Method and system for extractable randomness scaling in quantum random number generators
A method for entropy scaling in quantum random number generators, comprising dividing one spatial mode into multiple spatial modes, delaying each spatial mode, and recombing the spatial modes; detecting first temporal states with synchronisation to a photon generation time and encoding the first temporal states into first time bins; detecting second temporal states in an arbitrary clock, and encoding the second temporal states into second time-bins. The method comprises dividing a source of single photons into two paths in a first beam splitter and recombining the two paths in a next beam splitter, repeatedly, in a cascade of n beam splitters, consecutive beam splitters being separated by a length of fiber, yielding a number I=2 n of temporal states for each photon; detecting first temporal states by measuring a photon rate in a temporal window selected to measure photon arrival times, with synchronisation to a generation time of the photons, and encoding the first temporal states into first time bins, a number of the first temporal states being I=2 n ; detecting second temporal states by measuring a photon rate in the selected temporal window, in absence of synchronisation to the generation time of the photon, and encoding the second temporal states into second time-bins, a number of the second time bins being N v ; thereby generating a state space for each photon of N v ×I.
1. A method for entropy scaling in quantum random number generators, comprising:
dividing a single photon source of single photons into two paths in a first in a cascade of beam splitters BS 1 , BS 2 , . . . , consecutive beam splitters being separated by a fiber length length of fiber, each beam splitter in the cascade dividing an input spatial mode into, at an output, two equally probable modes that are temporally delayed due to the fiber lengths traversed by each mode, until a last beam splitter BS n ; yielding a number 1=2 n of temporal states for each photon, where n is the number of the beam splitters in the cascade;
detecting first a first set of temporal states 1 created by the beam splitter cascade by measuring photons a photon rate in a temporal window selected to measure with synchronisation to a generation time of the photons, using a heralding photon from a correlated source directly connecting the single photon source and a single-photon detector, wherein the heralding photon is used as a clock trigger to measure photon delay times and photon rates and encoding the first temporal states into;
detecting second a second set of temporal states N v with an arbitrary clock and encoding the temporal states of the second set into bit sequences by measuring a;
thereby generating an expanded state space of dimensions N v ×1 N v ×1.
2. The method of claim 1 , comprising determining a minimum entropy per bit of photon arrival events H η as:
H
η
=
1
-
H
dev
log
2
(
N
v
)
+
n
,
where H dev accounts for non-idealities; and increasing the number of the beam splitters in the cascade, each additional beam splitter resulting in an increase of the minimum entropy per bit of photon arrival events H η , as limited by the non-idealities and accumulated loss in the beam splitters.
3. The method of claim 1 , comprising determining a minimum entropy per bit of photon arrival events H η as:
H
η
=
1
-
H
dev
log
2
(
N
v
)
+
n
,
where H dev accounts for non-idealities; and adding a beam splitter in the cascade, to increase a random bit rate defined as H η *(log 2 (N v )+n)*Detected Photon rate.
4. The method of claim 1 , comprising determining a minimum entropy per bit of photon arrival events H η as:
H
η
=
1
-
H
dev
log
2
(
N
v
)
+
n
,
where H dev accounts for non-idealities; determining a range for the number of beam splitters optimizing minimum entropy per bit of photon arrival events H η depending on losses accumulated in the beam splitters; and adding at least one beam splitter in the cascade within the determined range, thereby increasing a random bit rate defined as H η *(log 2 (N v )+n)*Detected Photon rate.
5. The method of claim 1 , comprising determining a minimum entropy per bit of photon arrival events H η as:
H
η
=
1
-
H
dev
log
2
(
N
v
)
+
n
,
where H dev accounts for non-idealities; determining a range for the number of beam splitters optimizing minimum entropy per bit of photon arrival events H η , depending on losses accumulated in the beam splitters; and adding at least one beam splitter in the cascade within the determined range, thereby increasing a random bit rate defined as H η *(log 2 (N v )+n)*Detected Photon rate, the method further comprising at least one of: i) by changing source and detector parameters; and ii) changing beam splitters parameters in the cascade.
6. The method of claim 1 , wherein the single photon source is an attenuated laser source.
7. The method of claim 1 , wherein the single photon source is an entangled photon pairs source.
8. A method for entropy scaling in quantum random number generators, comprising successively dividing one initial spatial mode into two consecutive equally probable temporally delayed spatial modes; detecting a first set of resulting temporal states 1 with synchronisation to a photon generation time using a heralding photon from a correlated source directly connecting the single photon source and a single-photon detector and detecting a second set of resulting temporal states N v with an arbitrary clock, and encoding the temporal states of the second set into bit sequences.
9. The method of claim 8 , using a cascade of fiber-based beam splitters.
10. The method of claim 8 , using a cascade of fiber-based beam splitters and fiber delays.
11. The method of claim 8 , using a cascade of fiber-based beam splitters, a number of the beam splitters being n, and adding at least one beam splitter in the cascade.
12. The method of claim 8 , comprising using one of: entangled photon sources, nonlinear materials sources and attenuated laser sources.
13. The method of claim 8 , comprising using one of: detectors superconducting nanowires detectors, transition edge detectors, avalanche photodiodes detectors, charge coupled device cameras detectors, and photomultiplier tubes detectors.