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Maximal randomness from partially entangled states · Around

2019

Maximal randomness from partially entangled states

Woodhead, Erik, Kaniewski, Jędrzej, Bourdoncle, Boris et al.

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We investigate how much randomness can be extracted from a generic partially entangled pure state of two qubits in a device-independent setting, where a Bell test is used to certify the correct functioning of the apparatus.

For any such state, we first show that two bits of randomness are always attainable both if projective measurements are used to generate the randomness globally or if a nonprojective measurement is used to generate the randomness locally.
We then prove that the maximum amount of randomness that can be generated using nonprojective measurements globally is restricted to between approximately 3.58 and 3.96 bits.
The upper limit rules out that a bound of four bits potentially obtainable with extremal qubit measurements can be attained.

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M. McKague and M. Mosca, in Theory of Quantum Computation, Communication, and Cryptography , Lecture Notes in Computer Science, Vol. 6519 (Springer Berlin Heidelberg, Berlin, Heidelberg, 2011) pp. 113–130, arXiv:1006.0150 [quant-ph]

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