Witnessing entanglement sequentially: Maximally entangled states are not special

TL;DR

This paper explores how multiple observers can sequentially detect entanglement sharing a bipartite quantum state, revealing a limit of twelve Bobs for maximally entangled states and a reduction in Bobs with less entanglement.

Contribution

It establishes the maximum number of sequential Bobs who can detect entanglement from a single Alice, and shows how this number depends on the initial entanglement level.

Findings

Maximum of twelve Bobs detect entanglement with a maximally entangled state.

Number of Bobs remains constant over a range of near-maximal entanglement.

Fewer Bobs can detect entanglement as initial entanglement decreases.

Abstract

We investigate sharing of bipartite entanglement in a scenario where half of an entangled pair is possessed and projectively measured by one observer, called Alice, while the other half is subjected to measurements performed sequentially, independently, and unsharply, by multiple observers, called Bobs. We find that there is a limit on the number of observers in this entanglement distribution scenario. In particular, for a two-qubit maximally entangled initial shared state, no more than twelve Bobs can detect entanglement with a single Alice for arbitrary -- possibly unequal -- sharpness parameters of the measurements by the Bobs. Moreover, the number of Bobs remains unaltered for a finite range of near-maximal pure initial entanglement, a feature that also occurs in the case of equal sharpness parameters at the Bobs. Furthermore, we show that for non-maximally entangled shared pure states, the number of Bobs reduces with the amount of initial entanglement, providing a coarse-grained but operational measure of entanglement.