PT-symmetric photonic quantum systems with gain and loss do not exist

TL;DR

This paper demonstrates that PT-symmetric photonic quantum systems with gain and loss cannot exist due to fundamental differences in quantum operator transformations, challenging previous assumptions in quantum optics.

Contribution

It provides a theoretical proof that PT-symmetric quantum optics with gain and loss is impossible, clarifying the role of operator transformations in quantum systems.

Findings

Gain and loss correspond to non-compact and compact operators.

Quantum correlations are fundamentally affected by these operator types.

PT-symmetry cannot be realized in quantum photonic systems with gain and loss.

Abstract

We discuss the impact of gain and loss on the evolution of photonic quantum states and find that PT-symmetric quantum optics in gain/loss systems is not possible. Within the framework of macroscopic quantum electrodynamics we show that gain and loss are associated with non-compact and compact operator transformations, respectively. This implies a fundamentally different way in which quantum correlations between a quantum system and a reservoir are built up and destroyed.