SCIENCE@home

Quantum interval-valued probability: Contextuality and the Born rule

Yu-Tsung Tai,A. Hanson,G. Ortiz,Amr Sabry Department of Mathematics,Indiana University,Department of Materials Science,Department of Biomedical Informatics,D. Physics

Published 2017 in Physical Review A

ABSTRACT

We present a mathematical framework based on quantum interval-valued probability measures to study the effect of experimental imperfections and finite precision measurements on defining aspects of quantum mechanics such as contextuality and the Born rule. While foundational results such as the Kochen-Specker and Gleason theorems are valid in the context of infinite precision, they fail to hold in general in a world with limited resources. Here we employ an interval-valued framework to establish bounds on the validity of those theorems in realistic experimental environments. In this way, not only can we quantify the idea of finite-precision measurement within our theory, but we can also suggest a possible resolution of the Meyer-Mermin debate on the impact of finite-precision measurement on the Kochen-Specker theorem.

PUBLICATION RECORD

CITATION MAP

EXTRACTION MAP

CLAIMS

  • No claims are published for this paper.

CONCEPTS

  • No concepts are published for this paper.

REFERENCES

Showing 1-44 of 44 references · Page 1 of 1

CITED BY