Peter Brown (ENS Lyon ): On nonlocality of one half of a maximally entangled qubit pair
Channel: Centrum Fizyki Teoretycznej PAN
Date: 11/04/2021

Peter Brown (ENS Lyon )
An unbounded number of independent observers can share the nonlocality of one half of a maximally entangled qubit pair.
Devising efficient means to generate nonlocal correlations is important for the development of device-independent technologies. It is known that unsharp measurements (which do not fully destroy entanglement) can be used to produce multiple instances of nonlocal correlations from a single entangled system. Hence, unsharp measurements could be utilized within device-independent protocols to reduce the required number of entangled quantum systems. Here we analyse the setting in which a single party, Alice, attempts to simultaneously violate the CHSH Bell-inequality with multiple other parties, Bobs, using only a single maximally entangled qubit pair. It was conjectured in [Phys. Rev. Lett. 114, 250401 (2015)] and claimed in [Mathematics, 4(3), 48 (2016)] that when the Bobs act independently and with unbiased inputs then at most two of them can expect to violate the CHSH Bell-inequality with Alice. Here we show, contrary to the conjecture and claim, that arbitrarily many independent Bobs can expect to violate the CHSH inequality with Alice. Our proof is constructive and we provide a sequence of explicit measurement strategies that allow a strictly increasing number of Bobs to violate. Moreover, we show that these strategies can be generalized to work with a larger class of two-qubit states. In particular, we are able to show that the number of possible violations remains unbounded if Alice initially shares any pure entangled two-qubit state. We conclude with some comments on the application of our measurement scheme to device-independent tasks. 
CTP Quantum Information Days (online), 22-24 February 2021.
Center for Theoretical Physics PAS (Warsaw, Poland)