Locally optimal control of continuous variable entanglement

TL;DR

This paper develops local symplectic control strategies to minimize entanglement loss in continuous-variable quantum systems under thermal noise, showing that initial state preparation is often optimal and extending results to multi-mode symmetric systems.

Contribution

It introduces optimal local control routines for continuous-variable entanglement preservation, including initial state preparation and dynamic control, applicable to multi-mode symmetric systems.

Findings

Finite local squeezing can counteract decoherence effects.

Preparing an optimal initial state often suffices for entanglement preservation.

Control strategies are effective even in asymmetric and multi-mode symmetric systems.

Abstract

We consider a system of two bosonic modes each subject to the dynamics induced by a thermal Markovian environment and we identify instantaneous, local symplectic controls that minimise the loss of entanglement in the Gaussian regime. By minimising the decrease of the logarithmic negativity at every instant in time, it will be shown that a non-trivial, finite amount of local squeezing helps to counter the effect of decoherence during the evolution. We also determine optimal control routines in the more restrictive scenario where the control operations are applied on only one of the two modes. We find that applying an instantaneous control only at the beginning of the dynamics, i.e. preparing an appropriate initial state, is the optimal strategy for states with symmetric correlations and when the dynamics is the same on both modes. More generally, even in asymmetric cases, the delayed decay of entanglement resulting from the optimal preparation of the initial state with no further action turns out to be always very close to the optimised control where multiple operations are applied during the evolution. Our study extends directly to mono-symmetric systems of any number of modes, i.e. to systems that are invariant under any local permutation of the modes within any one partition, as they are locally equivalent to two-mode systems.