On consistency of the quantum-like representation algorithm

Abstract

In this paper we continue to study so called ``inverse Born's rule problem'': to construct representation of probabilistic data of any origin by a complex probability amplitude which matches Born's rule. The corresponding algorithm -- quantum-like representation algorithm (QLRA) was recently proposed by A. Khrennikov [1]--[5]. Formally QLRA depends on the order of conditioning. For two observables $a$ and $b,$ $b|a$- and $a|b$ conditional probabilities produce two representations, say in Hilbert spaces $H^{b|a}$ and $H^{a|b}.$ In this paper we prove that under natural assumptions these two representations are unitary equivalent. This result proves consistency QLRA.

References in corpus (1)

• Quantum entanglement, fair sampling, and reality: Is the moon there when nobody looks?

Cited by in corpus (1)

• Quantum-like representation algorithm for trichotomous observables