Comments on Indeterminism and Undecidability

In a recent paper \cite{Landsman1}, it has been claimed that the outcomes of a quantum coin toss which is idealized as an infinite binary sequence is {\it 1-random}. We also defend the correctness of this claim and assert that the outcomes of quantum measurements can be considered as an infinite {\it 1-random} or {\it n-random} sequence. In this brief note we present our comments on this claim. We have mostly positive but also some negative comments on the arguments of the paper \cite{Landsman1}. Furthermore, we speculate a logical-axiomatic study of nature which we believe can intrinsically provide quantum mechanical probabilities based on {\it 1(n)-randomness}.

Quantum walking in curved spacetime: discrete metric

A discrete-time quantum walk (QW) is essentially a unitary operator driving the evolution of a single particle on the lattice. Some QWs have familiar physics PDEs as their continuum limit. Some slight generalization of them (allowing for prior encoding and larger neighbourhoods) even have the curved spacetime Dirac equation, as their continuum limit. In the(1+1)−dimensional massless case, this equation decouples as scalar transport equations with tunable speeds. We characterise and construct all those QWs that lead to scalar transport with tunable speeds. The local coin operator dictates that speed; we provide concrete techniques to tune the speed of propagation, by making use only of a finite number of coin operators-differently from previous models, in which the speed of propagation depends upon a continuous parameter of the quantum coin. The interest of such a discretization is twofold : to allow for easier experimental implementations on the one hand, and to evaluate ways of quantizing the metric field, on the other.