The measurement problem and the completeness of quantum states

TL;DR

This paper proposes a solution to the quantum measurement problem by linking the equivalence of reduced and mixed states to the completeness of quantum states, emphasizing entanglement as the origin of quantum randomness.

Contribution

It offers a novel interpretation of quantum measurement as a two-step process rooted in standard quantum mechanics, connecting measurement postulate to state completeness.

Findings

Measurement process involves controllable entanglement and uncontrollable detection

Wave function collapse is subjective and linked to entanglement

Quantum randomness originates from entanglement

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.