# Analyzing Innsbruck Bell experiment raw data sample

1. Aug 25, 2014

### Jabbu

Raw data sample source:
http://people.isy.liu.se/jalar/belltiming/

999 detections parsed in .txt format:

This below is the first 99 detections. It's unmatched raw data, so A-B pairs on the right are going to be different once the data is sorted out and ready for counting coincidences. Alice and Bob have four detectors each (0,1,2,3), two for 0 degrees and two for 45 degrees polarizer rotation.

Code (Text):

# 0=vertical, no rotation
# 1=horizontal, no rotation
# 2=vertical, 45degree rotation
# 3=horizontal, 45degree rotation

A-TIME    B-TIME      A-B
1:  0.0000022 0.0000529   0-0
2:  0.0000080 0.0000776   1-3
3:  0.0000127 0.0000927   0-0
4:  0.0000497 0.0001099   1-3
5:  0.0000529 0.0001300   0-0
6:  0.0000973 0.0002323   2-1
7:  0.0001282 0.0002482   0-0
8:  0.0001301 0.0002905   2-3
9:  0.0001443 0.0003017   0-0
10:  0.0001562 0.0003396   0-0
11:  0.0002056 0.0003470   0-0
12:  0.0002165 0.0003603   2-1
13:  0.0002194 0.0003883   0-0
14:  0.0002808 0.0004288   3-0
15:  0.0002983 0.0005772   0-0
16:  0.0003171 0.0005891   0-0
17:  0.0003296 0.0006135   0-0
18:  0.0003309 0.0006371   0-0
19:  0.0003424 0.0006647   0-0
20:  0.0003554 0.0007317   3-0
21:  0.0003615 0.0007469   0-0
22:  0.0003676 0.0007601   0-0
23:  0.0003898 0.0007825   0-0
24:  0.0004362 0.0008330   3-1
25:  0.0004437 0.0008839   0-0
26:  0.0004539 0.0008957   2-3
27:  0.0004914 0.0008982   0-0
28:  0.0004991 0.0009989   3-3
29:  0.0005282 0.0010620   0-0
30:  0.0005351 0.0010826   0-0
31:  0.0005416 0.0011126   0-0
32:  0.0005655 0.0011489   0-3
33:  0.0006468 0.0011678   0-0
34:  0.0006708 0.0012064   3-0
35:  0.0006767 0.0012985   0-0
36:  0.0006962 0.0013142   2-0
37:  0.0007817 0.0013765   0-0
38:  0.0007857 0.0014157   0-1
39:  0.0007993 0.0015135   0-0
40:  0.0008088 0.0015221   1-2
41:  0.0008259 0.0015419   0-0
42:  0.0008357 0.0015776   2-0
43:  0.0008391 0.0016791   0-0
44:  0.0008424 0.0017757   2-0
45:  0.0008485 0.0017868   0-0
46:  0.0008640 0.0018922   1-0
47:  0.0008770 0.0019115   0-0
48:  0.0008957 0.0019672   3-2
49:  0.0009142 0.0019713   0-0
50:  0.0009252 0.0019919   2-0
51:  0.0010379 0.0020254   0-0
52:  0.0010510 0.0020501   1-3
53:  0.0010650 0.0021090   0-0
54:  0.0010687 0.0021181   1-2
55:  0.0010735 0.0021392   0-0
56:  0.0010751 0.0021629   2-1
57:  0.0010763 0.0021994   0-0
58:  0.0010855 0.0022013   1-3
59:  0.0010991 0.0022063   0-0
60:  0.0011117 0.0022513   0-3
61:  0.0011236 0.0022674   0-0
62:  0.0011500 0.0023667   1-3
63:  0.0011513 0.0023788   0-0
64:  0.0012012 0.0024184   1-0
65:  0.0012200 0.0025019   0-0
66:  0.0012253 0.0025062   1-1
67:  0.0012410 0.0026088   0-0
68:  0.0012471 0.0026173   3-1
69:  0.0012574 0.0026490   0-0
70:  0.0012875 0.0026576   2-3
71:  0.0013107 0.0028493   0-0
72:  0.0013316 0.0028756   1-0
73:  0.0013761 0.0029057   0-0
74:  0.0014241 0.0029142   2-3
75:  0.0014748 0.0029372   0-0
76:  0.0014851 0.0029474   2-2
77:  0.0015024 0.0030059   0-0
78:  0.0015044 0.0030309   2-3
79:  0.0015106 0.0031342   0-0
80:  0.0015129 0.0031550   2-1
81:  0.0015150 0.0031565   0-0
82:  0.0015295 0.0032586   0-1
83:  0.0015542 0.0032745   0-0
84:  0.0015822 0.0032994   2-0
85:  0.0016125 0.0033041   0-0
86:  0.0016299 0.0033495   1-3
87:  0.0016477 0.0033801   0-0
88:  0.0016560 0.0033820   2-2
89:  0.0016966 0.0034207   0-0
90:  0.0016975 0.0034965   1-0
91:  0.0017108 0.0035036   0-0
92:  0.0017323 0.0036224   3-1
93:  0.0018108 0.0037002   0-0
94:  0.0018483 0.0037304   0-1
95:  0.0018778 0.0037377   0-0
96:  0.0019019 0.0037468   0-0
97:  0.0019060 0.0037955   0-0
98:  0.0019224 0.0038050   1-2
99:  0.0019713 0.0038233   0-0

Out of 999 ticks Alice recorded 649 "+" and 115 "-" detections on her 0 degrees detectors (0,1), while there was 135 "+" and 100 "-" detections for 45 degrees rotation (2,3).

Out of 999 ticks Bob recorded 634 "+" and 121 "-" detections on his 0 degrees detectors (0,1), while there was 116 "+" and 128 "-" detections for 45 degrees rotation (2,3).

Time-stamps and match-making. This is really the only problem here, but what a strange problem it is. You would think true matching pairs would be detected close together in the timeline and far away from other pairs, so they can be recognized and singled out, but for some reason they obviously are not.

The most peculiar thing, however, is that Alice's detectors constantly trigger at higher rate than Bob's. Almost half of Alice's data simply can not be matched and it needs to be discarded, but what to throw out and what to keep? So what in the world are those "extra" detections and why there is constantly much more detections on Alice's than Bob's detectors?

Last edited: Aug 25, 2014
2. Aug 25, 2014

### Jabbu

The ratio does smooth out close to 50%-50% for 45 rotation, but 649:115 and 634:121 ratio for 0 degrees polarizer rotation is still far away. Doesn't that look like incoming photons polarization averages out around a certain angle rather than being uniformly random?

Their software wouldn't run for me, I guess I need older Python version. Does it work for you?

3. Aug 25, 2014

### DrChinese

The issue about unmatched detections is not much really once you follow the logic. Here are a few points:

a. Perhaps 1 in a billion input photons are down converted. Virtually all of the rest are filtered out. But some light may bounce around a bit and not be filtered. If so, it may be unmatched and it will obviously not be entangled.

b. The creation time of the 2 photons is not exactly the same. But pairs are generally created far enough apart that 2 pairs will not "overlap". Keep in mind that a nanosecond translates into about a foot of distance.

c. Consequently, a time window must be defined to match up pairs. This is something the data analyst can work with. Extensive review of this parameter has not turned up any bias to date. PF member Peter Morgan (a mathematical physicist) has done substantial work on that.

d. Pairs may be created which are NOT polarization entangled. This can occur for a variety of reasons. Usually it is because they are distinguishable in some manner.

e. The actual collection of pairs is done by harvesting output photons at certain conic angles, ie a small deviation from straight out. Usually, it is about 2% off straight. Virtually all of the unconverted photons go straight through so this helps to filter out the unwanted ones as well.

In the end:

i) You end up losing some entangled pairs - these cannot assist in getting accurate entangled stats. This can be because either one or both of the photons in the pair are lost.
ii) You end up counting some unentangled pairs by mistake - these cannot assist in getting accurate entangled stats either.

The results of i) and ii) is always that your results is a smaller violation of your Bell inequality than expected. A typical result for CHSH inequality is 2.40 where 2.00 is the max possible for local realism, and 2.8 is the absolute max predicted by QM assuming perfect efficiency. A 2.40 reading, depending on the setup, may amount to 30 or more standard deviations.

4. Aug 25, 2014

### Jabbu

When detection pair is 2-2, 2-3, 3-2, or 3-3, it means both Alice and Bob polarizers are rotated at 45 degrees, but does that mean 0 or 90 degrees relative angle?

I think it's like this:

0-0, 0-1, 1-0, 1-1: theta_A = 0, theta_B = 0
0-2, 0-3, 1-2, 1-3: theta_A = 0, theta_B = +45
2-2, 2-3, 3-2, 3-3: theta_A = -45, theta_B = +45
2-0, 2-1, 3-0, 3-1: theta_A = -45, theta_B = 0

...so there are three possible relative angles: 0, 45, and 90 degrees, which makes two possibilities for 45 degrees, one possibility for 0 and one for 90 degrees?

Consider B-time: 0.0001300, it's easy to match it with A-time: 0.0001301, but there is about two possibilities of A-time for each B-time, and sometimes they are equally apart, so we have to choose the time before or the time after B-time. Is one preferred choice over the other? Is distance on both sides supposed to be the same, or is one photon actually supposed to arrive later than the other?

One A-time will usually be closer to each B-time than any other, so is it then reasonable to match every B-time with the closest A-time?

5. Aug 25, 2014

### Jabbu

Can you single out several matching pairs from the data to give an example how to apply that "time-window" and what value is it supposed to be for this data set?

6. Aug 25, 2014

### jk22

It is surprising that only one side has more photons, but i suppose there are double events when the detector click on both side and single events when it is only on one side.

7. Aug 25, 2014

### Staff: Mentor

A closed thread is not an invitation to continue the same discussion in another place.