Staruszkiewicz theory and is based on the classical Schoenberg's theorem for conditionally negative definite functions, as well as on the generalized Bochner's theorem.

Nathaniel Johnston, Jamie Sikora

In this work we examine quantum states which have non-negative amplitudes (in a fixed basis) and the channels which preserve them. These states include the ground states of stoquastic Hamiltonians and they are of interest since they avoid the Sign Problem and can thus be efficiently simulated. In optimization theory, the convex cone generated by such states is called the set of completely positive (CP) matrices (not be confused with completely positive superoperators). We introduce quantum channels which preserve these states and call them completely positive completely positive. To study these states and channels, we use the framework of resource theories and investigate how to measure and quantify this resource.

Berthold‐Georg Englert