Decoherence quantification through commutation relations decay for open quantum harmonic oscillators

TL;DR

This paper analyzes how the decay of commutation relations in open quantum harmonic oscillators quantifies quantum decoherence, providing bounds and asymptotic behavior insights relevant for quantum information processing.

Contribution

It introduces a system-theoretic decoherence time based on commutator decay and investigates its bounds and asymptotics using Lyapunov techniques in weak-coupling regimes.

Findings

Decoherence time can be bounded using algebraic Lyapunov inequalities.

Asymptotic behavior of Lyapunov exponents is characterized for weak coupling.

Results are demonstrated on one- and two-mode oscillators with multichannel fields.

Abstract

This paper is concerned with multimode open quantum harmonic oscillators (OQHOs), described by linear quantum stochastic differential equations with multichannel external bosonic fields. We consider the exponentially fast decay in the two-point commutator matrix of the system variables as a manifestation of quantum decoherence. Such dissipative effects are caused by the interaction of the system with its environment and lead to a loss of specific features of the unitary evolution which the system would have in the case of isolated dynamics. These features are exploited as nonclassical resources in quantum computation and quantum information processing technologies. A system-theoretic definition of decoherence time in terms of the commutator matrix decay is discussed, and an upper bound for it is provided using algebraic Lyapunov inequalities. Employing spectrum perturbation techniques, we investigate the asymptotic behaviour of a related Lyapunov exponent for the oscillator when the system-field coupling is specified by a small coupling strength parameter and a given coupling shape matrix. The invariant quantum state of the system, driven by vacuum fields, in the weak-coupling limit is also studied. We illustrate the results for one- and two-mode oscillators with multichannel external fields and outline their application to a decoherence control problem for a feedback interconnection of OQHOs.