Robustness of spatial Penning trap modes against environment-assisted entanglement

TL;DR

This paper investigates whether environmental interactions induce entanglement in the spatial modes of a charged particle in a Penning trap, finding that under realistic conditions, entanglement does not occur, preserving quantum protocols.

Contribution

It demonstrates that weak Markovian environmental coupling does not generate entanglement in Penning trap modes at realistic temperatures, supporting quantum information applications.

Findings

Environmental coupling does not induce entanglement at realistic temperatures.

The effectiveness of quantum protocols in Penning traps remains unaffected.

Entanglement is unlikely to be generated by environment in typical experimental conditions.

Abstract

The separability of the spatial modes of a charged particle in a Penning trap in the presence of an environment is studied by means of the positive partial transpose (PPT) criterion. Assuming a weak Markovian environment, described by linear Lindblad operators, our results strongly suggest that the environmental coupling of the axial and cyclotron degrees of freedom does not lead to entanglement at experimentally realistic temperatures. We therefore argue that, apart from unavoidable decoherence, the presence of such an environment does not alter the effectiveness of recently suggested quantum information protocols in Penning traps, which are based on the combination of a spatial mode with the spin of the particle.