- initial commit

.gitignore

@@ -34,3 +34,5 @@ nosetests.xml
 .mr.developer.cfg
 .project
 .pydevproject
+
+*.npy.gz

LICENSE

@@ -290,8 +290,8 @@ to attach them to the start of each source file to most effectively
 convey the exclusion of warranty; and each file should have at least
 the "copyright" line and a pointer to where the full notice is found.
 
-    {description}
-    Copyright (C) {year}  {fullname}
+    Clocked EPR simulation violating the CHSH
+    Copyright (C) 2014  Michel Fodje
 
     This program is free software; you can redistribute it and/or modify
     it under the terms of the GNU General Public License as published by

README.md

@@ -1,4 +1,112 @@
-epr-clocked
+EPR-clocked
 ===========
 
-Simulation of a clocked EPR experiment violating the CHSH
+A somewhat more complicated but still simple enough simulation of a clocked EPR experiment violating the CHSH.
+
+How it works:
+------------
+Based on my previous epr-simple simulation with some tweaks (more on this later):  
+
+        - `p`, and `p'` are now instrument random variables using a very similar 
+        ½ sin²t, t ∈ [0..π/6) distribution. Separately for each station
+        - All particles emitted by the source are now detected. No zero outcomes.
+        - A(a,λ) = sign(-1ⁿ cos n(a − e)), B(b,λ') = sign(-1ⁿ cos n(b − e'))
+
+Running it:
+-----------
+There are 3 programs in the distribution.  
+
+1) 'source.py':  
+
+        Usage:
+	         python source.py <spin> <duration in seconds>
+
+Generates two files containing the emitted particles, one for each arm of the experiment.
+Each file is a gzipped binary numpy array file containing 4 columns with the rows representing a the 
+parameters of a single emitted particle. The files are named `SrcLeft.npy.gz` and `SrcRight.npy.gz`.
+The columns are:  
+
+        'emission-time'
+        'hidden-variable 1'
+        'hidden-variable 2'
+        'hidden-variable 3'
+        
+The source program takes as input, 2 parameters:
+
+        `spin` : (either 0.5 or 1.0) Whether to generate spin-½ or spin-1 particles
+        `duration`: (in seconds), determines how long the source will run, and how many 
+          particles pairs will be generated. The number of particles in each file is printed at the end.
+
+NOTE, VERY IMPORTANT: 0.01% of particles emitted are randomly discarded so that 
+for 0.01% of particles, there will be no counterpart in the other file. Other 
+than that, the particles are recorded sequentially in time. This means it won't 
+work to simply assume that the nth particle in one file is a pair with the nth 
+particle of the other file. This also means 99.9% of emitted particles are paired.
+
+
+2) `station.py`:  
+
+        Usage:
+	         python station.py <ArmSrcFile> <StationName> [seting1,setting2,setting3,...]
+
+Reads one of the source files generated by `source.py` and generates another file
+containing the outcomes. The same program is run on both arms just with a different
+source file. The input parameters are:  
+
+        `ArmSrcFile`: one of `SrcLeft.npy.gz` or `SrcRight.npy.gz`
+        `StationName`: The name of the station, e.g. "Alice" or "Bob"
+        `settings sequence`: optional comma separated list of settings to randomly chose between
+           for example 0,22.5,45,67.5 (no spaces between). if no sequence is provided, a sequence of
+           33 evenly spaced angles between 0 and 2π will be generated and used.
+
+The output file will be named based on the `StationName` provided (like `<StationName>.npy.gz`). The format is also 
+a gzipped binary numpy array file containing 3 columns with the rows representing a detected 
+outcome. The columns are:  
+
+        `detection-time`: The time the detector fired
+        `active-setting`: The setting that was active at the time
+        `outcome`: +1 or -1
+
+NOTE: There will be as as many rows in the output file as there were in the corresponding source file. 
+Since all particles are detected. In other words, every particle which reaches the station is detected (100%).
+
+3) `analyse.py`:  
+Although not required to run and test the simulation, this is an analysis program which does
+the analysis in a manner similar to how it is done in typical EPR experiments. It borrows some matching algorithms
+from Jan-Åke Larsson's BellTiming code (Jan-Åke Larsson). At some point, I might rewrite the matching algorithm but this suffices for now.
+
+The analysis program does not take any inputs. Instead it expects to find two files named `Alice.npy.gz` and `Bob.npy.gz`. It prints some 
+Statistics.
+
+
+Results:
+--------
+
+For a 120second simulation of the source, I get the following results:  
+
+        No. of detected particles, non-zero outcomes only
+	        Alice:         2654386
+	          Bob:         2654381
+
+
+        Calculation of expectation values
+          Settings       N_ab     Trials   <AB>_sim    <AB>_qm
+           0, 22.5       1646       2034      0.738      0.707
+           0, 67.5       1599       1963     -0.739     -0.707
+          45, 22.5       1632       2012      0.714      0.707
+          45, 67.5       1615       2024      0.714      0.707
+
+	        Same Angle <AB> = +1.00
+	        Oppo Angle <AB> = -1.00
+	        CHSH: <= 2.0, Sim: 2.905, QM: 2.828
+
+        Statistics of residuals between exact QM curve and Simulation
+              Skew:         -0.4193
+             Range: -0.01045 : 0.007545
+            Length:              32
+          Variance:        1.76e-05
+          Kurtosis:        -0.08083
+              Mean:        0.000445
+
+
+The file `analysis.png` shows the curves. You might not even notice that there are two curves because the fit is good.