Analytical approach for treating unitary quantum systems with initial mixed states

TL;DR

This paper introduces an analytical method for solving the evolution of unitary quantum systems with initial mixed states, especially when the evolution operator is unknown, by expressing mixed states via phase states.

Contribution

The paper presents a novel analytical approach that enables solving for the density matrix of systems with mixed initial states without requiring the evolution operator.

Findings

Method accurately derives density matrices for mixed states.

Results agree with existing literature.

Approach applicable to complex quantum systems.

Abstract

The mixed states are important in quantum optics since they frequently appear in the decoherence problems. When one of the components of the system is prepared in the mixed state and the evolution operator of this system is not available, one cannot deduce the density matrix. We present analytical approach to accurately solve this problem. The approach can be applied on the condition that the Schr\"odinger's equation of the system is solvable with any arbitrary initial state. In deriving the solution we exploit the fact that any mixed state can be expressed in terms of a phase state. The approach is illustrated by deriving the density matrix of a single-mode heat environment interacting asymmetrically with two qubits. Our results are in good agreement with the available results in the literature. This approach opens new perspectives for treating complicated systems and may impact other applications in the quantum theory.