Amplifying, generating, or certifying randomness

1. A security test system comprising:

a non-transitory memory configured to store measurement outputs from a measurement apparatus, the measurement outputs comprising indications of presence or absence of coincidences where particles are detected at more than one detector at substantially the same time, the detectors being at an end of different channels from a particle source, the different channels having lengths that permit the detectors to detect the presence or the absence of coincidences; and

a processor configured to:

test for interaction between measurement devices of the measurement apparatus by:

generating a baseline histogram for a measurement device from a first set of measurements;

generating one or more test histograms for the measurement device from a second set of measurements; and

comparing the baseline histogram with the one or more test histograms;

compute a test statistic from the stored measurement outputs, the test statistic expressing a Bell inequality;

compare the test statistic with a threshold; and

generate a certificate certifying that the measurement outputs are from a quantum system if a value of the computed test statistic is below the threshold.

2. The security test system of claim 1 wherein the processor is configured to compute the test statistic by multiplying a reciprocal of a number of rounds of measurements by a sum, over the number of the rounds of measurements, of binary-valued array entries corresponding to the rounds of measurements, the corresponding entries determined according to values of measurement settings of detectors used in the measurement apparatus when individual ones of the rounds of measurements were made.

3. The security test system of claim 2 wherein the binary-valued array entries act to assess the coincidences as being evidence for or against quantum effects having generated individual ones of the measurements.

4. The security test system of claim 1 wherein a channel of the different channels carries qubits which are in either of the following quantum states:

a quantum state equal to the reciprocal of the square root of two times a sum of the quantum states of two pairs of qubits, where the quantum states of the pairs of qubits are entangled and in superposition; or

a quantum state equal to one half of a sum, over i from 0 to 3, of a tensor product of a qubit on an i th channel with the same qubit.

5. The security test system of claim 1 wherein the processor is further configured to compute a second test statistic and take the second test statistic into account before generating the certificate.

6. The security test system of claim 1 wherein the coincidences comprise detection of the particles at more than one detector in a specific time period.

7. The security test system of claim 6 wherein the specific time period is 15 nanoseconds or shorter.

8. The security test system of claim 7 wherein the specific time period is from 5 to 15 nanoseconds.

9. The security test system of claim 1 further comprising a detector configuration apparatus that automatically configures, according to values of control parameters for each detector, a measurement basis of the detector.

10. The security test system of claim 1 wherein the particles comprise photons, and each detector is arranged to detect single photons.

11. The security test system of claim 10 wherein the different channels comprise two photon paths, one path for each of two possible mutually orthogonal photon polarizations, each photon path travelling to a different one of the detectors.

12. The security test system of claim 11 wherein each of the measurement devices comprises four detectors comprising a first pair of detectors for each of two mutually orthogonal polarizations, and a second pair of detectors for each of two mutually orthogonal polarizations, where the first pair of detectors operates for a first optical mode, and the second pair of detectors operates for a second optical mode.