  Alice and Bob each have half of a pair of entangled qubits. Bob measures his
half and then passes his qubit to a second Bob who measures again and so on.
The goal is to maximize the number of Bobs that can have an expected violation
of the Clauser-Horne-Shimony-Holt (CHSH) Bell inequality with the single Alice.
This scenario was introduced in [Phys. Rev. Lett. 114, 250401 (2015)] where the
authors mentioned evidence that when the Bobs act independently and with
unbiased inputs then at most two of them can expect to violate the CHSH
inequality with Alice. Here we show that, contrary to this evidence,
arbitrarily many independent Bobs can have an expected CHSH violation with the
single Alice. Our proof is constructive and our measurement strategies can be
generalized to work with a larger class of two-qubit states that includes all
pure entangled two-qubit states. Since violation of a Bell inequality is
necessary for device-independent tasks, our work represents a step towards an
eventual understanding of the limitations on how much device-independent
randomness can be robustly generated from a single pair of qubits.
