The measurement problem and the completeness of quantum states

Abstract

In this paper, we present a thought experiment that demonstrates that the equivalence of quantum reduced states and statistical mixed states of ensembles is not merely a simple mathematical formulation in quantum mechanics, but rather possesses profound physical underpinnings. Based on the equivalence, we give a possible solution to the quantum measurement problem. We describe quantum measurement process as two-step physical process: one microscopically controllable process which generates an entanglement between the system being measured and a marking system (or property), and one macroscopic process (uncontrollable microscopically) which detects states (or properties) of the marking system. With the solution, we conclude that the measurement postulate is just a corollary of the completeness of quantum states. Our solution is entirely rooted in the traditional formalism of quantum mechanics, requiring no extensions or modifications to it. We also point out that quantum randomness originates from entanglement, and the collapse of the wave function is a subjective process.