Reformulation of the hidden variable problem using entropic measure of uncertainty

✍ Scribed by Miklós Rédei

• Publisher: Springer Netherlands
• Year: 1987
• Tongue: English
• Weight: 435 KB
• Volume: 73
• Category: Article
• ISSN: 0039-7857
• DOI: 10.1007/bf00484748

✦ Synopsis

Using a recently introduced entropy-like measure of uncertainty of quantum mechanical states, the problem of hidden variables is redefined in operator algebraic framework of quantum mechanics in the following way: if M, ~, E(M), E(~) are von Neumann algebras and their state spaces respectively, (~, E(~)) is said to be an entropic hidden theory of (M, E(M)) via a positive map L from ~ onto M if for all states q~ ~ E(~d) the composite state ~0 o L ~ E(~) can be obtained as an average over states in E(~) that have smaller entropic uncertainty than the entropic uncertainty of q~. It is shown that if L is a Jordan homomorphism then (~, E(~)) is not an entropic hidden theory of (s~, E(s0) via L.