Quantum measuring systems: considerations from the holographic principle

TL;DR

This paper explores the connection between quantum measurement, holographic principles, and the transition from unitary quantum evolution to classical stochastic processes via analytic continuation, offering insights into the Euclidean regime of the holographic universe.

Contribution

It introduces a novel perspective on how quantum systems can be classically represented through holography and analytic continuation, bridging quantum and classical regimes.

Findings

Unitary quantum evolution can be analytically continued to a classical stochastic process.

In the Euclidean regime, the von Neumann entropy becomes positive, indicating classicalization.

The approach sheds light on the Euclidean regime of the holographic universe.

Abstract

In quantum mechanics without application of any superselection rule to the set of the observables, a closed quantum system temporally evolves unitarily, and this Lorentzian regime is characterized by von Neumann entropy of exactly zero. In the holographic theory in the classicalized ground state, we argue that the unitary real-time evolution of a non-relativistic free particle with complex-valued quantum probability amplitude in this Lorentzian regime can be temporally analytically continued to an imaginary-time classical stochastic process with real-valued conditional probability density in the Euclidean regime, where the von Neumann entropy of the classicalized hologram and the information of a particle trajectory acquired by the classicalized hologram are positive valued. This argument could shed light on the Euclidean regime of the holographic Universe.