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Simulating quantum correlations as a distributed sampling problem

Julien Degorre·Sophie Laplante·Jérémie Roland
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Abstract

It is known that quantum correlations exhibited by a maximally entangled qubit pair can be simulated with the help of shared randomness, supplemented with additional resources, such as communication, post-selection or non-local boxes. For instance, in the case of projective measurements, it is possible to solve this problem with protocols using one bit of communication or making one use of a non-local box. We show that this problem reduces to a distributed sampling problem. We give a new method to obtain samples from a biased distribution, starting with shared random variables following a uniform distribution, and use it to build distributed sampling protocols. This approach allows us to derive, in a simpler and unified way, many existing protocols for projective measurements, and extend them to positive operator value measurements. Moreover, this approach naturally leads to a local hidden variable model for Werner states.

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Julien Degorre, Sophie Laplante, Jérémie Roland. 2005-07-13. Simulating quantum correlations as a distributed sampling problem. https://doi.org/10.1103/physreva.72.062314

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