Eigenvalue Formulation of Quantum Mechanics Near Closed Timelike Curves

TL;DR

This paper reformulates the Deutsch equation for quantum systems near closed timelike curves as an eigenvalue problem, revealing entanglement disappearance and discontinuous evolution of qubits in such spacetime regions.

Contribution

It introduces an eigenvalue formulation of the Deutsch equation, providing new insights into quantum behavior near closed timelike curves.

Findings

Entanglement between qubits vanishes near CTCs

Discontinuous evolution of qubits observed near CTCs

Eigenvalue approach offers a novel analysis method

Abstract

Einstein's field equations of gravitation are known to admit closed timelike curve (CTC) solutions. Deutsch approached the problem from the quantum information point of view and proposed a self-consistency condition. In this work, the Deutsch equation is formulated as an eigenvalue problem. The disappearance of entanglement between two qubits in an Einstein-Podolsky-Rosen (EPR) state near a CTC is demonstrated. The method is utilized to analyze the discontinuous evolution of two chronology respecting (CR) qubits near a CTC.