PRL2018.ipynb

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   "source": [
    "import numpy as np\n",
    "\n",
    "def hFun(x):\n",
    "    return -x*np.log2(x)-(1-x)*np.log2(1-x)\n",
    "\n",
    "def gFun(p):\n",
    "    if p >= (2.0+np.sqrt(2.0)) / 4.0:\n",
    "        return 1\n",
    "    else:\n",
    "        return 1-hFun(1.0/2.0+1.0/2.0*np.sqrt(16.0*p*(p-1) + 3.0))\n",
    "    \n",
    "def NDFun(f, x, dx):\n",
    "    return (f(x+dx) - f(x)) / dx;\n",
    "    \n",
    "def fminFun(p, pt):\n",
    "    if p <= pt:\n",
    "        return gFun(p)\n",
    "    else:\n",
    "        return NDFun(gFun, pt, 1E-7)*p+(gFun(pt)-NDFun(gFun, pt, 1E-7)*pt)\n",
    "    \n",
    "def rFun(p, pt, n, eS, eEA):\n",
    "    return fminFun(p, pt) - 1/np.sqrt(n)*2*(np.log2(13)+NDFun(gFun, pt, 1E-7))*np.sqrt(1-2*np.log2(eS*eEA))\n",
    "\n",
    "def rOpt(omega, n, eS, eEA, dEst):\n",
    "    pList = np.linspace(0.75+1E-5, (2.0+np.sqrt(2.0))/4.0-1E-5, int(1E5))\n",
    "    result = [rFun(omega-dEst, pList[i], n, eS, eEA) for i in np.arange(pList.size)]\n",
    "    rmax = np.amax(result)\n",
    "    rindex = np.argmax(result)\n",
    "    return rmax\n",
    "\n",
    "n = 4E5 # experiement run number\n",
    "eS = 1/np.sqrt(n) # smoothing error\n",
    "eEA = 1/np.sqrt(n) # EAT error\n",
    "dEst = np.sqrt(10.0 / n) # confidence level\n",
    "rOpt(0.803, n, eS, eEA, dEst) # the first parameter is CHSH score in range [0.75, 0.853]"
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      "/var/folders/xs/rnkzw7gd4yz5rf2t9t85j7rc0000gn/T/ipykernel_19968/1632648679.py:10: RuntimeWarning: invalid value encountered in sqrt\n",
      "  return 1-hFun(1.0/2.0+1.0/2.0*np.sqrt(16.0*p*(p-1) + 3.0))\n"
     ]
    }
   ],
   "source": [
    "scorelis = np.linspace(0.7501, (2+np.sqrt(2))/4-0.0001, 200)\n",
    "resultlis = [rOpt(i, n, eS, eEA, dEst) for i in scorelis]\n",
    "np.savetxt('PRL2018.txt', np.vstack((scorelis, resultlis)).transpose())"
   ]
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