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

Two spatially separated observers, Alice and Bob, share a bipartite two-qubit entangled state and perform measurements to witness entanglement. After their measurements, they pass their qubits to a subsequent pair of observers who try to perform the same task independently, and so on. Here we ask: what is the maximum number of such pairs that can perform this task successfully? It has previously been conjectured that not more than one pair of observers can detect Clauser-Horne-Shimony-Holt “Bell-nonlocal” correlations in this setup. We prove that, on the contrary, entanglement can be witnessed by arbitrarily many pairs of observers. The dissimilar nature between entanglement and Bell-nonlocal correlations is therefore uncovered in a rather radical way, when considering sequentially acting pairs of observers. We prove this statement to be true when the initial shared state is any pure entangled state, a class of Bell-nonlocal mixed states, or a class of Bell-local entangled states.

Figure 1

Schematic of sequential entanglement detection by independent pairs of observers. Let ${\mathrm{Alice}}_1$ and ${\mathrm{Bob}}_1$ share a bipartite quantum system in the state ${\rho }_{A{B}_1}$, with one subsystem in possession of ${\mathrm{Alice}}_1$ and the other in control of ${\mathrm{Bob}}_1$. Their task is to detect entanglement and then pass on their subsystems to ${\mathrm{Alice}}_2$ and ${\mathrm{Bob}}_2$, respectively. Now, ${\mathrm{Alice}}_2$ and ${\mathrm{Bob}}_2$ act on their subsystems to detect entanglement and pass the quantum system to another subsequent pair, and this continues till the entanglement content of the shared state vanishes. The question is: how many such pairs of observers can detect entanglement acting sequentially and independently?