Spectral stabilizability

TL;DR

This paper develops spectral conditions to determine which quantum states can be maintained against decoherence through coherent control, providing a comprehensive framework for stabilizability in open quantum systems.

Contribution

It introduces necessary and sufficient spectral conditions for stabilizability applicable to general and Gaussian states, improving upon previous criteria.

Findings

Derived spectral conditions for stabilizability of quantum states.

Established upper bounds on stabilizability in various open system scenarios.

Demonstrated stabilization of GHZ, W, and squeezed thermal states under dissipation.

Abstract

Decoherence represents a major obstacle towards realizing reliable quantum technologies. Identifying states that can be uphold against decoherence by purely coherent means, i.e., {\it stabilizable states}, for which the dissipation-induced decay can be completely compensated by suitable control Hamiltonians, can help to optimize the exploitation of fragile quantum resources and to understand the ultimate limits of coherent control for this purpose. In this work, we develop conditions for stabilizability based on the target state's eigendecomposition, both for general density operators and for the covariance matrix parameterization of Gaussian states. Unlike previous conditions for stabilizability, these spectral conditions are both necessary and sufficient and are typically easier to use, extending their scope of applicability. To demonstrate its viability, we use the spectral approach to derive upper bounds on stabilizability for a number of exemplary open system scenarios, including stabilization of generalized GHZ and W states in the presence of local dissipation and stabilization of squeezed thermal states under collective damping.