Physical Realizability Conditions for Mixed Bilinear-Linear Quantum Cascades with Pure Field Coupling

TL;DR

This paper establishes algebraic conditions ensuring that mixed bilinear-linear quantum stochastic differential equations can be physically realized as cascades of quantum systems, preserving canonical commutation relations for combined SU(2) and harmonic oscillator dynamics.

Contribution

It derives algebraic conditions for the physical realizability of mixed bilinear-linear quantum cascades involving SU(2) and harmonic oscillator systems.

Findings

Algebraic conditions for CCR preservation in mixed quantum systems

Characterization of QSDEs as bilinear-linear quantum cascades

Conditions ensuring physical realizability of combined quantum dynamics

Abstract

This paper aims to provide conditions under which a quantum stochastic differential equation can serve as a model for interconnection of a bilinear system evolving on an operator group SU(2) and a linear quantum system representing a quantum harmonic oscillator. To answer this question we derive algebraic conditions for the preservation of canonical commutation relations (CCRs) of quantum stochastic differential equations (QSDE) having a subset of system variables satisfying the harmonic oscillator CCRs, and the remaining variables obeying the CCRs of SU(2). Then, it is shown that from the physical realizability point of view such QSDEs correspond to bilinear-linear quantum cascades.