LOCAL TO GLOBAL THEOREMS FOR QUANTUM HISTORIES

Marcelo Losada, Leonardo Vanni, Roberto Laura

Matthew Rick Brown Brown

This paper investigates whether locally consistent quantum probability histories can always be combined into a single globally consistent unitary history. It demonstrates, through an explicit and independently verified counterexample in the simplest nontrivial setting, that every three-time subset of a multi-time history can be individually realizable even though no single sequence of unitary transformations can reproduce the complete collection of transition probabilities. The paper identifies shared connecting phases as the mechanism behind this local-to-global obstruction, develops a general parameter-counting condition for when global realization may be possible, and relates the result to broader quantum compatibility and marginal problems as well as the independently developed Quantum Composition Paradox.

Takuya Machida

We consider 2-state quantum walks (QWs) on the line, which are defined by two matrices. One of the matrices operates the walk at only half-time. In the usual QWs, localization does not occur at all. However, our walk can be localized around the origin. In this paper, we present two limit theorems, that is, one is a stationary distribution and the other is a convergence theorem in distribution.

Giuseppe Nisticò

TAKUYA MACHIDA

We consider 2-state quantum walks (QWs) on the line, which are defined by two matrices. One of the matrices operates the walk at only half-time. In the usual QWs, localization does not occur at all. However, our walk can be localized around the origin. In this paper, we present two limit theorems, that is, one is a stationary distribution and the other is a convergence theorem in distribution.

Giuseppe Antonio NISTICO', BENEDUCI R.