{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Using the Gaussian State Toolkit\n",
"\n",
"*Ryan P. Marchildon*"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Gaussian states can be fully described by a covariance matrix and displacement vector, using a phase-space representation where we have phase quadratures \"x\" and \"p\" associated with each mode. Different modes refer to different eigenstates of a degree of freedom, such as optical path or polarization. Using a formalism called \"simplectic transformations\", we can evolve N-mode Gaussian states simply by transforming their covariance matrix and displacement vector, without the need to compute the full Wigner function (which is far more computationally expensive). \n",
"\n",
"The simplectic transformation recipes used in this toolkit are outlined in the following references:\n",
"1. Stefano Olivares, \"Quantum optics in the phase space\", ArXiv:1111.0786v2 (2011).\n",
"2. Alessandro Ferraro, Stefano Olivares, and Matteo G. A. Paris, \"Gaussian states\n",
" in continuous variable quantum information\" ArXiv:quant-ph/0503237 (2005).\n",
" \n",
"The code below provides a working example of the toolkit in action. \n",
" \n",
"You can download the toolkit source code here from github. \n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### Import Libraries"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"import GaussianStateTools as gs\n",
"import numpy as np\n",
"from IPython.display import HTML, display\n",
"\n",
"%matplotlib inline "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### Useful Helper Functions:"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"def print_covariance_matrix(sigma_):\n",
" print('Covariance Matrix:')\n",
" display(HTML('
'.join('{} | '.format(\n",
" ''.join(str(_) for _ in row)) for row in sigma_))))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"***"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### 1) Unitary Transformations"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Unitary transformations do not involve any dissipation (information loss to the environment or other systems, caused by optical loss or interactions). These transformations include squeezing, displacement, rotation, and two-mode mixing (the beamsplitter operation). \n",
"\n",
"Below we'll see how these transformations are easily implemented with our toolkit. "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### a) Basic One-Mode Examples:"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"First we'll initialize and plot a one-mode Gaussian state (which begins in vacuum)."
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
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ubZM31HckzIdyzTwh79snrZs52K3ligz0rH6aBbzD3bqVg91aKk+o5wn0Zw6ov17c4Jjs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\nF+AVw73AhsHHFt+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"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"psi_1 = gs.GaussianState(n_modes=1) # initialize instance of class GaussianState()\n",
"wigner_1 = gs.OneModeGaussianWignerFunction(state=psi_1, \n",
" range_min=-6, range_max=6, \n",
" range_num_steps=100)\n",
"wigner_1.plot()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Next we'll sequentially squeeze, displace, and rotate this state, plotting the Wigner function after each step:"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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3dLoiBkC95WlEREwUufM0IqJiEuwRERUzIYN9Ik5HIOk0SZbUyzWxpZL0MUm3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\nAAAASUVORK5CYII=\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# Squeeze...\n",
"# Note: beta_mag = r (the squeezing parameter)\n",
"psi_1.single_mode_squeeze(mode_id=1, beta_mag=0.7, beta_phase=0) \n",
"wigner_1A = gs.OneModeGaussianWignerFunction(state=psi_1, \n",
" range_min=-6, range_max=6, \n",
" range_num_steps=100)\n",
"wigner_1A.plot()"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# ...displace...\n",
"# alpha_mag and alpha_phase set the coherent magnitude and phase of the displacement\n",
"psi_1.displace(mode_id=1, alpha_mag=3, alpha_phase=np.pi/4) \n",
"wigner_1B = gs.OneModeGaussianWignerFunction(state=psi_1, \n",
" range_min=-6, range_max=6, \n",
" range_num_steps=100)\n",
"wigner_1B.plot()"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# ...and rotate state\n",
"psi_1.rotate(mode_id=1, phase=np.pi/4) # 45 degree rotation (pi/4)\n",
"wigner_1C = gs.OneModeGaussianWignerFunction(state=psi_1, \n",
" range_min=-6, range_max=6, \n",
" range_num_steps=100)\n",
"wigner_1C.plot()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Next, we'll generate a second state, with slightly different transformation parameters, and compare its fidelity with the first:"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The Wigner Function Overlap Between States 1 and 2 is: 0.758367735777\n",
"The Ulhmann Fidelity Between States 1 and 2 is: 0.7498749153556576\n",
"The Wigner Function Overlap of State 1 with Itself is: 1.0\n",
"The Ulhmann Fidelity of State 1 with Itself is: 1.0\n",
"\n",
"\n"
]
},
{
"data": {
"image/png": 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"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"psi_2 = gs.GaussianState(n_modes=1)\n",
"psi_2.single_mode_squeeze(mode_id=1, beta_mag=1, beta_phase=0)\n",
"psi_2.displace(mode_id=1, alpha_mag=2.7, alpha_phase=np.pi/4)\n",
"psi_2.rotate(mode_id=1, phase=np.pi/4)\n",
"\n",
"wigner_2 = gs.OneModeGaussianWignerFunction(state=psi_2, \n",
" range_min=-6, range_max=6, \n",
" range_num_steps=100)\n",
"\n",
"print('The Wigner Function Overlap Between States 1 and 2 is:', \n",
" gs.WignerOverlap(wigner_1C, wigner_2))\n",
"print('The Ulhmann Fidelity Between States 1 and 2 is:',\n",
" gs.OneModeFidelity(psi_1, psi_2))\n",
"print('The Wigner Function Overlap of State 1 with Itself is:', \n",
" gs.WignerOverlap(wigner_1C, wigner_1C))\n",
"print('The Ulhmann Fidelity of State 1 with Itself is:', \n",
" gs.OneModeFidelity(psi_1, psi_1))\n",
"print('\\n')\n",
"\n",
"# Visualize the overlap:\n",
"# initialize such that we share the same x_mesh and p_mesh\n",
"wigner_sum = wigner_1C \n",
"# reassign values, adding both wigner functions together\n",
"wigner_sum.values = (wigner_1C.values + wigner_2.values) \n",
"wigner_sum.plot()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### Basic Two-Mode Examples:"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Next we'll generate and plot a two-mode squeezed state. Note that computing Wigner functions becomes very computationally expensive, so we'll need to keep the sampling low. Thankfully, we don't need to compute the wigner function to obtain state fidelities, so we can easily represent multi-dimensional states without hitting computational bottlenecks. I generally use the Wigner function (or slices thereof) only for visualization."
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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A85mhX4zrFVIm/YLNipgJH4jLRZFvpR2SzrG9zvZKSZdL2jawzDZJVxY/Xyrp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\noL5ZOgZS9a5B01h43C+EgpaU2VBStuem7WgIBAAAzK7Mhc6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K+kREbEw8FKBz6BQAAAAA\nPUenAAAAAOg5OgUAAABAzxEKAAAAgJ4jFAAAAAA9RygAAAAAeo5QAAAAAPQcoQAAAADouf8DaWiZ\nxx2btX0AAAAASUVORK5CYII=\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"psi_3 = gs.GaussianState(n_modes=2)\n",
"psi_3.two_mode_squeeze(mode_1_id=1, mode_2_id=2, beta_mag=1.0, beta_phase=0.0)\n",
"wigner_3 = gs.TwoModeGaussianWignerFunction(state=psi_3, \n",
" range_min=-3, range_max=3, \n",
" range_num_steps=30)\n",
"wigner_3.plot_all() # see Figure 3(b) in \"Squeezed Light\" review article by Lvovsky."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now we will show interconversion between a two-mode squeezed state and two single-mode squeezed states, mediated by a 50:50 beamsplitter:"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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loylA4+Re7GkMACC9sg49zWGFedr3vJHIC0yPpgCNdMr3Hxv5WA6NwSjMAAFA\nfco49FSqLi8muaR1D40BqkZTgMaqsjGYt9hT6AEgD+OyQko/kTTv6rI0Pi+ASdEUoNGqWh6Wqlsi\nLqvQ0xgAwGRO+f5jlR56WtUq8zR5MQpZgUnRFKDxpi300uTFXpp9JmjcagEzQABQv6oaA2m+5qCM\nvGASCfOiKUAr1NEYzFLsy2oMRqHQA8B0qlxhlqo5N43GAHWgKUBrVHlCWU/ZxZ5CDwD1y3EiaZpz\n0XrIC5SJpgCtMq7QS9MtD5dV7Cn0AJCfqhsDqdzzDSa9ep1EXmA2SZoC25fZ3mP7uO1NKcaA9pr1\nTc5SFftRhZ7GAACqVeYKcxl5sdQkEheqQJVSrRTslvTzkv4x0ddHB9QxCySV0xwwAwQAaZS1wiyl\nywsaA5QhSVMQEXdGxPTHVABTKrMxmLXYTxoAFHoASGPWxmCWiSRp/rwYhrzAvDinAK1XVmMgTVfs\nyzq8iEIPANWb5dBTabYV5p7+nJgmL6Y57FQiLzCZypoC239ne/eQjy1TPs9W27ts7zpy/HBVw0XL\nzXrc6DzFfhYUemB25AXKUOcKc88sE0jTHHYKTKKypiAiXhkRFwz5+PiUz7MtIjZFxKYVp6yqarjo\ngFmWh6X5ZoFSozFAl5AXKEvdK8xlYhIJs+LwIXRK2Y1BFcW+zNUCAMBsZm0M6pxIYnUZZUp1SdJ/\nY3tB0r+Q9Le2b04xDnRTmceNStUUewo9AKQ3y6GnUr0TSaOQF5hWqqsPfSwi1kbEaRFxbkS8KsU4\n0G1lzwLVVewp9ABQnzJXmKXyJ5LGnVtAXmAaHD6ETitzFkgqt9hT6AEgD1WsMJMXyA1NATov91mg\nUSj0AFCvMleYpbwvWkFedA9NAaBqGoMyiv2sl5yjMQCAalSxwlx1czDrhSrIi26hKQAK8zQGqYr9\nqEK/FAp9PWxvtr3X9j7b1wx5/KW2v2L7qO3XDDx2pe1vFh9X1jdqAEspeyJJmn/VYKlJJBqDvOWQ\nFzQFQJ9ZjxuVli72VTUHFPo82V4m6XpJl0jaKOkK2xsHNrtH0q9K+tDAvk+R9CZJL5J0kaQ32V5d\n9ZgBTK6JE0mjkBdp5ZIXNAXAEGUvD/fMUvDneddKCn1SF0naFxH7I+KIpBslnfCO7hHxrYi4XdJg\nZ/cqSbdExMGIOCTpFkmb6xg0gMnN2hhIaSaSxq0u8543SWWRFzQFwAhVzAL1lF3s5yn0NAaVWSPp\n3r7bC8V9Ve8LoEZVrTBL0zcHk0wicdhplrLIi+Wz7AR0xardB8YWwtV7j4z8o/vMu04ZW3z7C/08\nqwE9D59/fGTAHNqwYmwwHb6+FpCPAAAgAElEQVRgzZJNUNstezTG/oxGONv2rr7b2yJiW/G5h2wf\nEz7vPPsCSGBcXvRqy7C86NXtSfKijKzofa1heUFWTGaGvBiXFVImecFKAbCESWaB5lk1kJ6YDRo1\nIzRpEMw6AyQxCzSjByJiU99Hf5FfkHRe3+21ku6b8Hnn2RdAIlUdTtSzVFZI8zcOrC5XYlxWSJnk\nBU0BMKGqi33PJEV/FhwvWrudktbbXmd7haTLJW2fcN+bJV1se3VxwtjFxX0AMjdvVkyaF/NmBYed\nZiWLvKApAKZQV2PQM0vRp9DnISKOSrpai8X5Tkk3RcQe29fZvlSSbL/Q9oKkyyS91/aeYt+Dkt6i\nxaDYKem64j4ADTDPCrM0fV70Z0VdVy8iL8qTS15wTgEwpXnPM5DmO8xnXhwzWp+I2CFpx8B91/Z9\nvlOLS73D9r1B0g2VDhBApao8L60M85yLJpEXZcohL1gpAGYwz4qBNNuqwTTmDRJmgACgHHUdTlQF\nDjvtFpoCYEZ1Lw+XaZJCT2MAAOXIeSJpqUkkDjvtDpoCYE65zgLNW+glij0AlKWMiaRUk0k0Bt1A\nUwCUYJLGIMdiz9IwANQrx1WDMs5doDFoPpoCoCRLzQJJ9Rd7Cj0A5KeJE0msLrcfTQFQsjIagzqL\nPYUeAOo3yVV76pxImmQSibxoN5oCoALzzgJJ5RT7SZ+DQg8A9StrhZm8QBloCoCKlDULNGuxr2K1\ngUIPAOWbtzGQ5qv5Ka+Gh3zwKgAqVMYskDR9czBLgeekYwBIp6wV5lzygkmk5qEpAGpQRrGXJiv4\n88z4UOgBIJ0yVph7JmkOql4hIC+ahaYAqEmZxV4aXvDrWgKm0ANANSZdYZ62OSg7LyZdXSYvmoOm\nAKjRpI3BLM1BWQ0BhR4A0it7IklKlxdoBpoCoGaTzAJJ0xf7MtEYAEB6VUwkpUBWNANNAZBI7o3B\npCj2AFCdSbJCSpcXTCK1B00BkFDOs0AsCwNAHqZZYc45L2gM8kZTACQ2zSxQrisHFHoAqF7uqwaT\nIC/yRVMAZGDSWSCp3mI/zWoBhR4AqteGiSTkiaYAyEiOjQEAIC+TZoVUX14widR8NAVAZnKbBaLQ\nA0B+pl1hzm0yibzID00BkKEcZ4EmRaEHgPrklBdcoKLZkjQFtv/I9jds3277Y7Z/JMU4gJw1fRYI\nAFCPaRuDXPKCSaS8pFopuEXSBRHxPEn/XdLvJRoHkL0civ20sz8UegCo1zRZIeXTHJAX+UjSFETE\npyPiaHHzi5LWphgH0BRNLPYUegCo1zQrzD1lZ8UshxCRF3nI4ZyC/13SJ1MPAshdDsUeAJC/lBNJ\n5E5zVdYU2P4727uHfGzp2+aNko5K+ssxz7PV9i7bu44cP1zVcIHGSFHsZ92f2R/UibwAnjDrRNI8\neTHPvuRFepU1BRHxyoi4YMjHxyXJ9pWSXi3ptRERY55nW0RsiohNK05ZVdVwgUaZttBLsxf7eRsK\nCj3qQl4AJ6srL8pYISAv0kp19aHNkt4g6dKI+EGKMQBNN8sskPREsV+qgJe5nNzVQm97s+29tvfZ\nvmbI46fZ/nDx+JdsP7O4/5m2D9u+rfj4z3WPHUB7zJIV0nR5gfnkkBepzil4t6QzJd1C4AHzmbXY\nS6MLPgV+fraXSbpe0iWSNkq6wvbGgc2uknQoIp4l6Z2S3tb32F0RcWHx8fpaBg2gtebJCmn0RFHZ\nedHFSaRc8mL5rDvOo/iGAJRk1e4DcxfSqhuBwxesmTuUGuYiSfsiYr8k2b5R0hZJd/Rts0XSfyw+\n/4ikd9t2nYME0B29GjxPXtQxaURepMmLHK4+BKAEsx5OVKeOzQCtkXRv3+2F4r6h2xSXaX5Q0lOL\nx9bZ/qrtf7D9U1UPFkB35J4VHZRFXiRZKQBQnTJWDbrolMOPzxKUZ9ve1Xd7W0RsKz4fNoMzeFGF\nUdt8R9IzIuK7tl8g6b/afm5EPDTtAAFgmDJWDaqU82rBDHkxLiukTPKCpgBooZyLfc6FfgYPRMSm\nEY8tSDqv7/ZaSfeN2GbB9nJJZ0k6WFyR7TFJiogv275L0rMl7RIAlIi8qMW4rJAyyQsOHwJarCXF\ntKl2Slpve53tFZIul7R9YJvtkq4sPn+NpM9ERNh+WnHimWz/mKT1kvbXNG4AHUReJJVFXtAUAC2X\n47kGOc5Ila045vNqSTdLulPSTRGxx/Z1ti8tNnufpKfa3ifpdyT1LkP3Ukm32/6aFk8oe31EHKz3\nOwDQNbllhURe1JkXHD4EdATnGtQvInZI2jFw37V9nz8q6bIh+31U0kcrHyAADCAr0sghL1gpADok\np1UDQgcA8pRTVkjkRV1oCoAOyqnYAwDylFtzgGrRFAAdlUOxZ/YHAPKXOisk8qIONAVAx6Uu9hR6\nAMhfDhNJqBZNAQCKPQBgIinzgkmkatEUAPghmgMAwCTIivahKQBwkrqLPbM/ANA8TCS1C00BgKEo\n9gCASZAX7UBTAGAsij0AYBJ1ZAUry9WhKQAwERoDAMBSmEhqLpoCABOj2AMAJkFeNA9NAYCpUewB\nAJMgL5qDpgDAzMos9hwnCgDtRXOQv+WpBwCg+foLPX/cAwBG6eUFWZEfVgoAlGrWmSBmkACgO1g5\nyA8rBQBKN6rQj5oZIhgAoJuG1X+yIg2aAgC1oaADAJZCVqTB4UMAAABAx9EUAAAAAB1HUwAAAAB0\nHE0BAAAA0HE0BQAAAEDH0RQAAAAAHUdTAAAAAHQcTQEAAADQcTQFAAAAQMclaQpsv8X27bZvs/1p\n2/9zinEAQJVsb7a91/Y+29cMefw02x8uHv+S7Wf2PfZ7xf17bb+qznEDAOqVQ16kWin4o4h4XkRc\nKOkTkq5NNA4AqITtZZKul3SJpI2SrrC9cWCzqyQdiohnSXqnpLcV+26UdLmk50raLOlPi+cDALRM\nLnmRpCmIiIf6bp4uKVKMAwAqdJGkfRGxPyKOSLpR0paBbbZIen/x+UckvcK2i/tvjIjHIuJuSfuK\n5wMAtE8WeZHsnALbb7V9r6TXipUCAO2zRtK9fbcXivuGbhMRRyU9KOmpE+4LAGiHLPJi+Sw7TcL2\n30n6n4Y89MaI+HhEvFHSG23/nqSrJb1pxPNslbS1uPnYpw68a3clA67G2ZIeSD2IKTRmvJ968buk\nBo23wHirtWGenR96/P6bP3XgXWdPudtK27v6bm+LiG3F5x6y/eCq6KhtJtkXA8iLWjVmvA3MiyaN\nVWreeOfKCmmmvBiXFVImeVFZUxARr5xw0w9J+luNaAqKH9o2SbK9KyI2lTPC6jHeajHeajVxvPPs\nHxGbyxpLYUHSeX2310q6b8Q2C7aXSzpL0sEJ98UA8qI+jLc6TRqr1Mzxzvscbc2LVFcfWt9381JJ\n30gxDgCo0E5J622vs71CiyeCbR/YZrukK4vPXyPpMxERxf2XF1ebWCdpvaR/qmncAIB6ZZEXla0U\nLOEPbW+QdFzStyW9PtE4AKASEXHU9tWSbpa0TNINEbHH9nWSdkXEdknvk/RB2/u0OONzebHvHts3\nSbpD0lFJvxkRx5J8IwCASuWSF0magoj4X2fcddvSm2SF8VZrpe3vSfp8RLw69WAm0LSfL+OdU0Ts\nkLRj4L5r+z5/VNJlI/Z9q6S3VjrAdsvu9bAExlsR2xdKWm17j6Rjkt4aER9OPKxxGvOzLTDeEuSQ\nF15ceQCax/YrJD1J0q81pCkAANTM9rMlRUR8s3iz1C9Lek5EfC/x0ICsJLskKTAp2y8s3gF7pe3T\nbe+xfUFE/L2kh1OPDwCQh2F5IWlFRHxTkiLiPkn3S3pa0oECGUp1TgEwsYjYaXu7pP8kaZWkv4iI\nJl1qEABQg6XywvZFklZIuivREIFscfgQGqE4G3+npEclvbh3Eo3tl0v6XQ4fAgBIY/Pi6ZI+J+nK\niPhiuhECeeLwITTFUySdIelMSSsTjwUAkK+T8sL2k7X4nki/T0MADEdTgKbYJukPJP2lpLclHgsA\nIF8n5EWxcvAxSR+IiL9OOjIgY5xTgOzZ/hVJRyPiQ7aXSbrV9k9LerOkfybpDNsLkq6KiJtTjhUA\nkM6wvNDi9dxfKumptn+12PRXI+K2RMMEssQ5BQAAAEDHcfgQAAAA0HE0BQAAAEDH0RQAAAAAHUdT\nAAAAAHQcTQEAAADQcTQFAAAAQMfRFAAAAAAdR1MAAAAAdBxNAQAAANBxNAUAAABAx9EUAAAAAB1H\nUwAAAAB0HE0BAAAA0HE0BQAAAEDH0RQAAAAAHUdTAAAAAHQcTQEAAADQcTQFAAAAQMfRFAAAAAAd\nR1MAAAAAdBxNAQAAANBxNAUAAABAx9EUAAAAAB1HUwAAAAB0HE0BAAAA0HE0BQAAAEDH0RQAAAAA\nHUdTAAAAAHQcTQEAAADQcTQFAAAAQMfRFAAAAAAdR1MAAAAAdBxNAQAAANBxyZoC2ytt/5Ptr9ne\nY/vNqcYCAFWwvdn2Xtv7bF8z5PGX2v6K7aO2XzPw2JW2v1l8XNl3/+eK57yt+Dinju8FAFCdHPJi\neXnfztQek/TTEfGI7VMlfd72JyPiiwnHBAClsL1M0vWSfkbSgqSdtrdHxB19m90j6Vcl/e7Avk+R\n9CZJmySFpC8X+x4qNnltROyq+FsAANQgl7xItlIQix4pbp5afESq8QBAyS6StC8i9kfEEUk3StrS\nv0FEfCsibpd0fGDfV0m6JSIOFoX9Fkmb6xg0AKB2WeRF0nMKbC+zfZuk+7X4DX0p5XgAoERrJN3b\nd3uhuK+Mff+sWAr+A9ueb5gAgMSyyIuUhw8pIo5JutD2j0j6mO0LImJ3/za2t0raKknLfOoLTl++\nOsFIkZu15y8eFrdw1/2JR4JcPPT4/Q9ExNNm3f8lL18Z3zs4OAEz3h1ff3yPpEf77toWEduKz4cV\n30lXQ8ft+9qIOGD7TEkflfQ6SR+Y8HlbjbzAMOQF+s2bFdL0ebFEVkiZ5EXSpqAnIr5n+3NaXO7Y\nPfDYNknbJOmsFefGi8/5xfoHiOy87YbfkiS94bJ3JR4JcvGpA+/69jz7f+/gcX3oE+dOtc+FP7rw\naERsGvHwgqTz+m6vlXTfhE+9IOnlA/t+TpIi4kDx78O2P6TFZWeaApEXGI68QL95s0KaPi+WyAop\nk7xIefWhpxUrBLK9StIrJX0j1XgAoGQ7Ja23vc72CkmXS9o+4b43S7rY9mrbqyVdLOlm28ttny1J\nxQUaXq2BiRQAQONkkRcpzyl4uqTP2r5diz+MWyLiEwnHAwCliYijkq7WYsG+U9JNEbHH9nW2L5Uk\n2y+0vSDpMknvtb2n2PegpLdosTbulHRdcd9pWiz2t0u6TdIBSf+l5m8NAFCiXPIi2eFDxRnUz0/1\n9QGgahGxQ9KOgfuu7ft8pxaXeofte4OkGwbu+76kF5Q/UgBASjnkBe9oDAAAAHQcTQEAAADQcTQF\nAAAAQMfRFAAAAAAdR1MAAAAAdBxNAQAAANBxNAUAAABAx9EUAAAAAB1HUwAAAAB0HE0BAAAA0HE0\nBQAAAEDH0RQAAAAAHUdTAAAAAHTc8tQDQHcdvmDNzPseP/20uZ9j1e4DM+8LAKjHPHVeIi+ASdEU\noDLzFvKqLTU+QgAAqpd7VkjkBbqBpgClaEJRn9aw74nCDwCza2NWSOQF2oGmAFNra1GfBIUfACZH\nXjyBrEDuaAqwpC4X9Un0/3wo+gC6jLwYjSYBuaMpwFAU9tlQ9AF0CVkxO/ICuaEpwA9R3MvHKgKA\ntiErqkFeIDWago6juNeHgg+gyciL+vR+1mQF6kRT0EEU9vQo+ACagLxIi8kk1ImmoEMo7vmh4API\nEXmRHyaTUDWagg6guDcDBR9ASmRFMzCZhKrQFLQYBb6ZaA4A1ImsaC7yAmWiKWghCnw7UOwBVIms\naA/yAmU4JfUAUJ7DF6yhyLcQ/6/NZXuz7b2299m+Zsjjp9n+cPH4l2w/s7h/he0/s/1121+z/fK+\nfV5Q3L/P9p/Ydm3fEFqBmtJe/N82Vw55QVPQAhSBbuD/uVlsL5N0vaRLJG2UdIXtjQObXSXpUEQ8\nS9I7Jb2tuP//kKSI+HFJPyPp/7bdq9fvkbRV0vriY3OV3wfagxrSHfxfN0sueUFT0GD80ncT/++N\ncZGkfRGxPyKOSLpR0paBbbZIen/x+UckvaKYydko6e8lKSLul/Q9SZtsP13SkyPiCxERkj4g6eeq\n/1bQdNSMbuL/vTGyyAuaggbij0JIFPsGWCPp3r7bC8V9Q7eJiKOSHpT0VElfk7TF9nLb6yS9QNJ5\nxfYLSzwn8EPkBXgNNEIWecGJxg3DLzb6cXJZcmfb3tV3e1tEbCs+H3bsZgzcHrXNDZKeI2mXpG9L\nulXS0QmfE5BEXuBEhy9YQ1akMy4rpEzygqagISjuGIdiP7/vHjtDHzz04in3uumBiNg04sEFLc7W\n9KyVdN+IbRZsL5d0lqSDxVLv/9nbyPatkr4p6VDxPOOeEx1HXmAUJpLKMX1ejM0KKZO8SHb4kO3z\nbH/W9p2299j+7VRjyR0FHpNgiTg7OyWtt73O9gpJl0vaPrDNdklXFp+/RtJnIiJsP8n26ZJk+2ck\nHY2IOyLiO5Ietv0TxbGkvyLp47V8N2gEagAmweskO1nkRcqVgqOS/n1EfMX2mZK+bPuWiLgj4Ziy\nwy8upsWqQR4i4qjtqyXdLGmZpBsiYo/t6yTtiojtkt4n6YO290k6qMUgkKRzJN1s+7ikA5Je1/fU\nvy7pzyWtkvTJ4gMdR1ZgWqwa5COXvEjWFBQdzHeKzx+2facWT4CgKVC3CvyhDSum3ufxVZ5539V7\nj0y9T9PQGOQhInZI2jFw37V9nz8q6bIh+31L0oYRz7lL0gWlDhSN1pW8mKXeS+TFUsiLPOSQF1mc\nU1C8AcPzJX0p7Ujy0OYCP2tRr3oMbSz8zAIB7dfWvMghK6Ru5QVZgeRNge0zJH1U0r+LiIeGPL5V\ni2+8oJXLzqx5dPVrU4HPpahPos2Fn2KPruhSXrQpK6Rm50WbskJiIqnLkjYFtk/VYkPwlxHxN8O2\nKS7ZtE2SzlpxbmsvvdeGAt+koj6J/u+n6UWfxgBdQF40R5vyom1NAnnRXcmaguJM6PdJujMi3pFq\nHDlocoFvU2Efpw1Fn1kgoPnIi/y1YUKJxqCbUq4UvESLZ0h/3fZtxX3/oTjRojOaWOC7UtjHaXLR\np9gDzUReNA9ZgSZJefWhz2v4u611RtMKfNeL+yi9n0uTCj7FHmiWJuUFWTFcExsEsqJbkp9o3FVN\nKfAU98k1rTmg2APNQF60T5PygkNPu4OmIIEmFHiK++yaNBtEYwDki6xoP/ICOTkl9QC6Jvcif2jD\nCop8iZrw88z9NQl0URN+L3OvbU3ThJ9nE16XmB1NQY1y/mVqwh+vTZb7zzfn1ybQNbn/PuZez5qs\nCT/b3F+fmB1NQU1y/SVqQgFqk5x/1rm+RoEuyfn3kLyoT+4/65xfp5gdTUENcvzlyb3gtFnOP/sc\nX6tAV+T6+5dzzWq7nH/2ub5eMTuagorl+EuTa4HpmlyLfY6vWaDtcvy9y7VGdVGu/xc5vm4xO5qC\nCuX2y5JrUem6HP9PcnvtAqhXjnUJ/L+gWjQFFcntjyoKSd5ybNhyew0DbZXT71qOtQgnyu3/KKfX\nL+ZDU1CBnH5BciseGI//K6BbcssLNEdO/185vY4xO968rGQ5/WLkVDAm8fD5xyfe9tiq6fc5865m\n9MA5vdMlb1YDVIe8mF2VedGUrJAW/99yyAqJvGgDmoISUeAnN01Br/Jr5lz8cyn2FHqgfLnkBVkx\n+dfMNS+YSEJZaApaJtcCn6KwT2JwXLkVfRoDoH1oCEbLNSsk8mJS5EVz0RSUJIcin1OBz7mwj9M/\n7lwKfi6zQBR6oD3Ii/nlmhepswLNlceruOFoCJ7w8PnHG1vgB/W+l1y+nxz+j3N4rQNNlsPvUA61\nRCIvqpLD/28Or3NMj5WCOeXwwk9dAHIoglXrfY+pZ4OYBQKaK3VepM4KibyoSw4rzKwuNw8rBQ2X\nssjnMitSpxxmg1IHe+o/bIAmSv17k0NWkBf1Iy8wDZqCOaR+saf6ZU9d5HKR8udAoQcwKbIivS7n\nBZqDpmBGqf8oSvFLToEfLtXPhUIPNEPKvEjZEOBkXWwMUv+9hMnRFDRQ3b/cNAOTSfFzotADeeta\nQ0BeLK2LE0nkRTPQFMwg1Yv70IYVtf5SU9xnQ2OAHtubbe+1vc/2NUMeP832h4vHv2T7mcX9r7V9\nW9/HcdsXFo99rnjO3mPn1PtdoQmYPMpf1yaSMF4OeUFTMKWUDUGdKO7zqbvYU+jzY3uZpOslXSJp\no6QrbG8c2OwqSYci4lmS3inpbZIUEX8ZERdGxIWSXifpWxFxW99+r+09HhH3V/7NYCZdyAuagfl1\nJS+YRBotl7ygKcAJKPDlotB32kWS9kXE/og4IulGSVsGttki6f3F5x+R9ArbHtjmCkl/VelI0Rp1\nNwQoTxfyAiNlkRc0BVNo+6wPBb4adTZaFPqsrJF0b9/theK+odtExFFJD0p66sA2v6iTi/yfFUvB\nfzAkFJCBFHlBQ9B8bW8MmEQaKYu8oCnIHA1Be7S5MehwoT/b9q6+j619jw0rvjFwe+w2tl8k6QcR\nsbvv8ddGxI9L+qni43Uzjh2YGqvJ1Wv7z7ijeTEuK6RM8oJ3NJ5QW2d9ci88Z6x7cOj9y1YeHfv4\nI3efVdmY5vHw+cdreZdL3vl4eg8dWalP37Nh2t0eiIhNIx5bkHRe3+21ku4bsc2C7eWSzpJ0sO/x\nyzUw6xMRB4p/H7b9IS0uO39g2oGjOuRFGrPkRa5ZIdWTF2TFbGbIi3FZIWWSFzQFmepagR9VzMt+\nvhwCoPdzr6M5qBNvaX+SnZLW214n6YAWC/YvDWyzXdKVkr4g6TWSPhMRIUm2T5F0maSX9jYuguBH\nIuIB26dKerWkv6v6G8HkaAiqVVdWSPnkRRsbA/LiJFnkBU3BBOou8l0o8GUX9lm/bsqiX3WxZwYo\nrYg4avtqSTdLWibphojYY/s6SbsiYruk90n6oO19WpzxubzvKV4qaSEi9vfdd5qkm4sCv0yLBf6/\n1PDtIFNV50XqrJDyyIvUWSFVO5FEXqSVS17QFHRQqiKfqrCPk7rot60xYPbnRBGxQ9KOgfuu7fv8\nUS3O7gzb93OSfmLgvu9LekHpA0Up2jaBlLIhyC0vUmeFRF60XQ55QVOwhDYV+RQFPrfCPk6qok+h\nB5Ab8mK0lA1CXeeloZt4ZWWkTQ3BGesebEyBH6bu8Vf9/8OlSoFqMYE0uybnRYqxV/n/U3dWdPRK\nRNmiKRiDF+v0mlzch6nz+8nh2F0A+WtLQ9CmvGjTRBKTSN2VtCmwfYPt+23vXnrrdmt6kW9TcR+m\nDY1BnYWehhponroagjbnBRNJaLLUKwV/Lmlz4jEMVecfNU1uCNpc3AfV9b1S6IFmaUNeMHlUrqbn\nBZNI3ZS0KYiIf9SJb7yAEtXREHRRHcWeQg9gUFMP6+hSMzCoyd97U19vmF3qlYLOa+KsT5OLXJlo\nDAC0ofmtOi9Q7c+hDavLbfg9aoPsmwLbW23vsr3ryPHDtXzNul6cTW0I8ISqG6Q2FHugLinyoi7k\nRfM1MSuYROqW7JuCiNgWEZsiYtOKU1alHk72KPBpNO1nU1ehZ/YHdWprXjStIWA1ebQqfzZNbwzI\ni/Sybwrq1uRVAgp8WhR6oFua/EdMlXmBpTUtL9ANqS9J+leSviBpg+0F21elHA9ORoGfDoX+ZE3+\nwwlIrWkTSJhck/KCSaRuSH31oSsi4ukRcWpErI2I96UcT12aUuQp8LNpUqEHMBua3RORF7Ph53Yi\nfq/S4vChPk19MdIQ5Kcph1wx+wPkiwmkbqji58dqAWaxPPUAuqYJv1S5FPiLn7F35GNPWfmDJbf5\n9D0bSh/TtM5Y96Aeufus0p7v4fOP68y76OUB5CGHvBiXA1Iz8qLsrABmQVPQcGXPBqQq8EsV9TKe\nM3XRz9WhDSu0eu+RSr/G4QvWaNXuA5V+DaBNmrBKQF6UqwmTSHXkBdKhKahR7qsEdRf4Kgr7pF+v\nzoLfhEIPYHJNPNS06Q0BeTGbJuYFk0jp0BQUKPL1qbu4jxtDXcU+90LP7A+ASdXZEJAXQH2a1T42\nWNmrBE2c9bn4GXuzKPD96hxTDsfeptTExhtIIee8qKuOkRfl/ZzL/nsh96MeMDuaAlRe5HMs7oPq\nGiOFHmi2pjW3TVtRJi+q0bTXQdN+z9qCpkDNe/E1adanaYWzicUeQHvk3JyTFyeqOi9yXl3O+XWK\n2dEU1KCrvzxNK/D9mlLomzb7A6CZqvwDtemTMU3JC2ApNAUdVnWRb7ouFvqqG9imrcoBTdaESYM2\nZIXUjO+jCa8HpEVT0DBl/VLTEEymCd8LhR6oR9VNba6rylXlRRPq6zSq+n6YREJdaAoqlmuRr0LT\nl4BH6VqhB9B8uU8gtTErpPzzgkkkjNP5pqBJnWjORb6tBb6n7d9fvy41sgDq1/Z62vbvD+3V+aYA\n8+tKAazi++zi7E+TGnGgLmU240wgpdeVvGASqV1oCirUhSLflQLfk3OhB4CckRdA3mgKgCnlWuiZ\n/cmP7c2299reZ/uaIY+fZvvDxeNfsv3MvseeZ/sLtvfY/rrtlcX9Lyhu77P9J7Zd33fUXV1b4WIC\nqRxlf99dm0Tq0u9dDnlBU9AhFPnydPl7x2RsL5N0vaRLJG2UdIXtjQObXSXpUEQ8S9I7Jb2t2He5\npL+Q9PqIeK6kl0t6vNjnPZK2SlpffGyu9jtBkzTpUEKkw+skL7nkBU1BA+T4y8sfxeXq2uxPR1wk\naV9E7I+II5JulLRlYJstkt5ffP4RSa8oZnIulnR7RHxNkiLiuxFxzPbTJT05Ir4QESHpA5J+ro5v\nBtVp+8pc1/Oi7d9/2yhmk5YAACAASURBVF+/NckiLzrdFFS5LMUvSfvlWOhzbCA7bI2ke/tuLxT3\nDd0mIo5KelDSUyU9W1LYvtn2V2z/X33bLyzxnMBcypykyLFOplDmz4FJpFbKIi+Wzzx8NApFvhoX\nP2OvPn3PhlKe64x1D+qRu88q5bkwvWOPLZvl53+27V19t7dFxLbi82HHbsbA7VHbLJf0k5JeKOkH\nkv7e9pclPTTBcwIAKjRDXozLCimTvOj0SgGA0apc7WrRyWMPRMSmvo/+Ir8g6by+22sl3Tew/w+3\nKY4LPUvSweL+f4iIByLiB5J2SPpfivvXLvGc6KgyVgqZQKpObqsFrCzXalxWSJnkBU1B5ijy+eNn\nghF2Slpve53tFZIul7R9YJvtkq4sPn+NpM8Ux37eLOl5tp9UFP+XSbojIr4j6WHbP1EcS/orkj5e\nxzeDanCoKdqA1/HcssgLmgIgI8z+tEdxzOfVWizYd0q6KSL22L7O9qXFZu+T9FTb+yT9jqRrin0P\nSXqHFoPiNklfiYi/Lfb5dUn/j6R9ku6S9MmaviVgYkyWDMfPZXotWlkeKZe84JyCCrS1Y6aYjVbm\nuQVoj4jYocWl3P77ru37/FFJl43Y9y+0eJm5wft3Sbqg3JFinC78USJxAmvTlHEe2sPnH9eZdzE/\nnIMc8oJXAgAADccKIYB50RS0HDM/mEdbV70AVIdV5fH4+SBXNAUZy2nmhyIGAADQXp1tCrpyjCjq\nU1bjxOoOAACoGycaoxFet/rWE26fu/yhofd/8NCLaxtTzjh5DEAKqVeVBzNByjMv2nhxikMbVmj1\n3iOph4E58FcDsjesyJexLQCklNM5O21YoZy2/rchL9rw/4Z80BRgSSlnfmYp2m0o9ACAyc1a98kL\n4Ak0BS3W5BmE162+da5inarQp146B9A9OV2UIoV5633XG4Ouv37whLFNge0n2z5/yP3PK+OL295s\ne6/tfbavKeM5AQAAAExnZFNg+xckfUPSR23vsf3Cvof/fN4vbHuZpOslXSJpo6QrbG+c93kBAO1g\ne5ntX7P9FtsvGXjs91ONCwDaaNxKwX+Q9IKIuFDS/ybpg7Z/vnjMJXztiyTti4j9EXFE0o2StpTw\nvACAdnivpJdJ+q6kP7H9jr7Hfn74LgCAWYy7JOmyiPiOJEXEP9n+l5I+YXutpCjha6+RdG/f7QVJ\nLxq3w9rzz9HbbvitEr60dPz000p5nmEeX1VGzyQdWzXf/stWHi1lHE9Z+YNSnmcavUvIjbJqxeKi\n0vnn3DRym19/ypNLHdOkfnHNk+Z+jmPPn/9qwcsOz/0UkqRTD5fx636yU77/WKnP96kXv6vU50MW\nLoqI50mS7XdL+lPbfyPpCi0xOdWEvMglKyTyIkVelJEVEnkxLbJitHErBQ/3n09QNAgv1+Js/nNL\n+NrDquFJrybbW23vsr3reBwr4csCABrih9fsjIijEbFV0tckfUbSGYMbkxcAMLtx7eWvSzrF9saI\nuEOSIuJh25slXV7C116QdF7f7bWS7hvcKCK2SdomSWetODfecFk5HV6V72hc1rWn570iQFlXH0px\nRZ2lrgbRm/G56/5fGLlNqjemKeMNaR65+6y5n6OsNy+r6s1oVu0+UMnzolV22d4cEZ/q3RERb7Z9\nQNJ7BjduWl7kkhUSeZEiL8p68zLyAmUZ2RRExNckyfZu2x+U9HZJK4t/N0n64Jxfe6ek9bbXSTqg\nxUbjl+Z8TgBAS0TEL0uS7ZWSfkPST2pxRfnzktIcHwgALTVJa/giLc7o36rFP+Tvk/SSsXtMICKO\nSrpa0s2S7pR0U0Tsmfd5AQCt8wEtHrb6LknvlvQcSe9POiIAaJlJzk55XNJhSau0uFJwd0SU8k4X\nEbFD0o4yngsA0FobIuKf993+rO2vJRsNALTQJCsFO7XYFLxQi0u3V9j+SKWjQuelOh8AQJa+avsn\nejdsv0jSf0s4HmRk3rwgb4BFkzQFV0XEtRHxeET8vxGxRdLHqx4Y5lfGyUcpzVOom3ySMYCTvEjS\nrba/Zftbkr4g6WW2v2779rRDS6+sk0SbbNaaT0PA6wdPWPKVEBG7htw370nGaJCUf+jOUrAp8kDr\nbJa0TotvZPay4vOflfRqSf864biQkWlrP1kBnGj+d7wAKjascPfeaIaiPhwzP2iTiPh26jFUYfXe\nI6VdlnRej9x9VimXJf30PRuSXJa0pyl5kdPlSMtS1eVIUZ/O/uXANW9RNg4dAgAATdXZpgDIVU4z\nPwAAoBtoCjKW0yEgzIJ3E8vBAAB0Qz5/daISzDoDAOrEJNJ4/HyQK5oCoAQUeQAplbGyzCRSs5Tx\n/5XTEQlIj1dDBdp6yAV/+FaPUG4X25tt77W9z/Y1Qx4/zfaHi8e/ZPuZA48/w/Yjtn+3775vFdfn\nv832SZeMRvm4MAWQTld+/3LIC5qCDuAPzWrl1iwx85MH28skXS/pEkkbtfhu8BsHNrtK0qGIeJak\nd0p628Dj75T0ySFP/y8j4sKI2FTysFEzJpG6pa0/l7a+juuSS17w10PmcvsDr60FDfXqyMzPRZL2\nRcT+iDgi6UZJWwa22SLp/cXnH5H0CtuWJNs/J2m/pD01jRcodRKJvDhRmT8PJvtaJ4u8yOsvTqBh\n2lzkmfmZ2xpJ9/bdXijuG7pNRByV9KCkp9o+XdIbJL15yPOGpE/b/rLtraWPGo2V2yQS8sbrJStZ\n5AXvaFyRnN6pUirv3Sql9O9YidEo8rNb9thMP7+zB47T3BYR24rPPWT7GLg9aps3S3pnRDxSTAT1\ne0lE3Gf7HEm32P5GRPzjtAMH6kBeLGLVpF1myItxWSFlkhedbgpW7T6gwxcMNmL5OfOuU/Tw+cdT\nD+MEFHqKPCRJD4w5TnNB0nl9t9dKum/ENgu2l0s6S9JBSS+S9Brbb5f0I5KO2340It4dEfdJUkTc\nb/tjWlx2/v/bu/dY2cryjuPfh4OAUkpbMF6AFhIJKRJrU8TY2EsKKjYtaAMRYiypJsRY0jbGRCkR\nW1obqUkvUXs5LbZWsUqhxlOhoNQaaxMVaoEePNAcb+FgU4P3C4hHn/6xZ9c5+8zMnr33rPW+71rf\nT3LCzJ61h3dmr/X85nnfmTU2BVqZVU4iafVqW1XWUhZlBVSSF04rStuw6obAIj9IdwCnR8RpEXEU\ncAmwZ8M2e4DLJpcvAj6Ya34mM0/NzFOBPwH+IDPfHBHHRsRxAJMl4+cCe/t4MOrOKt+qV+Nq4dgn\nUGp8/KvcT3yr6UpUkRf1VQ91ZtUvPGssdFoNi/zOTd7zeQVwG7APuCEz742IayLigslm17H2ntD9\nwCuBw05Dt8ETgI9ExN3Ax4GbM/PWbh6Bpo3kw/GdGWtejPVxr8pYjrta8mLUbx/q2io/V1DjW4hg\nnG8jqnWVoMYZwrHLzFuAWzb87Oqpy48AF29yH78zdfnTwE+sdpTS4XwLUZ1cVR6uGvLCVxEj00VB\nGdNMyJgea1fGMvMjbUWNbyHqYnV5LDW0i8fqBJK65p4xQjYG29PFY6yxyPvWIUldGnpeDP3xTTMv\nhmX0TUHXs5Y1zv50ZciFcMiPTdLw1LpasG6oNbWrx+XbhtSHul9lqjMW+uXVXuRrbxaloWhpEqkF\nQ8uLFh5PS3nhW037187eIaCNA7qFwris2hsCSepal/VqKHnR5eOoNS/G1sSOQf2vMNUZC/18Y/pA\n3LSui7wzP1J/VjmJZF7M10pD0MKkospyD6G9JeGWCn2Lxb7rMVvkJc0z1tnXFrMC2h23NIvfU6DO\ntfJdBn0U91qXgSUN0yq/46br7y5Yr8HmxZqaJ5DG2rwOndOMPRnrasG6mlcNah7bIhZ5qX9jfwuc\nedHP2MY+gTT246wUVwoE9PftlTXNBPUdOjXP+vTBIi8t54fvf5Qvn3HUyu5vlasFYF50bdUNgRNI\nWlZ7ryw60scLlppXC6DfmYmSM0El/t+1z/pY5KVhMy/a+3+vQosTSCrHlYLGtToDtG5WsV31rFDp\ngl77rI+krXns3gd5+KyTOv1/rHq1YAg21vIuVhCGlher1scEkqvK5dgU6DB9NwYb7bTwly7q02ov\n8GCRl8ai9UmkjVbRJAw5L5xA0lbZFExpdfZn1YUeyhf7abOK9otOetzc22rRRUNgkZfGo4XVgtqz\nAsabF6vm20yHr8grjIi4OCLujYjvRcTZJcagzbVQpGrVSkNgkZe2p9XVry7qiFmxM63kRR9aPa6G\notResxf4FeDDhf7/RXXxQqyrAmCx3zqfs0NZ5KXtayUvrHvb00pD4ATSOBRpCjJzX2aWP8fYDC2/\ngLExKK+r58oiL6l23/jM8ebFknyuVKM215cGoKsXZDYGZXRZ4FtdBpaGrq9JpFZWC9aZF4t1+fy0\nPIHU8qTsUHRWFSLi9ojYO+PfhVu8n8sj4s6IuPPR7z3c1XCLaLExsNgfrrUCDxZ5DdOQ86ILNgb9\nazEvNB6dnX0oM89b0f3sBnYDHH/UE3IV97mZPs5C1LKazjZRWosF3rcNaaiGnBddnYmoi7PXrVuv\nj+ZF902SeaFVsK0srLXVgnVjXzXo+vEPYcbHVQJptVrOizGzIdiceVGHUqckfWFEHACeBdwcEbeV\nGMcife6grRZ6GF+x76MZ6vLv5qyPpFmcSFq91vNC41Pq7EPvycyTM/PozHxCZj6vxDjGoK/GYAzF\nvvXHaEMgdWMIk0hgXqxKX49xKBNIrhLUwxazEq0Xehhuse/zcQ1l1sciL7XJvNg+s0Ktc69aYEgv\nbPosIEMp9n0/jqHM+khjNJTVAug/L4ZgKFkBrhKMWWdnH9LWdXV2iXVdnmVilhbPPFEqoIbUEFjk\npe4NKS+m6655sdiQGgLVx5WCTfT9AmdIM0Dr1mfca11BKD02l4GHKyLOj4j7I2J/RLxmxu1HR8S7\nJ7d/LCJOnfz8nIi4a/Lv7oh44bL3qXLMi50rXY83U3J8Q2sInEA6VA154UpBhYY0AzRLDbNCNQRO\nH4FrkS8nInYBbwGeAxwA7oiIPZn5yanNXgZ8OTOfEhGXANcCLwL2Amdn5sGIeBJwd0T8E5BL3KdG\nZMh5UUNWbBxHKUNrCHSoWvLCpmAJJb7MrI9CDxRtDmB2sV118a+hoG80xIZAhzkH2J+ZnwaIiHcB\nFwLTBflC4Hcml28E3hwRkZnfmtrmGNaK+7L3qYKG+OWXpSeSYH4dNy/a5ATSYarIC5uCJQ2xMYA6\niv1GyxTl7/7kkUtvW5uhNgQW+cOcBDwwdf0A8Mx520xmeb4KnAA8FBHPBN4K/Bjwksnty9ynRqav\nrIDyE0kbDTkv+moGnECqQhV5Mbz2U1s2xFmIGh33qSMG2xCM2IkRcefUv8unbosZ2+eG63O3ycyP\nZeZTgWcAV0bEMUvepwor0SD3ddybF/0YckMw0gmkRVkBleSFKwVbMNTVAqh3Fmgohh6kQyjyux7J\n7QTkQ5l59pzbDgCnTF0/Gfj8nG0ORMSRwPHAl6Y3yMx9EfFN4Kwl71Mj1WdemBXdGXJDMBTbyItF\nWQGV5MWwX6kMRJ8H7tBfvJbQ53Nqka/KHcDpEXFaRBwFXALs2bDNHuCyyeWLgA9mZk5+50iAiPgx\n4Azgs0vepypQqlHuc8XAvFitPp/TUlkxhAmkjlSRFx7RWzT0Qg82BqvSd2ha5OuSmQeBK4DbgH3A\nDZl5b0RcExEXTDa7DjghIvYDrwTWTxn3bNbOIHEX8B7gFZn50Lz77O9RqQXmRXvGkBWar5a88O1D\nDelraRh8O9FOlAhJG4I6ZeYtwC0bfnb11OVHgItn/N7bgbcve5+qU8kzEZkXbeg7L0o2BObFYjXk\nhS3+NpTcsfs+oF0i3poxNQSSNmdeaJYSz5UNgTbj0btNYyr0YLHfTKnnxyIvaRHzoi5jzAq1w6O2\nUaUOcIv9oUoWeBsCqQ2lj5eSeaHvK/V8lG4ISu//Wp5H7A6U3tFLHuhjbw5KPv7SBV7S1o01L9Zr\n5VjzovTjL50Xpfd7bc04j9IVKr3Dlz7gSxe8PtXwWEv/vaH8Pi9pe0rXj9L1s081PNbSf2+1ZxxH\nZ8dKv0iq5cCvoQh2oZbHVcPfufS+LrWshuOnhjpSwwRLF2p6XDX8nWvY37U1npJ0INYLQF+noFtk\nuiC2eoq6Gor6NAu8NAwlT1O6rs/TlW5mCKczNS8OZ160yaZgRWoo9FBXsYfDi2Wthb+2oj6thgIv\naXVqyIuaJpKgnayAevOilqywIWiXTcEK1VDoob7GYFothb/Woj6tlgIPFnlp1cyLxWrJCjAvtsKs\naJtNwYrVVOihnlmgeRYV252GQAuFfJ5aCjxY5KWhq7UxmLZZPd9JXrScFVBXXqhtNgUdqKUxgDaK\n/TyLCvWuhzffplU1FXgbAqk7tWUF1D+RNM8Y86KmrADzYgiGdYRoptoKh2Yr/YVkG1ngpe7VdpzV\nVIM0X21/p9r2Y22PTUFHajtAanvBqUPV9repbf+Vhqy24828qFeNf5va9l9tn01Bh2o8UGosKGNW\n49+jxv1WGroaj7vaatPY1fj3qHG/1fbZFHSs1gOmxuIyJjU2A5LKqjEvrFXl1fo3qHF/1c7YFPSg\n1gOn1kIzdDU/57Xuq9JY1HoMmhf9q/k5r3U/1c7YFPSk5gOo5sIzJLU/zzXvo9KY1Hws1l7HhqD2\n57jm/VM7Y1PQo9oPpNoLUatqf14fu/fB6vdNaWxqPyZrrmktq/15rX2/1M74PQU9q+m81PO0fr7q\nWtRe3MECL9Ws9ryYrnHmxfa1kBVgXoyBTUEBtRf6dTYHW9dKcQcLvNQC82K4zAvVxqagkFYKPTgb\ntIyWijtY4KWWmBfD0VpWgHkxJkWagoh4I/DLwKPAp4Bfy8yvlBhLSesHWivFHpwNmtZicQcLvNSi\nlhqDdebF95kXakGplYIPAFdm5sGIuBa4Enh1obEU13KxXzeWot9qYV9ngZfa1WJWwHhXD8wLtaZI\nU5CZ75+6+lHgohLjqEmrxX7dkIt+64V9nQVeal+LK8zThjyhZFaodTV8puClwLtLD6IGrTcG61ov\n+kMp7Oss8NLwmBflDS0rwLwYu86agoi4HXjijJuuysz3Tra5CjgIXL/gfi4HLgc4ZtdxHYy0Lq3P\nAs0yq3DWUviHWNSnWeA1JmPMiyFlBdSbF0PPCjAv1GFTkJn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"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"psi_3_before = psi_3.copy() # save the prior state, for later comparision\n",
"psi_3.two_mode_mix(mode_1_id=1, mode_2_id=2, R0=0.5) # mix both modes through a 50:50 splitter\n",
"wigner_3_after = gs.TwoModeGaussianWignerFunction(state=psi_3, \n",
" range_min=-3, range_max=3, \n",
" range_num_steps=30)\n",
"wigner_3_after.plot_all()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The correlations between x1-x2 and p1-p2 have been transferred to x1-p1 and x2-p2. Let's compute the two-mode overlaps and Uhlmann fidelities, before and after the beamsplitter transformation:"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Wigner Function Overlap, Before vs After Beamsplitter, is: 0.133\n",
"Check: wigner_3 overlap with itself is: 1.000\n",
"\n",
"Uhlmann Fidelity of States, Before vs After Beamsplitter, is 0.132\n",
"Check: Uhlmann Fidelity of psi_3 with itself is: 1.000\n"
]
}
],
"source": [
"print('Wigner Function Overlap, Before vs After Beamsplitter, is: %.3f' \n",
" % gs.WignerOverlap(wigner_3, wigner_3_after))\n",
"print('Check: wigner_3 overlap with itself is: %.3f' \n",
" % gs.WignerOverlap(wigner_3, wigner_3))\n",
"print('\\nUhlmann Fidelity of States, Before vs After Beamsplitter, is %.3f' \n",
" % gs.TwoModeFidelity(psi_3, psi_3_before))\n",
"print('Check: Uhlmann Fidelity of psi_3 with itself is: %.3f' \n",
" % gs.TwoModeFidelity(psi_3, psi_3))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Note that in general, for N-mode states, it is better to compute Uhlmann fidelities instead of overlaps due to the high computational expense of the latter; I have included the Wigner function overlap here only as validation."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"***"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### 2) Dissipative (Lossy) Transformations:"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Next, we show how we can also implement non-unitary dissipative transformations that model optical loss. We treat losses as a lumped beamsplitter of specified transmission, which mixes the optical mode with the environment (introducing vacuum noise). "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### a) One-Mode"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"First we'll initialize, squeeze, and displace a one-mode state. We'll also plot its Wigner function and print its covariance matrix. "
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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TedSR1NIn6S5J1+VVQ55GZbAXYDqCSyLiDRFxDHAdcEFOdawBjo6INwC/BBbn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\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"Covariance Matrix:\n"
]
},
{
"data": {
"text/html": [
"1.35914091423 | 0.0 | 0.0 | 0.183939720586 | "
],
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"psi_1 = gs.GaussianState(n_modes=1)\n",
"psi_1.single_mode_squeeze(mode_id=1, beta_mag=0.5, beta_phase=0) \n",
"psi_1.displace(mode_id=1, alpha_mag=1.5, alpha_phase=np.pi/4) \n",
"\n",
"wigner = gs.OneModeGaussianWignerFunction(state=psi_1, \n",
" range_min=-4, range_max=4, \n",
" range_num_steps=100)\n",
"wigner.plot()\n",
"\n",
"print_covariance_matrix(psi_1.sigma)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Next we'll apply dissipation to this state (optical losses of 67%, i.e. transmission of 33%) and view the results. "
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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zs4JxsJuZFYyD3cysYBzsZmYF42A3MysYB7uZWcE42M3MCsbBbmZWMA52M7OC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\nYDczK5j/D/1GXKvv2FXsAAAAAElFTkSuQmCC\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"Covariance Matrix:\n"
]
},
{
"data": {
"text/html": [
"0.783516501696 | 0.0 | 0.0 | 0.395700107793 | "
],
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"psi_1.dissipate(mode_id=1, transmission=0.33)\n",
"wigner = gs.OneModeGaussianWignerFunction(state=psi_1, \n",
" range_min=-4, range_max=4, \n",
" range_num_steps=100)\n",
"wigner.plot()\n",
"print_covariance_matrix(psi_1.sigma)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Note that the diagonal terms of the covariance matrix have both shifted closer towards 0.5, which is the vacuum quadrature variance. The optical loss has mixed our squeezed quadratures with uncorrelated vacuum noise as we'd expect, reducing the overall squeezing of the state. The state has also shifted towards the x-p origin, since its coherent amplitude has been reduced. "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let's also check the case where we set transmission to be 100%."
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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TedSR1NIn6S5J1+VVQ55GZbAXYDqCSyLiDRFxDHAdcEFOdawBjo6INwC/BBbn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\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"Covariance Matrix:\n"
]
},
{
"data": {
"text/html": [
"1.35914091423 | 0.0 | 0.0 | 0.183939720586 | "
],
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"psi_1 = gs.GaussianState(n_modes=1)\n",
"psi_1.single_mode_squeeze(mode_id=1, beta_mag=0.5, beta_phase=0)\n",
"psi_1.displace(mode_id=1, alpha_mag=1.5, alpha_phase=np.pi/4) \n",
"psi_1.dissipate(mode_id=1, transmission=1.0)\n",
"\n",
"wigner = gs.OneModeGaussianWignerFunction(state=psi_1, \n",
" range_min=-4, range_max=4, \n",
" range_num_steps=100)\n",
"wigner.plot()\n",
"print_covariance_matrix(psi_1.sigma)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Next, we check 0% transmission, which should return the vacuum state. "
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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gP2CHpJci4mu1OmtbsNcjaWpEPJIszgYezqMOM7MOWQFMlTQF+AMwFzijos0S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\nZlYwDnYzs4JxsJuZFcz/B2KvvChPR8HcAAAAAElFTkSuQmCC\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"Covariance Matrix:\n"
]
},
{
"data": {
"text/html": [
""
],
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"psi_1 = gs.GaussianState(n_modes=1)\n",
"psi_1.single_mode_squeeze(mode_id=1, beta_mag=0.5, beta_phase=0) \n",
"psi_1.displace(mode_id=1, alpha_mag=1.5, alpha_phase=np.pi/4) \n",
"psi_1.dissipate(mode_id=1, transmission=0.0)\n",
"\n",
"wigner = gs.OneModeGaussianWignerFunction(state=psi_1, \n",
" range_min=-4, range_max=4, \n",
" range_num_steps=100)\n",
"wigner.plot()\n",
"print_covariance_matrix(psi_1.sigma)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### b) Two Single-Mode Squeezed States"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Next we initialize two single-mode squeezed states:"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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W1QxNWR35qMF/0ll/1/tLGmTUySLrxaFGnSSyXkw/w79KNckAYKETGLZTX+hkhunUFzqv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\nJEmS1BEW/5IkSVJHWPxLkiRJHWHxL0mSJHWExb8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"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"Covariance Matrix:\n"
]
},
{
"data": {
"text/html": [
"1.35914091423 | 0.0 | 0.0 | 0.0 | 0.0 | 0.183939720586 | 0.0 | 0.0 | 0.0 | 0.0 | 1.35914091423 | 0.0 | 0.0 | 0.0 | 0.0 | 0.183939720586 | "
],
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"psi_2 = gs.GaussianState(n_modes=2)\n",
"psi_2.single_mode_squeeze(mode_id=1, beta_mag=0.5, beta_phase=0)\n",
"psi_2.single_mode_squeeze(mode_id=2, beta_mag=0.5, beta_phase=0)\n",
"psi_2.displace(mode_id=1, alpha_mag=1.5, alpha_phase=np.pi/4)\n",
"psi_2.displace(mode_id=2, alpha_mag=1.5, alpha_phase=np.pi/4)\n",
"\n",
"wigner_2A = gs.TwoModeGaussianWignerFunction(state=psi_2, \n",
" range_min=-4, range_max=4, \n",
" range_num_steps=40)\n",
"wigner_2A.plot_all()\n",
"\n",
"print_covariance_matrix(psi_2.sigma)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We'll apply dissipation to only one of these modes:"
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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eCXwHWEpaL+x89ksDbt/LDuCEJMcDtwBnAy8aY3+SpPWpVx/0Dsbrg7SGjXst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\n4l+SJEnqCIt/SZIkqSNaKf6TvCbJDUmuS/LhJA9vIw5JmqY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"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"Covariance Matrix:\n"
]
},
{
"data": {
"text/html": [
"1.35914091423 | 0.0 | 0.0 | 0.0 | 0.0 | 0.183939720586 | 0.0 | 0.0 | 0.0 | 0.0 | 0.783516501696 | 0.0 | 0.0 | 0.0 | 0.0 | 0.395700107793 | "
],
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"psi_2.dissipate(mode_id=2, transmission=0.33)\n",
"wigner_2B = gs.TwoModeGaussianWignerFunction(state=psi_2, \n",
" range_min=-4, range_max=4, \n",
" range_num_steps=40)\n",
"wigner_2B.plot_all() \n",
"print_covariance_matrix(psi_2.sigma)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### c) A Two-Mode Squeezed State"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Finally, we'll initialize a two-mode squeezed state..."
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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D+5wNvK33+irgxRERwEuBz2fm9QCZ+T8y86Ga2i1Jqlet+cLiX5KqcRxwR9/7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\nSZIk9YTNvyRJktQTNv+SJElST/w/uZVN/jDWQEMAAAAASUVORK5CYII=\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"Covariance Matrix:\n"
]
},
{
"data": {
"text/html": [
"0.771540317408 | 0.0 | 0.587600596822 | 0.0 | 0.0 | 0.771540317408 | 0.0 | -0.587600596822 | 0.587600596822 | 0.0 | 0.771540317408 | 0.0 | 0.0 | -0.587600596822 | 0.0 | 0.771540317408 | "
],
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"psi_3 = gs.GaussianState(n_modes=2)\n",
"psi_3.two_mode_squeeze(mode_1_id=1, mode_2_id=2, beta_mag=0.5, beta_phase=0.0)\n",
"psi_3.displace(mode_id=1, alpha_mag=1.5, alpha_phase=np.pi/4)\n",
"psi_3.displace(mode_id=2, alpha_mag=1.5, alpha_phase=np.pi/4)\n",
"\n",
"wigner_3A = gs.TwoModeGaussianWignerFunction(state=psi_3, \n",
" range_min=-4, range_max=4, \n",
" range_num_steps=40)\n",
"wigner_3A.plot_all() \n",
"print_covariance_matrix(psi_3.sigma)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"...and apply dissipation to mode 2 only:"
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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Ay9q4GlBX4F9m8NdKDP+SJGlh1DUAgB8P5HUPBuoO/MsM/hrF8C9JkhbKtH6r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\nf0mSJKkn/h84cMVKt7rp0QAAAABJRU5ErkJggg==\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"Covariance Matrix:\n"
]
},
{
"data": {
"text/html": [
"0.771540317408 | 0.0 | 0.193908196951 | 0.0 | 0.0 | 0.771540317408 | 0.0 | -0.193908196951 | 0.193908196951 | 0.0 | 0.589608304745 | 0.0 | 0.0 | -0.193908196951 | 0.0 | 0.589608304745 | "
],
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"psi_3.dissipate(mode_id=2, transmission=0.33)\n",
"wigner_3B = gs.TwoModeGaussianWignerFunction(state=psi_3, \n",
" range_min=-4, range_max=4, \n",
" range_num_steps=40)\n",
"wigner_3B.plot_all() \n",
"print_covariance_matrix(psi_3.sigma)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Since these modes are entangled, applying dissipation to only one of them nonetheless reduces the correlations in both the x1-x2 and p1-p2 quadrature slices. "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"***"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Closing Remarks:"
]
},
{
"cell_type": "markdown",
"metadata": {
"collapsed": true
},
"source": [
"The GaussianStateTools library provides a simple object-oriented pipeline that makes it easier to simulate Gaussian state evolution through complex sets of transformations, such as quantum circuits. \n",
"\n",
"Its uses include: \n",
"* designing integrated quantum circuits \n",
"* simulating quantum computing protocols\n",
"* modeling experimental setups\n",
"\n",
"To get started with the toolkit or contribute to its development, visit its source code here at github.\n"
]
}
],
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