Randomness in post-selected events

Understand

Bell inequality violations can be used to certify private randomness for use in cryptographic applications.

• In photonic Bell experiments, a large amount of the data that is generated comes from no-detection events and presumably contains little randomness.
• This raises the question as to whether randomness can be extracted only from the smaller post-selected subset corresponding to proper detection events, instead of from the entire set of data.
• This could in principle be feasible without opening an analogue of the detection loophole as long as the min-entropy of the post-selected data is evaluated by taking all the information into account, including no-detection events.