Statistics of the Bifurcation in Quantum Measurement

• Main Authors: Karl-Erik Eriksson, Kristian Lindgren
• Format: Article
• Language: English
• Published: MDPI AG 2019-08-01
• Series: Entropy
• Subjects: quantum measurement; scattering theory; statistics; Born’s rule
• Online Access: https://www.mdpi.com/1099-4300/21/9/834

We model quantum measurement of a two-level system <inline-formula> <math display="inline"> <semantics> <mi>&#956;</mi> </semantics> </math> </inline-formula>. Previous obstacles for understanding the measurement process are removed by basing the analysis of the interaction between <inline-formula> <math display="inline"> <semantics> <mi>&#956;</mi> </semantics> </math> </inline-formula> and the measurement device on quantum field theory. This formulation shows how inverse processes take part in the interaction and introduce a non-linearity, necessary for the bifurcation of quantum measurement. A statistical analysis of the ensemble of initial states of the measurement device shows how microscopic details can influence the transition to a final state. We find that initial states that are efficient in leading to a transition to a final state result in either of the expected eigenstates for <inline-formula> <math display="inline"> <semantics> <mi>&#956;</mi> </semantics> </math> </inline-formula>, with ensemble averages that are identical to the probabilities of the Born rule. Thus, the proposed scheme serves as a candidate mechanism for the quantum measurement process.