Breaking absolute separability with quantum switch

TL;DR

This paper demonstrates that a quantum switch can transform absolute separable states into ordinary separable states, revealing a new way to manipulate quantum entanglement properties.

Contribution

It introduces the use of quantum switches to break the robustness of absolute separable states, a novel approach in quantum resource theory.

Findings

Quantum switch can convert absolute separable states into separable states.

The effect is demonstrated on bipartite qubit systems, including Werner and Bell diagonal states.

The method generalizes to higher-dimensional systems.

Abstract

Absolute separable (AS) quantum states are those states from which it is impossible to create entanglement, even under global unitary operations. It is known from the resource theory of non-absolute separability that the set of absolute separable states forms a convex and compact set, and global unitaries are free operations. We show that the action of a quantum switch controlled by an ancilla qubit over the global unitaries can break this robustness of AS states and produce ordinary separable states. First, we consider bipartite qubit systems and find the effect of quantum switch starting from the states sitting on the boundary of the set of absolute separable states. As particular examples, we illustrate what happens to modified Werner states and Bell diagonal (BD) states. For the Bell diagonal states, we provide the structure for the set of AS BD states and show how the structure changes under the influence of a switch. Further, we consider numerical generalisation of the global unitary operations and show that it is always possible to take AS states out of the convex set under switching operations. We also generalised our results in higher dimensions.