Information Constraints in Quantum Measurements and State Collapse

Abstract

Quantum-mechanical constraints on information transfer in measuring systems and their influence on measurement results studied. As the example, measurement of binary observable $S_z$ of object $\mathcal{S}$ by measuring apparatus $\mathcal{A}$ considered. It's shown that during the measurement these constraints obstacle the acquisition of information by $\mathcal{A}$, characterizing purity of $\mathcal{S}$ ensemble. Due to it, $\mathcal{A}$ can't discriminate pure and mixed $\mathcal{S}$ ensembles with the same $S_z$ expectation value. In algebraic measurement ansatz by Emch such information loss results in stochastic $S_z$ measurement outcomes for pure $\mathcal{S}$ ensemble, their probabilities obey to Born postulate, i.e. it corresponds to quantum state collapse. Account of $\mathcal{A}$ state decoherence doesn't change obtained results principally.

16 pages, Submitted to Int. J. Theor. Phys