Quantum Cryptography BB84 simulation
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{
"cells": [
{
"cell_type": "code",
"execution_count": 19,
"id": "cc79f1dd",
"metadata": {},
"outputs": [],
"source": [
"from matplotlib import pyplot as plt\n",
"import sympy as sp\n",
"sp.init_printing()\n",
"plt.style.use('seaborn-deep')\n",
"plt.rcParams['figure.dpi'] = 140\n",
"f, mu, delta, l, p_dc, p_opt, f, eta, n = sp.symbols(r'f \\mu \\delta l p_{dc} p_{opt} f \\eta n')"
]
},
{
"cell_type": "code",
"execution_count": 20,
"id": "1ac718e2",
"metadata": {},
"outputs": [],
"source": [
"approx_values = {\n",
" r'\\mu': 1,\n",
" 'f': 1,\n",
" r'\\delta': 0.2,\n",
" 'l': 1,\n",
" r'p_{dc}': 0.02,\n",
" r'p_{opt}': 0.01,\n",
" r'\\eta': 0.2\n",
"}\n",
"variables = {\n",
" r'\\mu': mu,\n",
" 'f': f,\n",
" r'\\delta': delta,\n",
" 'l': l,\n",
" r'p_{dc}': p_dc,\n",
" r'p_{opt}': p_opt,\n",
" r'\\eta': eta\n",
"}"
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "b65f4f73",
"metadata": {},
"outputs": [],
"source": [
"def pop_in_place(d, k):\n",
" return {key: d[key] for key in d.keys() if key != k}"
]
},
{
"cell_type": "markdown",
"id": "01aa0680",
"metadata": {},
"source": [
"**Key generation rate:**\n",
"\n",
"$$R=\\dfrac 12 f (\\mu t \\eta + 2p_{dc})$$\n",
"\n",
"**Error rate:**\n",
"\n",
"$$E=\\dfrac{p_{dc} + p_{opt} n t \\eta}{2 p_{dc} + n t \\eta}$$"
]
},
{
"cell_type": "code",
"execution_count": 21,
"id": "e7c63373",
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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\n",
"text/latex": [
"$\\displaystyle 10^{- \\frac{\\delta l}{10}}$"
],
"text/plain": [
" -\\delta⋅l \n",
" ──────────\n",
" 10 \n",
"10 "
]
},
"execution_count": 21,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"t = 10 ** (-l * delta / 10)\n",
"t"
]
},
{
"cell_type": "code",
"execution_count": 22,
"id": "9a69c84c",
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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\n",
"text/latex": [
"$\\displaystyle \\frac{f \\left(2 p_{dc} + 10^{- \\frac{\\delta l}{10}} \\eta \\mu\\right)}{2}$"
],
"text/plain": [
" ⎛ -\\delta⋅l ⎞\n",
" ⎜ ────────── ⎟\n",
" ⎜ 10 ⎟\n",
"f⋅⎝2⋅p_{dc} + 10 ⋅\\eta⋅\\mu⎠\n",
"────────────────────────────────────\n",
" 2 "
]
},
"execution_count": 22,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"R = f * (mu*t*eta+2*p_dc) / 2\n",
"R"
]
},
{
"cell_type": "code",
"execution_count": 23,
"id": "6637fe0a",
"metadata": {},
"outputs": [],
"source": [
"E = (p_dc + p_opt * n * t * eta) / (2 * p_dc + n * t * eta)"
]
},
{
"cell_type": "code",
"execution_count": 24,
"id": "82a82472",
"metadata": {},
"outputs": [],
"source": [
"def plot_for_key(key, key_range, title='', show=True):\n",
" subs = pop_in_place(approx_values, key)\n",
" if subs.get('\\mu') is not None:\n",
" subs['n'] = subs['\\mu']\n",
" plot = sp.plotting.plot(R.evalf(subs=subs), E.evalf(subs=subs), (variables[key], *key_range), xlabel=f'${key}$', ylabel='', show=False, title=title or f'$R$ and $E$ vs. ${key}$')\n",
" plot[1].line_color = 'r'\n",
" if show:\n",
" plot.show()\n",
" return plot"
]
},
{
"cell_type": "code",
"execution_count": 25,
"id": "bf4db181",
"metadata": {},
"outputs": [
{
"ename": "ValueError",
"evalue": "The same variable should be used in all univariate expressions being plotted.",
"output_type": "error",
"traceback": [
"\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
"\u001b[0;31mValueError\u001b[0m Traceback (most recent call last)",
"\u001b[0;32m<ipython-input-25-9cbfa17e5309>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mplot_for_key\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34mr'\\mu'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0;36m0.5\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m3\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
"\u001b[0;32m<ipython-input-24-2836792b187f>\u001b[0m in \u001b[0;36mplot_for_key\u001b[0;34m(key, key_range, title, show)\u001b[0m\n\u001b[1;32m 3\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0msubs\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mget\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'\\mu'\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mis\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0;32mNone\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 4\u001b[0m \u001b[0msubs\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m'n'\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0msubs\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m'\\mu'\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 5\u001b[0;31m \u001b[0mplot\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0msp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mplotting\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mplot\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mR\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mevalf\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0msubs\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0msubs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mE\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mevalf\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0msubs\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0msubs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0mvariables\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mkey\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m*\u001b[0m\u001b[0mkey_range\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mxlabel\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34mf'${key}$'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mylabel\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m''\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mshow\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mFalse\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mtitle\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mtitle\u001b[0m \u001b[0;32mor\u001b[0m \u001b[0;34mf'$R$ and $E$ vs. ${key}$'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 6\u001b[0m \u001b[0mplot\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mline_color\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m'r'\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 7\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mshow\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
"\u001b[0;32m/usr/lib/python3.9/site-packages/sympy/plotting/plot.py\u001b[0m in \u001b[0;36mplot\u001b[0;34m(show, *args, **kwargs)\u001b[0m\n\u001b[1;32m 1726\u001b[0m \u001b[0mfree\u001b[0m \u001b[0;34m|=\u001b[0m \u001b[0ma\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mfree_symbols\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 1727\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mfree\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m>\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 1728\u001b[0;31m raise ValueError(\n\u001b[0m\u001b[1;32m 1729\u001b[0m \u001b[0;34m'The same variable should be used in all '\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 1730\u001b[0m 'univariate expressions being plotted.')\n",
"\u001b[0;31mValueError\u001b[0m: The same variable should be used in all univariate expressions being plotted."
]
}
],
"source": [
"plot_for_key(r'\\mu', (0.5, 3))"
]
},
{
"cell_type": "code",
"execution_count": 9,
"id": "a4d125cc",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 840x560 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
},
{
"data": {
"text/plain": [
"<sympy.plotting.plot.Plot at 0x7fd53264ddf0>"
]
},
"execution_count": 9,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"plot_for_key(r'l', (0.5, 10))"
]
},
{
"cell_type": "code",
"execution_count": 18,
"id": "35cb0bcc",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 840x560 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
},
{
"data": {
"text/plain": [
"<sympy.plotting.plot.Plot at 0x7fd53209ceb0>"
]
},
"execution_count": 18,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"plot_for_key(r'p_{dc}', (0, 1))"
]
},
{
"cell_type": "code",
"execution_count": 11,
"id": "5cc66fa2",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 840x560 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
},
{
"data": {
"text/plain": [
"<sympy.plotting.plot.Plot at 0x7fd5325d3c70>"
]
},
"execution_count": 11,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"plot_for_key(r'p_{opt}', (0, 1))"
]
},
{
"cell_type": "code",
"execution_count": 12,
"id": "9c2bd9df",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 840x560 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
},
{
"data": {
"text/plain": [
"<sympy.plotting.plot.Plot at 0x7fd5325cac70>"
]
},
"execution_count": 12,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"plot_for_key(r'\\eta', (0, 1))"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "b0675f39",
"metadata": {},
"outputs": [],
"source": [
"h = lambda p: - (p * sp.log(p, 2) + (1 - p) * sp.log(1 - p, 2))\n",
"R_sec = R * (- h (E))"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.9.7"
}
},
"nbformat": 4,
"nbformat_minor": 5
}