Recycled entanglement detection by arbitrarily many sequential and independent pairs of observers

TL;DR

This paper demonstrates that two-qubit entangled states can be repeatedly used to witness entanglement by multiple independent pairs of observers acting sequentially, challenging previous assumptions about the limitations of entanglement detection.

Contribution

It proves that entanglement can be detected multiple times by different observer pairs, even with mixed states and arbitrarily small initial entanglement, expanding understanding of entanglement sharing.

Findings

Arbitrarily many pairs of observers can detect entanglement sequentially.

Pure and certain mixed entangled states enable repeated entanglement witnessing.

The phenomenon persists even as initial entanglement approaches zero.

Abstract

We investigate the witnessing of two-qubit entangled states by sequential and independent pairs of observers, with both observers of each pair acting independently on their part of the shared state from spatially separated laboratories, and subsequently passing their qubits to the next pair in the sequence. It has previously been conjectured that not more than one pair of observers can detect Clauser-Horne-Shimony-Holt "Bell-nonlocal" correlations in a similar set-up. This is intriguing since it is possible to have an arbitrarily long sequence of Bell-nonlocal correlations when only a single observer is allowed to share a bipartite state with multiple observers at the other end. It is therefore interesting to ask whether such restrictions are also present when entangled correlations are considered in the scenario of multiple pairs of observers. We find that a two-qubit entangled state can be used to witness entanglement arbitrarily many times, by pairs of observers, acting sequentially and independently. We prove the statement to be true when the initial pair of observers in the sequence share any pure entangled state or when they share a state from a class of mixed entangled states. We demonstrate that the phenomenon can also be observed for a certain class of entangled states in which an arbitrarily long sequence of observer pairs witnessing entanglement is reached in the limit of the initial entanglement content tending to a vanishing amount.