Single-copy activation of Bell nonlocality via broadcasting of quantum states

Joseph Bowles1, Flavien Hirsch2, and Daniel Cavalcanti1

1ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain
2Institute for Quantum Optics and Quantum Information (IQOQI), Austrian Academy of Sciences, Boltzmanngasse 3, 1090 Vienna, Austria

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Activation of Bell nonlocality refers to the phenomenon that some entangled mixed states that admit a local hidden variable model in the standard Bell scenario nevertheless reveal their nonlocal nature in more exotic measurement scenarios. We present such a scenario that involves broadcasting the local subsystems of a single-copy of a bipartite quantum state to multiple parties, and use the scenario to study the nonlocal properties of the two-qubit isotropic state:

\nonumber \rho_\alpha = \alpha\,|\Phi^+ \rangle\langle \Phi^+|+(1-\alpha)\frac{\mathbb{1}}{4}.

We present two main results, considering that Nature allows for (i) the most general no-signalling correlations, and (ii) the most general quantum correlations at the level of any hidden variable theory. We show that the state does not admit a local hidden variable description for $\alpha>0.559$ and $\alpha>\frac{1}{2}$, in cases (i) and (ii) respectively, which in both cases provides a device-independent certification of the entanglement of the state. These bounds are significantly lower than the previously best-known bound of $0.697$ for both Bell nonlocality and device-independent entanglement certification using a single copy of the state. Our results show that strong examples of non-classicality are possible with a small number of resources.

Bell nonlocality is a highly counter-intuitive phenomena, which proves that any classical interpretation of quantum theory requires faster-than-light causality between particles. Bell nonlocality, however, is not easy to observe in experiment, and generally requires experimental set ups with low noise. A considerable effort has thus been put into lowering this noise threshold, and this work proposes a simple new technique to do this. The technique involves ‘broadcasting’ one part of the state, which conceptually can be thought of splitting that part of the state in two and sending the two parts to separate locations in space.

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