Two-site quantum random walk

We study the measure theory of a two-site quantum random walk. The truncated decoherence functional defines a quantum measure  μ n on the space of n -paths, and the  μ n in turn induce a quantum measure  μ on the cylinder sets within the space Ω of untruncated paths. Although  μ cannot be extended t...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:General relativity and gravitation 2011-12, Vol.43 (12), p.3451-3475
Hauptverfasser: Gudder, Stanley P., Sorkin, Rafael D.
Format: Artikel
Sprache:eng
Schlagworte:
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Beschreibung
Zusammenfassung:We study the measure theory of a two-site quantum random walk. The truncated decoherence functional defines a quantum measure  μ n on the space of n -paths, and the  μ n in turn induce a quantum measure  μ on the cylinder sets within the space Ω of untruncated paths. Although  μ cannot be extended to a continuous quantum measure on the full σ -algebra generated by the cylinder sets, an important question is whether it can be extended to sufficiently many physically relevant subsets of Ω in a systematic way. We begin an investigation of this problem by showing that  μ can be extended to a quantum measure on a “quadratic algebra” of subsets of Ω that properly contains the cylinder sets. We also present a new characterization of the quantum integral on the n -path space.
ISSN:0001-7701
1572-9532
DOI:10.1007/s10714-011-1245-z