On Realization of Back‐Action‐Evading Measurements and Quantum Non‐Demolition Variables via Linear Systems Engineering

ABSTRACT We establish a framework for realizing back‐action‐evading (BAE) measurements and quantum non‐demolition (QND) variables in linear quantum systems. The key condition, a purely imaginary Hamiltonian matrix with a real or imaginary coupling operator matrix, enables BAE measurements of conjugate observables. Symmetric coupling further yields QND variables. For non‐compliant systems, coherent feedback is designed to engineer BAE measurements. Crucially, the QND interaction condition simultaneously ensures BAE measurements and promotes the coupling operator to a QND observable.