Division of the two-qubit Hilbert space according to the entanglement sudden death under composite noise environment

TL;DR

This paper theoretically classifies the two-qubit Hilbert space into subspaces based on entanglement decay behavior under composite noise, explaining the violation of entanglement decay additivity.

Contribution

It introduces a novel division of the two-qubit Hilbert space into subspaces with distinct entanglement decay characteristics under composite noise.

Findings

Hilbert space divided into asymptotic and abrupt disentanglement subspaces

Explains violation of entanglement decay additivity

Provides a theoretical framework for entanglement dynamics under noise

Abstract

We show theoretically that according to the disentanglement behavior under composite noise environment, the Hilbert space of a two-qubit system can be divided into two separate parts: a 3-dimensional subspace in which all states disentangle asymptotically, and the rest in which all states disentangle abruptly. The violation of additivity for entanglement decay rates under weak noises [see, PRL 97, 140403 (2006)] therefore can be explained in terms of such division of the Hilbert space.