I am trying to imagine what would be the implications of the loopholes on Bell test on the random sequence generation scheme proposed by Vazirani and Vidick (VV protocol) in the paper titled 'Certifiable Quantum Dice Or, True Random Number Generation Secure Against Quantum Adversaries'.

To my knowledge there are six loopholes to be discussed here.

  1. Detection efficiency, or fair sampling
  2. Communication, or locality
  3. Disjoint sampling
  4. Failure of rotational invariance
  5. Sources of error in (optical) Bell test experiments
  6. Free choice of detector orientations

Let me try to express my understanding one by one.

Detection efficiency, or fair sampling If a very high efficiency detector is used it could be claimed that the loophole for Bell test is fixed. But the detector is a component of the device manufactured by the adversary. So, we should not be assured if the vendor claims that they are using very high efficiency detector.

Communication, or locality Non-locality is an assumption for the VV protocol so I assume this loophole has impact on the protocol.

Disjoint sampling I didn't get the whole thing but should I assume that this loophole will have impact if someone extends the VV protocol to a 3-party system?

Failure of rotational invariance I have no clue. Anyone with help?

Sources of error in (optical) Bell test experiments Is my logic used in case 1 applicable here too?

Free choice of detector orientations I am not sure but is it related to choosing the basis of measurements?

Are my understandings correct? Thanks in advance for your help.

  • $\begingroup$ I think Device-Independent Quantum Key Distribution with Local Bell Test by Lim et. al. discussed this issue. $\endgroup$ – Omar Shehab Oct 3 '13 at 16:45
  • $\begingroup$ Actually the paper by Lim didn't discuss this issue for the context of the VV protocol. $\endgroup$ – Omar Shehab Oct 3 '13 at 18:34
  • $\begingroup$ No help yet! :( $\endgroup$ – Omar Shehab Oct 6 '13 at 16:47
  • 6
    $\begingroup$ It's a very good question, +1. The issue might simply be that the Vazirani-Vidick protocol is recent enough that no one has nailed down these issues yet. Here are my first thoughts: (1) email Thomas Vidick and ask him, (2) look at the following conference program: fields.utoronto.ca/programs/scientific/13-14/CQIQCV/… (it includes talks on progress toward experimental realization of VV-like protocols), (3) wait a year or two for someone to write a paper that addresses your questions head-on, or (4) write that paper yourself! $\endgroup$ – Scott Aaronson Oct 7 '13 at 12:42
  • $\begingroup$ @ScottAaronson, I can at least put together my thoughts in a QIP poster. I will try. $\endgroup$ – Omar Shehab Oct 8 '13 at 7:24

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