CorrelationCurvesOutline.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": null,
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   "source": [
    "import numpy as np \n",
    "import matplotlib.pyplot as plt\n",
    "import scipy.optimize as opt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Import a curve file from the Correlation Curve quApp"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Graphing our data\n",
    "fileName = 'Unentangled'\n",
    "CoinData = np.loadtxt(fileName+'.txt', skiprows = 4, dtype=int)\n",
    "CoinData = np.transpose(CoinData)\n",
    "plt.plot(CoinData[0],CoinData[1],CoinData[0],CoinData[2],CoinData[0],CoinData[3],CoinData[0],CoinData[4])\n",
    "plt.legend(['H','+45','V','-45'], title = \"Polarizer 1 Angle\")\n",
    "plt.xlabel(\"Polarizer 2 Angle Degrees\")\n",
    "plt.ylabel(\"01 Coincidence Rates/1000ms\")\n",
    "plt.title(\"Correlation Curves (Coincidence Rates) for \"+ fileName)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The quED only measures integer angles at a time. If you set it to 180 degree steps, this will give you an array of half degree steps to use later."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "#This inserts .5 degree averages between two data points since the quED does not measure <1 degree\n",
    "\n",
    "Angles = []\n",
    "hA = CoinData[1]\n",
    "pA = CoinData[2]\n",
    "vA = CoinData[3]\n",
    "mA = CoinData[4]\n",
    "\n",
    "lastC = CoinData[0][0]\n",
    "for c in CoinData[0]:\n",
    "    Angles.append((c+lastC)/2)\n",
    "    Angles.append(c)\n",
    "    lastC = c\n",
    "Angles = np.array(Angles[1:])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here the indicies of the angles that will be used to perform CHSH are found"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Find index of Bell angles\n",
    "Pol2Angles = [22.5,67.5,112.5,157.5] #Bell Angles\n",
    "I = [] #Index Array\n",
    "for angle in Pol2Angles:\n",
    "    I = np.append(I, np.where(Angles==angle)[0]) #Find those angles\n",
    "I = np.int_(I)\n",
    "\n",
    "#Plot of where the Bell Angles are overlayed on the curves\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Create a fit function and store the parameters and covariance matrices generated by scipy curve fit. By calling the curve fit function with the store parameters you can reproduce the fit curve later."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Scipy fit\n",
    "Bases = [hA,pA,vA,mA]\n",
    "rad = np.pi*CoinData[0]/180 #convert to radians\n",
    "\n",
    "#Theoretical curve to fit our data to. This should have parameters for an x value and any fit parameters you need\n",
    "def QMCoincidences( ):\n",
    "    return \n",
    "\n",
    "#Optimize the parameters of the cos2 function to fit our data\n",
    "paramH, covH = opt.curve_fit(QMCoincidences, rad, Bases[0])\n",
    "paramP, covP = opt.curve_fit(QMCoincidences, rad, Bases[1])\n",
    "paramV, covV = opt.curve_fit(QMCoincidences, rad, Bases[2])\n",
    "paramN, covN = opt.curve_fit(QMCoincidences, rad, Bases[3])\n",
    "\n",
    "#Plot the curves with fitted data\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Graph residuals/use residual calculations to find closeness of fits metrics such as R^2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Residual graphs\n",
    "\n",
    "Hres = Bases[0]-QMCoincidences(rad, paramH[0], paramH[1], paramH[2])\n",
    "Pres = Bases[1]-QMCoincidences(rad, paramP[0], paramP[1], paramP[2])\n",
    "Vres = Bases[2]-QMCoincidences(rad, paramV[0], paramV[1], paramV[2])\n",
    "Nres = Bases[3]-QMCoincidences(rad, paramN[0], paramN[1], paramN[2])\n",
    "\n",
    "#Closeness of fit\n",
    "\n",
    "#Plot the residuals\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "After you have generated fits for each curve, use them to calculate expectation values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Use Fit Data and Bell Angles to calculate E and S using coincidence data \n",
    "rad = np.pi*Angles/180\n",
    "\n",
    "h1,h2,h3,h4 = QMCoincidences(rad[I], ) #Include the parameters used in your fit\n",
    "p1,p2,p3,p4 = QMCoincidences(rad[I], ) \n",
    "v1,v2,v3,v4 = QMCoincidences(rad[I], ) \n",
    "n1,n2,n3,n4 = QMCoincidences(rad[I], )\n",
    "\n",
    "#Calculate the expectation values. In addition to the formula from the prelab, you will need to \n",
    "#normalize the data since E takes probabilities as an input\n",
    "E1 =\n",
    "E2 = \n",
    "E3 = \n",
    "E4 =\n",
    "\n",
    "S = \n",
    "print(S)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Uncertainty calculations using the formula discussed in the procedure\n",
    "\n"
   ]
  }
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