Unsharp measurements are widely seen as the key resource for recycling the nonlocality of an entangled state shared between several sequential observers. Contrasting this, we investigate the recycling of nonlocality using only projective measurements and classical shared randomness. We show that one share of a maximally entangled qubit pair can be recycled, with such resources, for at least three sequential violations of the CHSH inequality. For two sequential violations, using the same state, we analytically obtain the optimal trade-off in the CHSH parameters. Furthermore, we show that non-maximally entangled qubit states enable larger sequential violations than the maximally entangled state. Our results establish standard, projective, measurements as a simple and useful resource for recycling quantum nonlocality.
The nonlocality of an entangled qubit pair can be recycled for several Bell experiments. Here, we go beyond standard Bell scenarios and investigate the recycling of nonlocal resources in a quantum network. First, we show that the ability to recycle nonlocality can be independent of the size of the network. Then, we realize a photonic quantum 3-branch star network in
which three sources of entangled pairs independently connect three outer parties with a central node. After measuring, each outer party respectively relays their system to an independent secondary measuring party. We experimentally demonstrate that the outer parties can perform unsharp measurements that are strong enough to violate a network Bell inequality with the central party, but weak enough to maintain sufficient entanglement in the network to allow the three secondary parties to do the same. Moreover, the violations are strong enough to exclude any model based on standard projective measurements on the EPR pairs emitted in the network. Our experiment brings together the research program of recycling quantum resources with that of Bell nonlocality in networks.
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