On the infeasibility of entanglement generation in Gaussian quantum systems via classical control

TL;DR

This paper proves that classical linear controllers are fundamentally incapable of generating entanglement in Gaussian quantum systems, both in steady state and finite time, highlighting a fundamental limitation rooted in quantum physics.

Contribution

It establishes a system theoretic framework demonstrating the infeasibility of classical control methods for entanglement generation in Gaussian quantum systems.

Findings

Classical linear controllers cannot generate steady state entanglement.

Classical control cannot produce entanglement in finite time from separable states.

Connects control theory limitations with quantum physical principles.

Abstract

This paper uses a system theoretic approach to show that classical linear time invariant controllers cannot generate steady state entanglement in a bipartite Gaussian quantum system which is initialized in a Gaussian state. The paper also shows that the use of classical linear controllers cannot generate entanglement in a finite time from a bipartite system initialized in a separable Gaussian state. The approach reveals connections between system theoretic concepts and the well known physical principle that local operations and classical communications cannot generate entangled states starting from separable states.