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

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.

Recycled detection of genuine multiparty entanglement of unlimitedly stretched array of parties and arbitrarily long series of sequential observers

“…Sequential detection of Bell nonlocality and bipartite entanglement has been a topic of recent studies [28][29][30][31][32][33][34][35][36][37][38][39][40][41][42][43][44][45]. It has been shown that there exist states for which Bell nonlocality or entanglement can be detected by arbitrarily many sequential observers.…”

“…The setup is such that one half of the shared bipartite state is controlled by a single observer while the other half is measured and passed on to multiple sequential observers, in order to witness CHSH inequality violation multiple times. In [29][30][31], it is shown that an arbitrary number of observers can sequentially detect Bell nonlocality of shared states and even entanglement of states which are not Bell nonlocal. A number of works have been conducted within this (or slightly generalized [31][32][33]) bipartite scenario [34][35][36][37][38][39][40][41][42][43][44][45].…”

“…In [29][30][31], it is shown that an arbitrary number of observers can sequentially detect Bell nonlocality of shared states and even entanglement of states which are not Bell nonlocal. A number of works have been conducted within this (or slightly generalized [31][32][33]) bipartite scenario [34][35][36][37][38][39][40][41][42][43][44][45]. Several experimental works have also been performed in this area [46][47][48][49][50].…”

Recycling nonlocality in a quantum network

“…to extract enough information to violate classical limitations, but afterwards preserve enough of the resource to enable further independent quantum information tasks. This includes recycling of quantum communications [2][3][4][5][6][7], entanglement and steering [8][9][10][11][12][13], and perhaps most remarkably nonlocality [14][15][16][17][18][19][20][21]. Using photonic setups, it has been experimentally demonstrated that one share of a singlet state can be recycled to produce two sequential violations of the CHSH inequality [22,23].…”

Recycling nonlocality in a quantum network

“…to extract enough information to violate classical limitations, but afterwards preserve enough of the resource to enable further independent quantum information tasks. This includes recycling of quantum communications [2][3][4][5][6][7], entanglement and steering [8][9][10][11][12][13], and perhaps most remarkably nonlocality [14][15][16][17][18][19][20][21]. Using photonic setups, it has been experimentally demonstrated that one share of a singlet state can be recycled to produce two sequential violations of the CHSH inequality [22,23].…”