Certified Randomness from Bell's Theorem and Remote State Preparation Dimension Witness
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Randomness can be device-independently certified from a set of experimental data by Bell's theorem without placing assumptions about the experimental devices. The certification procedure in previous studies underestimated the generated randomness, due to a non-optimal lower bound of the entropy. We solve this by developing an analytic upper bound for the joint outcome probability p(ab|xy), and show that the lower the Bell inequality violation value is, the more advantageous the use of the joint outcome probability becomes. In the same experimental data, when a few general assumptions are introduced to characterize the experimental setups, substantially more semi-device-independent randomness can be certified by a witness we call remote state preparation dimension witness without using Bell's theorem. This is one important step towards practical use.
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