{ "metadata": { "name": "", "signature": "sha256:cc1b557800b0507cb1f0090885bf889468ad24c9772a5ebb96ac92e3ca0299d8" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# QuTiP lecture: Evolution and quantum statistics of a quantum parameter amplifier\n", "\n", "Author: J. R. Johansson (robert@riken.jp), http://dml.riken.jp/~rob/\n", "\n", "The latest version of this [IPython notebook](http://ipython.org/ipython-doc/dev/interactive/htmlnotebook.html) lecture is available at [http://github.com/jrjohansson/qutip-lectures](http://github.com/jrjohansson/qutip-lectures).\n", "\n", "The other notebooks in this lecture series are indexed at [http://jrjohansson.github.com](http://jrjohansson.github.com)." ] }, { "cell_type": "code", "collapsed": false, "input": [ "%matplotlib inline\n", "import matplotlib.pyplot as plt\n", "from matplotlib import cm\n", "import numpy as np" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 36 }, { "cell_type": "code", "collapsed": false, "input": [ "from qutip import *" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 2 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Parameters\n", "----------" ] }, { "cell_type": "code", "collapsed": false, "input": [ "chi = 0.2\n", "N1 = 75\n", "N2 = 75" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 3 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Operators and Hamiltonian\n", "-------------------------" ] }, { "cell_type": "code", "collapsed": false, "input": [ "a = tensor(destroy(N1), qeye(N2))\n", "na = tensor(num(N1), qeye(N2)) \n", "b = tensor(qeye(N1), destroy(N2))\n", "nb = tensor(qeye(N1), num(N2)) " ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 4 }, { "cell_type": "code", "collapsed": false, "input": [ "H = - chi * (a * b + a.dag() * b.dag())" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 5 }, { "cell_type": "code", "collapsed": false, "input": [ "# start in the ground (vacuum) state\n", "psi0 = tensor(basis(N1,0), basis(N2,0))" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 6 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Evolution\n", "---------" ] }, { "cell_type": "code", "collapsed": false, "input": [ "tlist = np.linspace(0, 10, 100)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 7 }, { "cell_type": "code", "collapsed": false, "input": [ "c_ops = []" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 8 }, { "cell_type": "code", "collapsed": false, "input": [ "e_ops = []" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 9 }, { "cell_type": "code", "collapsed": false, "input": [ "output = mesolve(H, psi0, tlist, c_ops, e_ops)\n", "output" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 10, "text": [ "Odedata object with sesolve data.\n", "---------------------------------\n", "states = True\n", "num_collapse = 0" ] } ], "prompt_number": 10 }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Expectation values and standard deviations\n" ] }, { "cell_type": "code", "collapsed": false, "input": [ "na_e = zeros(shape(tlist))\n", "na_s = zeros(shape(tlist))\n", "nb_e = zeros(shape(tlist))\n", "nb_s = zeros(shape(tlist))\n", "\n", "for idx, psi in enumerate(output.states):\n", " na_e[idx] = expect(na, psi)\n", " na_s[idx] = expect(na*na, psi)\n", " nb_e[idx] = expect(nb, psi)\n", " nb_s[idx] = expect(nb*nb, psi)\n", "\n", "# substract the average squared to obtain variances\n", "na_s = na_s - na_e ** 2\n", "nb_s = nb_s - nb_e ** 2" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 11 }, { "cell_type": "code", "collapsed": false, "input": [ "fig, axes = plt.subplots(2, 2, sharex=True, figsize=(8,5))\n", "\n", "line1 = axes[0,0].plot(tlist, na_e, 'r', linewidth=2)\n", "axes[0,0].set_ylabel(r'$\\langle a^\\dagger a \\rangle$', fontsize=18)\n", "\n", "line2 = axes[0,1].plot(tlist, nb_e, 'b', linewidth=2)\n", "\n", "line3 = axes[1,0].plot(tlist, na_s, 'r', linewidth=2)\n", "axes[1,0].set_xlabel('$t$', fontsize=18)\n", "axes[1,0].set_ylabel(r'$Std[a^\\dagger a]$, $Std[b^\\dagger b]$', fontsize=18)\n", "\n", "line4 = axes[1,1].plot(tlist, nb_s, 'b', linewidth=2)\n", "axes[1,1].set_xlabel('$t$', fontsize=18)\n", "\n", "fig.tight_layout()\n" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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1lI3PgilxXTJXkKEkCdi3T6SKX34R2+ztxbJ0U6YAjRsrGp5F0/e6tLjHVW5u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\nf91g6LpP67aOr3e/v3hRTovZ+tlgkAVG66ux1tzc/trUJF9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"text": [ "" ] } ], "prompt_number": 12 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Wigner functions\n", "----------------" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# pick an arbitrary time and calculate the wigner functions for each mode\n", "xvec = np.linspace(-5,5,200)\n", "t_idx_vec = [0, 10, 20, 30]\n", "\n", "fig, axes = plt.subplots(len(t_idx_vec), 2, sharex=True, sharey=True, figsize=(8,4*len(t_idx_vec)))\n", "\n", "for idx, t_idx in enumerate(t_idx_vec):\n", " psi_a = ptrace(output.states[t_idx], 0)\n", " psi_b = ptrace(output.states[t_idx], 1)\n", " W_a = wigner(psi_a, xvec, xvec)\n", " W_b = wigner(psi_b, xvec, xvec)\n", " \n", " cont1 = axes[idx,0].contourf(xvec, xvec, W_a, 100)\n", " cont2 = axes[idx,1].contourf(xvec, xvec, W_b, 100)\n" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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XmW1XZOU3/NxSYpCutXqqt3pRnhfDBxqWZ2+WzeUdffm1C9cM0wzQE0HpTtSw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\nPbfh6oqVa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"text": [ "" ] } ], "prompt_number": 14 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Fock-state distribution\n", "-----------------------\n" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# pick arbitrary times and plot the photon distributions at those times\n", "#t_idx_vec = [0, 10, 20, 30]\n", "t_idx_vec = range(0,len(tlist),25) \n", "\n", "fig, axes = plt.subplots(len(t_idx_vec), 2, sharex=True, sharey=True, figsize=(8,2*len(t_idx_vec)))\n", "\n", "for idx, t_idx in enumerate(t_idx_vec):\n", " psi_a = ptrace(output.states[t_idx], 0)\n", " psi_b = ptrace(output.states[t_idx], 1)\n", " \n", " cont1 = axes[idx,0].bar(range(0, N1), real(psi_a.diag()))\n", " cont2 = axes[idx,1].bar(range(0, N2), real(psi_b.diag()))\n", " \n", "fig.tight_layout()" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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a29v1zDPPqLW1VbW1tfryyy/1/PPPzwo3AAAAxZR2BSevhXjWBZQsVnAA5Cqv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\nyXhqakp+v18DAwOqqKhQQ0P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"text": [ "" ] } ], "prompt_number": 15 }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Nonclassical correlations" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# second-order photon correlations\n", "g2_1 = zeros(shape(tlist))\n", "g2_2 = zeros(shape(tlist))\n", "g2_12 = zeros(shape(tlist))\n", "\n", "ad_ad_a_a = a.dag() * a.dag() * a * a\n", "bd_bd_b_b = b.dag() * b.dag() * b * b\n", "ad_a_bd_b = a.dag() * a * b.dag() * b\n", "\n", "cs_rhs = zeros(shape(tlist))\n", "cs_lhs = zeros(shape(tlist))\n", "\n", "for idx, psi in enumerate(output.states):\n", " # g2 correlations\n", " g2_1[idx] = expect(ad_ad_a_a, psi)\n", " g2_2[idx] = expect(bd_bd_b_b, psi)\n", " g2_12[idx] = expect(ad_a_bd_b, psi)\n", " \n", " # cauchy-schwarz \n", " cs_lhs[idx] = expect(ad_a_bd_b, psi)\n", " cs_rhs[idx] = expect(ad_ad_a_a, psi)\n", " \n", "# normalize the correlation functions\n", "g2_1 = g2_1 / (na_e ** 2)\n", "g2_2 = g2_2 / (nb_e ** 2)\n", "g2_12 = g2_12 / (na_e * nb_e)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stderr", "text": [ "-c:24: RuntimeWarning: invalid value encountered in true_divide\n", "-c:25: RuntimeWarning: invalid value encountered in true_divide\n", "-c:26: RuntimeWarning: invalid value encountered in true_divide\n" ] } ], "prompt_number": 16 }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Second-order coherence functions: Cauchy-Schwarz inequality\n", "\n", "Walls and Milburn, page 78: Classical states satisfy\n", "\n", "$[g_{12}^{(2)}]^2 \\leq g_{1}^{(2)}g_{2}^{(2)}$\n", "\n", "(variant of the Cauchy-Schwarz inequality)" ] }, { "cell_type": "code", "collapsed": false, "input": [ "fig, axes = plt.subplots(2, 2, figsize=(8,5))\n", "\n", "line1 = axes[0,0].plot(tlist, g2_1, 'r', linewidth=2)\n", "axes[0,0].set_xlabel(\"$t$\", fontsize=18)\n", "axes[0,0].set_ylabel(r'$g_1^{(2)}(t)$', fontsize=18)\n", "axes[0,0].set_ylim(0,3)\n", "\n", "line2 = axes[0,1].plot(tlist, g2_2, 'b', linewidth=2)\n", "axes[0,1].set_xlabel(\"$t$\", fontsize=18)\n", "axes[0,1].set_ylabel(r'$g_2^{(2)}(t)$', fontsize=18)\n", "axes[0,1].set_ylim(0,3)\n", "\n", "line3 = axes[1,0].plot(tlist[10:], g2_12[10:], 'b', linewidth=2)\n", "axes[1,0].set_xlabel(\"$t$\", fontsize=18)\n", "axes[1,0].set_ylabel(r'$g_{12}^{(2)}(t)$', fontsize=18)\n", "\n", "\n", "line4 = axes[1,1].plot(tlist[20:], abs(g2_12[20:])**2, 'b', linewidth=2)\n", "line5 = axes[1,1].plot(tlist, g2_1 * g2_2, 'r', linewidth=2)\n", "axes[1,1].set_xlabel(\"$t$\", fontsize=18)\n", "axes[1,1].set_ylabel(r'$|g_{12}^{(2)}(t)|^2$', fontsize=18)\n", "\n", "fig.tight_layout()" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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xI+3bt2f8+PHUrl2bgwcPsnbtWgIDA7nrrrvKHXRlUtIR8SxPHlNOyTOgXCPiaV4pcGbM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\n3bp1GTt2bGGBM3nyZK+tD3PuHLRta44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"text": [ "" ] } ], "prompt_number": 17 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Clearly the two-mode squeezed state from the parameteric amplifier does not satisfy this inequality, and is therefore not classical." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Cauchy-Schwarz inequality\n", "-------------------------\n", "\n", "Walls and Milburn, page 78: the Cauchy-Schwarz inequality for symmetric modes\n", "\n", "$\\langle a^\\dagger a b^\\dagger b\\rangle \\leq \\langle(a^\\dagger)^2a^2\\rangle$\n" ] }, { "cell_type": "code", "collapsed": false, "input": [ "fig, axes = plt.subplots(1, 2, figsize=(10,4))\n", "\n", "line1 = axes[0].plot(tlist, cs_lhs, 'b', tlist, cs_rhs, 'r', linewidth=2)\n", "axes[0].set_xlabel(\"$t$\", fontsize=18)\n", "axes[0].set_title(r'Cauchy-Schwarz inequality', fontsize=18)\n", "\n", "line1 = axes[1].plot(tlist, cs_lhs / (cs_rhs), 'k', linewidth=2)\n", "axes[1].set_xlabel(\"$t$\", fontsize=18)\n", "axes[1].set_title(r'Cauchy-Schwarz ratio inequality', fontsize=18)\n", "\n", "fig.tight_layout()" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stderr", "text": [ "-c:7: RuntimeWarning: invalid value encountered in true_divide\n" ] }, { "metadata": {}, "output_type": "display_data", "png": 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GDbNd7/5a7d69m8TERPtSVElJSdx6662sX78+1/zq5+eHr68vSUlJ2cZzy7ug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\nzv3nuCJWO/+bhOJt5kRyMqxaBYsXg9ZhdqveVss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"text": [ "" ] } ], "prompt_number": 18 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Two-mode squeezing correlations\n", "-------------------------------\n", "\n", "The two-mode squeezing can be characterized by the parameter $\\sigma_2$ defined as\n", "\n", "$\\sigma_2 = \\frac{2\\sqrt{\\omega_a\\omega_b}\\left[\\langle a b\\rangle e^{i2\\theta_\\Sigma} + \\langle a^\\dagger b^\\dagger\\rangle e^{-i2\\theta_\\Sigma}\\right]}{\\omega_a\\langle a^\\dagger a + a a^\\dagger \\rangle +\\omega_b\\langle b^\\dagger b + b b^\\dagger \\rangle}$\n", "\n" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# pre-compute operators outside the loop\n", "op_a_b = a * b\n", "op_ad_bd = a.dag() * b.dag()\n", "op_ad_a_p_a_ad = a.dag() * a + a * a.dag()\n", "op_bd_b_p_b_bd = b.dag() * b + b * b.dag()\n", "\n", "e_a_b = np.zeros(shape(tlist), dtype=complex)\n", "e_ad_bd = np.zeros(shape(tlist), dtype=complex)\n", "e_ad_a_p_a_ad = np.zeros(shape(tlist), dtype=complex)\n", "e_bd_b_p_b_bd = np.zeros(shape(tlist), dtype=complex)\n", "\n", "for idx, psi in enumerate(output.states):\n", " \n", " e_a_b[idx] = expect(op_a_b, psi)\n", " e_ad_bd[idx] = expect(op_ad_bd, psi)\n", " e_ad_a_p_a_ad[idx] = expect(op_ad_a_p_a_ad, psi)\n", " e_bd_b_p_b_bd[idx] = expect(op_bd_b_p_b_bd, psi)\n", " \n", "# calculate the sigma_2\n", "theta = 3*pi/4\n", "w_a = w_b = 1\n", "sigma2 = 2 * sqrt(w_a * w_b) * (e_a_b * exp(2j * theta) + e_ad_bd * exp(-2j * theta)) / (w_a * e_ad_a_p_a_ad + w_b * e_bd_b_p_b_bd)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 19 }, { "cell_type": "code", "collapsed": false, "input": [ "fig, axes = plt.subplots(1, 1, figsize=(8,4))\n", "\n", "line1 = axes.plot(tlist, real(sigma2), 'b', tlist, imag(sigma2), 'r--', linewidth=2)\n", "axes.set_xlabel(\"$t$\", fontsize=18)\n", "axes.set_ylabel(r'$\\sigma_2(t)$', fontsize=18)\n", "axes.set_ylim(-1, 1)\n", "fig.tight_layout()" ], "language": "python", "metadata": {}, "outputs": [ { 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"text": [ "" ] } ], "prompt_number": 20 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Quantum-classical indicator $\\langle:f^\\dagger f:\\rangle$\n", "---------------------------------------------------------\n", "\n", "Using $\\langle:f^\\dagger f:\\rangle$ we can again show that the output of the parametric amplifier is nonclassical. If we choose\n", "\n", "$f_\\theta = e^{i\\theta}b_- + e^{-i\\theta}b_-^\\dagger + ie^{i\\theta}b_+ -i e^{-i\\theta}b_+^\\dagger$\n", "\n", "we get\n", "\n", "$F_\\theta = \\langle:f_\\theta^\\dagger f_\\theta:\\rangle = 2\\langle a^\\dagger a\\rangle + 2\\langle b^\\dagger b\\rangle + 2i\\left(e^{2i\\theta} \\langle a b\\rangle - e^{-2i\\theta} \\langle a^\\dagger b^\\dagger\\rangle \\right)$" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# pre-compute operators outside the loop\n", "op_ad_a = a.dag() * a\n", "op_bd_b = b.dag() * b\n", "op_a_b = a * b\n", "op_ad_bd = a.dag() * b.dag()\n", "\n", "e_ad_a = np.zeros(shape(tlist), dtype=complex)\n", "e_bd_b = np.zeros(shape(tlist), dtype=complex)\n", "e_a_b = np.zeros(shape(tlist), dtype=complex)\n", "e_ad_bd = np.zeros(shape(tlist), dtype=complex)\n", "\n", "for idx, psi in enumerate(output.states):\n", " \n", " e_ad_a[idx] = expect(op_ad_a, psi)\n", " e_bd_b[idx] = expect(op_bd_b, psi)\n", " e_a_b[idx] = expect(op_a_b, psi)\n", " e_ad_bd[idx] = expect(op_ad_bd, psi)\n", " \n", "# calculate the sigma_2, function of the angle parameter theta\n", "def F_theta(theta):\n", " return 2 * e_ad_a + 2 * e_bd_b + 2j * (exp(2j * theta) * e_a_b - exp(-2j * theta) * e_ad_bd)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 21 }, { "cell_type": "code", "collapsed": false, "input": [ "fig, axes = plt.subplots(1, 1, figsize=(8,3))\n", "\n", "for theta in np.linspace(0.0, 2*pi, 100):\n", " line1 = axes.plot(tlist, real(F_theta(theta)), 'b', tlist, imag(F_theta(theta)), 'g--', linewidth=2)\n", "\n", "line = axes.plot(tlist, real(F_theta(0)), 'r', linewidth=4)\n", " \n", "axes.set_xlabel(\"$t$\", fontsize=18)\n", "axes.set_ylabel(r'$\\langle:f_\\theta^\\dagger f_\\theta:\\rangle$', fontsize=18)\n", "axes.set_ylim(-2, 5)\n", "fig.tight_layout()" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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B4O5oM8NGj7GiwujRUYWjojeWCiqeFpliZqDkwI5QnDkjxd/RqLG5J4WaGZau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dBWGSVWDAvj8zJlCnDbbSSibQGbN1NcvXo1z0Pf14iM0/fey8lBa7nHXC5g0SImCxX33Gql5ujZ\nZ/2vxz//ySSiisJz2r2bExE9rrmG7mWAk4vLLwceyPwPnj9ypfuG//3fwJNPun0lyY0OQSM3WtTX\nc8r99de04e7c6dffc5COtZiCdZiMdZiMfPQMUkWDB1+tOUaftf/TQlh0AHfLjogRDDSsVtUVFhdH\n15Sw8PTqReIyaBAH+fJyDgZaolJcTBfKyZOqi6y21jcXlYDNxs6hSxcSisxMYORIWnpGjDAe5Fwu\ndpw//EDycOAAPxcVUVNUXe39etntnLGlpfEcx47l4O4riampYRPYuJGWpwMHeE3OnPF8/uHhqu5H\nWJrOP795nXxZGS0xa9eqEWClpebHt9t5b4cMoS5kzpzAaGUaGkgWli6lNezgQZI5o3sgrDJDhvB6\nX3+9cQRdILB3L4nMunV09508aVyniAjOrkUW7YkTW2/QbWhgF/rZZyQGOTnGQn6Hg/dq8mQOqm2F\nzGzbphKxw4ebEviwMNb70kuB++4LrDbLF7hcwFNPkdQIK6HFwvq89VbziPxLLwH338/3XbrwOTPa\nz2uv0YoGcPsXXgDeerYUlzw8GF1RrG44ZAgvZHi42/8ludGhVciNHiUlnKp+8w1LcbH3/2hwBBnY\ngAvxLSbhW0xCNvqgPbixQgmrlR1HWBgHLa1eR0RgxcWp+p3oaG4jrDy1tap1x8jKU11NK09zdDwC\nDgePm5DATqBnT0bRDBxI4jJoUFPyUlWlansOHmRnf+wYHymh7/ElzB1QI8WE1Wf4cA4K553nWzRN\nWRkH7W3bWKfDh0mgysq81yE8nEQxM5OWrcmTqS9qjjWmsJDNa9MmkjkRKm+mywF43dPSaPafPJna\ni0DoVIqLSWLWryepO3rUOBQc4CCSkECSfMEFJFPNJXLekJVFd9f69apuyYjkaUPwZ84kmWnNaKY9\ne6iVWb+eg6KZNSs2lgRYrJk2cGDr1dEMLhdJzIcfsl0cPWpsjUxNZRu77TZaKkIhXi4sBB58kJZD\n0VYtFrqe3n67eaTG5SIZX7yYn9PS+KwZtemVK6kPc7nY1+3cyf5jS9+bcaOiLiBl5I4SkORGh5CQ\nGy0UhS145Upg9Wrm1PExAkugGCn4FpOwERfgO0zELgyH079lwdoMzLQ5Rt8Z/abdB+Cu1zF6H8xb\nHxamkqjYWA5cnTvTGtCzJ2e/wtojBIxVVSQoouTns+M5fpzRTaWlHBwFmfI3zD0ujsdKS1MJzIQJ\nrIO3TvXYMbqtdu0ikTpyRNX8VFV5d9+JXD6pqTzvkSM5+5840X83RkUFrUCbN6v1KSzktfFUD4eD\ng3XfvrQ+TZtGV0VL3Sjl5WzC335L91J2Ni0fZq41q5WWv/79ef2vuCI4FhDhWlq2jJazgwdZLzNr\nVXw8n4sLLqAAe9Kk1htsDx8m4Vq7luS4uNi4nmFhfIaEYHvePP+j64KBkydJZJYu5TNZUmLcPjt3\npqX1+utbX4+kx4oVjLLatUv9zmolkX377eZH1RUWkpjn5fHz8OEMdDA6182bmWPJ6aR1OD+fdbgj\n6Qt8UDHbfePHHqMIyACS3OgQcnKjR309n4I1a0h2Nm+Gxdep98+oQDS+x3h8h4nYjPPxPcajDIne\n/yjhFrautfKEh6uWnpgYDgKJiSydO/M1OpolMhKNK5qfOqUKjrVWn4qKptoef9xTWlitrJ8QQycn\nU9/Tty+FkqNGkcx4ynWzb59q/Tl8WE1yWFqqus98gc2mEpj0dB5/3DhaQ/yNQCks5Ix3+3bO2nNz\nWaczZ7wneIyI4PGE227SJBKZlq7Te+wY9RGbN3MAzsnhoObJKhQRQdfa4MEkMFdc0VRIGQgcO0ad\ngtAO5eXRumiGuDgS7LFjSRIuuaT1Bto9e6hz2rCB70tKzO9pQgKf5QsvJBkYO7Z16ugJdXV0j33+\nOcW/OTnmkXPdurENXH01NSWhJDMAXcKPP04Spp1Hx8UxTcCTT7Ys79EXX1CLJoYt4WIywp497J/q\n69l/ZWez/5o79ADe2DMeCdqlbocOpVnY5AJKcqNDmyM3elRXs/WsXQusWwdlyxa/yQ4AZGEANuP8\nRrKzD4PatXVHS0LM3nv7bKTt0UZiicgso++Cqe0R0VsRESRLcXEkLUJn06sXZ9cDBtACom/rDQ0k\nJ9nZqvWnoIBkQWv9qaryL7oL4LFiYkjotBFeY8aQRHgSLWvhcrGT3bGDHdzBg+46IF8E1IJIde2q\nCrUnTaKJvyUDSHk5CYKwCh0+TFLlzSpkt/MeCaHztGnUyQQ6QV5xMWfcGzawfkePetYOWa18fvr0\n4SA7axbD8FtjkK2poYtw5UqOS4cOkfCbXceYGF6/MWMY+dWahMsMDQ0ktF9+ya44O9s8W3dkJAn1\nxImMFGtNy5cnFBYy4unjj5uuAN6vH/CnP7G+LYHLRc3MG2/wc3g43VxmUVWHD5Pk19TwumVlsW97\n+FdncPvr4zEABxq3VcLCYNm61WOGTUludGjz5EaP6mpadr79Fvj2WyibNsFilEPeCyoQje0Yje8x\nHlsxDj9gLPLQE6HS7uhdSe0RgiiJ5SWE1UdEbkVHc3aSmKiSleRk1U2Vnk6LR3k5O6CSEpKREyc4\nIJw6pSYWFJofre5HLFnRnOsnxNIxMaxbSgqtPZmZ1C+MGcP3vnTU5eW0HGRlcTATiRFLStTlLjxZ\nOrRwODhzF2H5gwdTWDxpUvOtMCI6bfNm6mD27VOXyfAWHQbwfiYlcRAeNox5O6ZPD6xrxOVi3b79\nls193z6SVG8C7MhIWgoGDqRr6dJLfUu8GIj67tihLguSlUVC7alriovjMz96NC1Hl13mOzkOFioq\naNFYsYLnk5trTmS07rFZs2iVCXX2Yi22bQOee4735NQp99+Skljfxx8PTLTfmjW01ojj9O7N9mW2\n78JCkqrKSrbxH3/kM/vJh05E3fALXI6l7n949lng97/3WAdJbnRod+RGj/p6tsKNG9Wip+Y+4jiS\nsA1j8APGYhvGYDtGowgtSN/ayvBkvTHKiKx1P2m/F8JjfRG/iTWx9NmVRTbl+nr1vSAc9fVq0W6j\ntQ4F+jG02Th7iooiqercmZ1Nt24kUxkZJAsDBngeVFwudkbZ2arLKi9P1QJpLUH+6IAsFncdkEiI\nOGwYCYwvOiAjNDSQDIjszwcPss7Hj9M96Ckrs4DNpoqr+/alVerCC1tuFdJCkKz161nXrCwOpidO\neCYFgLrMRt++aobqKVOCTw5cLtZ11So1+3RhIUmh2X232Xh/heXosstITlszkZ8R9uyhG2/jRl77\nwkLzZ8NqVZc1mTSJYu/WII3+wNsyErGxJOF/+lPg3KIVFXS3ffMNP1ssTBr52mvmbTcnh4SwvJzP\nwKZNdDUeOAAsGfgHPKI85f6Hm29miJmXdYA6DLlZvHgxFi5ciP379+OHH37AKBNzVrsnN3ooCntM\nobbcvBnKnj0+LfxphCKkYgdGYTtGYwdGYSdGhszCI57tc+l2mUFvARKan+hod81P586cLXbtSkuL\nsADpIxIaGth5FxXRrSHC0k+coDXo1Cl2juXlKlERWZyb8+hYrRxoBakS1ikhoB4zpnnLHlRUsOMW\nriwRHXb8OK1CVVW+L7gqlsno2pUDryBV55/f/Jw5etTUcAb9/fdqHqOCAl5vbyH4Fgvvd0oKSYyI\nIrvwwuCTmNJSesJFxNmRI3xePJEukfNILP46aRKjf3qGOHPF0aMUVH/3HcmusICZXXu7nW1q4EBe\n69mzg6ORainKy5kxeMkS82UkUlPpFnr44cBHkL38MvDQQ6oeLyODZNFTQsR162jlqqtjH7FyJaMi\nT54EHu75Md6uvt79D2PHkv1HRnqtT4chN/v374fVasVdd92F5557ruOQGyOcPcunf/Nm9rLff89R\nrZkoRSJ+xAj8iBHYiZH4CcOQhYFtdgkJI62N/lX/HvC8ndaSY7W6r3Iu3oswcq0oWRThrtJ/53Cw\n062pUQlGTY0abl5V5f692K62Vi1aC5HQBwUCYWGqJUjogFJSSFKEDmjwYGMdkCeUl3PQP3RIzQtU\nWMjB9NQpDkQipN0fq1BEBElgSoqah2joUJIXX11s3lBWxua0axdn/0eOqMkXKyp8E4lHRpIA9uzJ\n6Knx49nhB3IxTbO6f/st8x/t3k3LnIg48yVxY/futPqNHcsw3mHDQqcvcblIHsVSIHv3kvSeOeP5\n+Y+L43UX7sXLL2/ZWmPBxN696kKw+/YZpxRojWUk3n2XZEkMIXY7RcgLFnj+32uvAXffzTYcEcF7\ndf75JGVz0ndg2dmJiIKqylZSU2HZto0Pmg/oMORGYMqUKZLc6KEotH9v3cqe+YcfoOzY0SztjkA9\nbMjCQOzCcPyEYdiNodiNoShEN8gcPG0HgogJsqWN/tKGqmt1QL17+5bOv6KCs2RBToqKVO2Q0AqV\nl5NrC0Lmq5VFfw4ikWKXLmpkVv/+HKRGjmx5p+5ycXD86ScOJNnZPDchyi4v9z1rdFgYLTBJSSqB\nGTGCHfuQIcEjBC4XLVxiyY6DB3lvjh/3jXhpEzeKqLcpU0KbQ6a4mBP5LVvU9dO8LQUC8Hnp2tU9\nGaSvq9mHAocPMxJr1SrPYfHh4bSYTJ9O4hDMZSQ+/hh44AH3tGyTJtFy5K1/ePBBrpMFsI/58UcG\nJJSVAVf0+glLyqeiC1RhkOJwwLJunV/ZF/0dy9tnOI2EZ1gsbBEZGY0SeUtDAx3oP/zAsmMHlF27\nYPFFoADAjgYMw24Mw26370uRiD0Ygt0Yir0Y3FhOIfQr05lFTpm5drXRUdo2pP3eYvE+4Bnl6DHS\nBwkLkCjCPRUezpmPKLGxaomLI1Hp0oWDaVISB//kZO7D5VJdT+Xl7FxEmLpYXPTMGQ7mP/6oipZF\n6HpVFS1INTWqlSgQ1iEhaNZahZKS2AFmZKhh7X37tkzzUlbmLnQWhEWEvYscQr4KngFeVyHE7taN\n9R0yhFqY8eMD5+LSo6qKyc527uQ5ZWer2qKzZ31L3mi3qxFnffsyH8nEiRxTAh3l5SsKCxkJtnUr\nrRU5OarY29NzZrHwWos8SmPHkoxNmBB6fY8Zamoas35g61Y+l57yEMXFkVzOmMFkhcG27rlcJCXP\nPcfJisC4ccA773gnug0NFLWvXMnPAwZQsxUVxbb2i4ymxAYALH//e9DTSrfRR4KYMWMGig2y+y5a\ntAhXXHFFCGrUjmGzsUceMoSpMvEz4cnKomB5+3Zg504SHk/JM3TohNOYhA2YhA1u35cgGXsxGFkY\niH0YhCwMRBYGohipaC1LjyAlgXLbaKEnS3ryYvSq/x+gio1FyLa+GCUl1H8frJB1s/PWWoa0EWKd\nO5OwCDdRRgYHIU85eDyhvJwGyNxcWlny89kBHz9Od5aIKqusbL6VyG7nOcTHq5aXPn2oGxo+nK/B\nCFUuK1MjuQ4cUN1dx4/znKqrfXN5WSzq4qzdurHuQ4aomadDEZ1UUUGDschflJ3N+yeSQXp7Vh0O\ndbHZgQN5HlOm0CLWVi0xZWXUMIn10w4d4r30NHeMjmYbGT+euZFaMyz+6FFaW776yp0kjx5NUuOL\nBmnjRrr5xFpfl13GcHqrVSU2n5Y1JTZ46CGqkoOMNk1uVgo62EIsXLiw8f3kyZMxefLkgOy33UMs\nQzt0KHDrrQBAYXJOjjpl/Oknttb8fL92nYLjSMFxTMVat+/LEI/9GNBYDqA/9mMADiOzVTU9RtYV\nwN1yY2TFEWhNQtFc6K1E+qSF2sVHhVUoIUENZRfranXrxtKli2+DS10dLSXHj3NwW7+eVhORg0eQ\nEm24u36Ji5YQUpH0MCqKpEUsbCpC3/v1Y+fdo0dgB0vRdISVJSdHdeGdPMlBwF9tkdXK80hMpHUu\nI4MD/vDhHBRbc6kEgbw8dg27dtEYnJvLcywtJXnxhZSFh/OcRLTa8OEkMRMmhD7vjRlqaijAFikG\nsrNJSE+f9kysw8LUPERCvzRtWuufZ00N8OKLzFNz6JD6vdVKPdL//i/dqd7gcpDn2+4AABgQSURB\nVNFF9vrr/GyxAP/v/wFimC0sBG4Y8hP+fdqA2DzwAPCXv/hU33Xr1mHdunU+bWuEc0Jz8+yzz2K0\nwVoUQAfV3AQDpaV0Du/aRcKzZw+jtLw5w32EE1bkIAOH0BcH0Q8H0Q+H0BeH0Bd56AkXwgJynEBD\nH36uDy232czDz7W/6V1U2uJwqEn/7HY1BFyIlMPD1ZXSHQ7uU1h1hFtJhKcLK5EQJYv3tbVq9JTI\nqCxcU3V1TYv4v9i31pIUSFgsqrtOkDBBWFJSODimpalWol69AueiqKlRF0c9epTWBxGNptUYiSzU\n/hKysDBVW5SczHPp3Zum/SFDGD0VLJeXEVwuDnpCPC3Ou7iYVhd/MlmHhanJINPSeE5iLbMhQ9qm\nG0mQU6Fh0uZHKi/37sq020nYxBpmkyZR+xNKAXNNDfDKKwwh37/fvX0mJgJ33EFS4quL8sABErOC\nAn7u2pUuN+G+WrMG+MPFO/BV/UxjYvO//+s15NsMHUZQvGTJEtx///04efIk4uPjMXLkSHz99ddN\ntpPkJogQy1Hv3k1l4969wN69UPbvh8XXXtAH1MGOI+iNbPRBNvrgMDIbSy7SUYdw7zvxA540ORK+\nQ0vctEtciHB3I3dWaioHh169OOC3xLLictF6dOyYqrsRa3hpw+PFchlCbyQi0ZoLu11db0yQsB49\n3EXRffu23gBfVcWBev9+WhuEm0+49wRB82d5EJEQUmTV7t1bTQY5Zkzo9DyeUFdH4rZjh7u7TLgC\nfZEfhoXxvqamqtqriRMZwt/SpT8ChW3bgH/8g2LlvDz3fstup4XskUeolfEVVVX0JH3yibq/2293\nz3fz178COxd8iDdwu1tUFIAWExugA5EbXyHJTQjQ0EARwb59nAJmZQH79pH0BMjSI+CEFcfQA0fQ\nGznIwBH0bnyfi3SUIAUKWtdRb6S5MRI1C3Gyp+zN4ndvbjIt9Poe/bHNrEgirF0UvbBZrKYuiElc\nnCoOTkxURc5xcb6RkoYGd5GzEEFrxc9C7Fxezlet8FkvfhYJFUWIfCCgtRxp9UVJSZyRC9IiVndv\njQUeq6rUhIva6DVhYSkrU119zVnFPjy8aSZroeUZPZqDelvTvpSW0tqydy+tTzk5ahLKsjL/yFtE\nBJ/hbt3UrNnjxtFl5ktUYWtjxw7gn/+k5mffvqbWNbud9X/gASYn9OfeuVzMcvyXv6janPh4amsm\nTVK3uW6uE2OXPIoF+GvTnQSA2ACS3DSBJDdtCCL+9sABTiO1r8eOBeWQNQjHUfRCLtKRi3QcRS+3\nUohubdbl5QlGeX3MsjXrvzPL+2MEPanSCpv1K7Hri5nwubWbo3APat1bYk0vrb4oOVm1GmVk0E0U\nLOuKy0XrkRBKFxSoofUnT7prk7QLsDbXoqRdfiMhwT3Evm9fCqeHDWtbg7cwDO/d657QUWiYRFJH\nf/MjRUXxGqSkUECu1fy0ReKmRV4eF65cu5aC7YICY9KWnMwEhbffTtdYc87pvfeA3/5WFQzb7eQp\nTz+t7i8vD7jqolI8lXs9ZsJAI/vQQ2RGLSQ2gCQ3TSDJTTtBZSWnowcPqiU7m9OwFiQk9IZ62FCA\n7shDT+ShJ/KR1qSUohMCFeEl2rjoHPRt3ohMdARoSZhW/KxftV24tQQ5Efl7EhPVAUssQZGSEtho\nIZdLFUZr1wQrLVXJiMgCrQ+v14fWt/S+CotSRISax0i7/EZ6Oq0t/fq1rgvME1wuWpe0VidBVrQL\nvorot+ZqmETkW9euFJALV+CIEW3HdeQNJ09Sv7JxI11pBw/yGpmR206daFm76iq6j5p7ng0NtNS8\n+qpKaiwWZnF+7z13DdjChcCyP23Dh8p1yMQRt/0oDgcs//hHY2RuICDJjQ6S3JwDOHOGvaFIcSuK\nCFcIMqoQiWPogQJ0RwG6u70XpQQpaIA96HXRw9PaWUZCZiPRszbnjpZcGAmdBdkQVhDxOTLSPStz\nVJS5O0u8F8TD5XIXJevX7BKvgiAIkqDN4iy+F9mexXfaz2bbG4mlhWtL1CtYXYg26aIgbiJqTeh1\nUlPp/hJh6mlpoSUrLhcHviNH3FekP35czTp9+rS66Ku4xs2NgBMaJuECFRY2Ib4W+ZHaAoHzB3l5\njLzavp3upKNHab07c8azhS4qilbFsWPpZrriipZHXhUXA7/5Da1CWuH02LFM7peRoX536BDwi+mV\nuD3v/+EBPI8wuN9YpVs3WD77jOF8AYQkNzpIcnOOo7qavcKRI7RbHznCIhKkiOlHkOGCBSVIQSG6\noQhdm7wWIxXFSEUJUnwWQPuSMFCi9aG1MOnF0lqXlxiMxYAsRNM9enBwDoUVQbjDxNpjJSUkJcIV\nVlqqJn7UrkgvCIogey2BfpkPodfq2lV1CfbpQw1TW3KT+QqRL3XvXr7m5JAECnfa2bO+RZ2JfD+9\nejFybtYslkBZI6uqKAJ+913WUcBmY86aF190XzesoQH43e+AQy+vwN9xNzKQ23SnEyZwZc8gLJ8u\nyY0Oktx0cJSVkeTk5JAE6cupU153EWicQqdGolOCFLf3ohxHMo4juUWRYPokg/rvjKAXLWtdY9pB\nzVdxc0uhraeRIFurI9ILpI2E0vocP4KQiGUq4uJoXUpIcB94O3Xia7BzkwiryJkzqpvLSGytzyyt\nzy6ttUgJkXWgk1kKgieInbh+QsMkQvV79aKVJTOzfZKVmhp2Hzk57EoEUdHqo86cUfU//lzn8HC6\n0bp2VSPOJk5k3plgRJxVVDDC6Y03moaGx8YCd90FPPGEO4ESouJ/PluEhTX/hVvwvvHO77qLjChI\njUSSGx0kuZHwiMpKOv7z8tSSn88i1J4BjvDyB2WIbyQ6J5DU+CrKSXRxe61F66Wk1RMMrctLv8io\nduFRkatHEA+z/D7a/+vdajabe/SX9lVAL6LUkzOxrIQo4rPIGi1cZNoILG1uH63bTP9e69YS/xGf\n9ccNVhZtTxDXSxA+bUJHoWXSJ3MU65H17Nm+SIrQ+hQWuq+JptVMiZxFIiWA1lLVHFgsaoRdQgKv\nYa9edJ+JHEaBWtzVE1wuYMUK5rnZsIFWOi0cDpKpP/yB+Wv0/33mGeCNJ4rwm+pncBf+D5FoGi+v\n9OrF5RQuuSSIZyLJTRNIciPRIigKp88FBSQ74lUoIUXR9xohQgWicRJdcBJdcAqd3Yr4rhSd3F7L\nEQetYNpTaLpE68GIMAoyIgiJkaZJWJ6ES6xzZzVLc0pK28xBI+BykWBocxEJ8iEsJHrRtjZHkVa4\nHeiUAMJKpY2069xZtU5lZFC8PGBA6yZf1KK4mBqZb76hELmoqClxDg+nuPrBB4G5c5sSrLIy4NFH\ngZXvFeHXVX/B3fiHMamxWmG5/36aelrhhCW50UGSG4lWQV0dexJRxBRRvBYXA8XFUI4f5xIXbQgN\nCMNpJOI0ElGKTihFp8bP+lKGBJQhofH9WcR6zCOkz7Hj7TNgvCyGkStN/53+P0YwsuxoX41yFBmJ\nso0sTiJjtLZERrq7wLRJDEURWZfj4/k51GLhmhqShcpKlTgIIlFdrb5WVanvtVFh4jeteFsv3NZb\nuIQVK5jQpgTQkkKRu0jrThNh8unpgc16HShUVTGaau1aLoWRnc35lZGWx2KhtU2sLD5mjPE+ly0D\nHvtvBbE/bsB8vIlr8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"text": [ "" ] } ], "prompt_number": 22 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Entanglement: logarithmic negativity\n", "------------------------------------" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Wigner covariance matrix:\n", "\n", "In order to evaluate the logarithmic negativity we first need to construct the Wigner covariance matrix:\n", "\n", "$V_{ij} = \\frac{1}{2}\\langle R_iR_j+R_jR_i \\rangle$\n", "\n", "where \n", "\n", "$R^T = (q_1, p_1, q_2, p_2) = (q_a, p_a, q_b, p_b)$\n", "\n", "is a vector with the quadratures for the two modes $a$ and $b$:\n", "\n", "$q_a = e^{i\\theta_a}a + e^{-i\\theta_a}a^\\dagger$ \n", "\n", "$p_a = -i(e^{i\\theta_a}a - e^{-i\\theta_a}a^\\dagger)$\n", "\n", "and likewise for mode $b$.\n" ] }, { "cell_type": "code", "collapsed": false, "input": [ "R_op = correlation_matrix_quadrature(a, b)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 27 }, { "cell_type": "code", "collapsed": false, "input": [ "def plot_covariance_matrix(V, ax):\n", " \"\"\"\n", " Plot a matrix-histogram representation of the supplied Wigner covariance matrix.\n", " \"\"\"\n", " num_elem = 16\n", " xpos,ypos = meshgrid(range(4),range(4))\n", " xpos = xpos.T.flatten()-0.5 \n", " ypos = ypos.T.flatten()-0.5 \n", " zpos = zeros(num_elem) \n", " dx = 0.75 * np.ones(num_elem) \n", " dy = dx.copy() \n", " dz = V.flatten()\n", "\n", " nrm = mpl.colors.Normalize(-0.5,0.5) \n", " colors = cm.jet(nrm((np.sign(dz)*abs(dz)**0.75))) \n", " \n", " ax.view_init(azim=-40,elev=60)\n", " ax.bar3d(xpos, ypos, zpos, dx, dy, dz, color=colors)\n", " ax.axes.w_xaxis.set_major_locator(plt.IndexLocator(1,-0.5))\n", " ax.axes.w_yaxis.set_major_locator(plt.IndexLocator(1,-0.5))\n", " ax.axes.w_xaxis.set_ticklabels((\"$q_-$\", \"$p_-$\", \"$q_+$\", \"$p_+$\"), fontsize=20)\n", " ax.axes.w_yaxis.set_ticklabels((\"$q_-$\", \"$p_-$\", \"$q_+$\", \"$p_+$\"), fontsize=20)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 40 }, { "cell_type": "code", "collapsed": false, "input": [ "# pick arbitrary times and plot the photon distributions at those times\n", "t_idx_vec = [0, 20, 40]\n", "\n", "fig, axes = plt.subplots(len(t_idx_vec), 1, subplot_kw={'projection':'3d'}, figsize=(6,3*len(t_idx_vec)))\n", "\n", "for idx, t_idx in enumerate(t_idx_vec):\n", " \n", " # calculate the wigner covariance matrix\n", " V = wigner_covariance_matrix(R=R_op, rho=output.states[idx])\n", "\n", " plot_covariance_matrix(V, axes[idx])\n", " \n", "fig.tight_layout()" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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co3EKLy8vD6oEk41wEnU5MUX7oLpcLvx+P1lZWQmPQ+3Dp7VVT00RVKS9vmgn/NAIKtzr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"text": [ "" ] } ], "prompt_number": 41 }, { "cell_type": "code", "collapsed": false, "input": [ "\"\"\"\n", "Calculate the wigner covariance matrix logarithmic negativity for each time step\n", "\"\"\"\n", "logneg = np.zeros(shape(tlist))\n", "\n", "for idx, t_idx in enumerate(tlist):\n", " \n", " V = wigner_covariance_matrix(R=R_op, rho=output.states[idx])\n", " \n", " logneg[idx] = logarithmic_negativity(V)\n", " \n", "fig, axes = plt.subplots(1, 1, figsize=(8,4))\n", "axes.plot(tlist, logneg, 'r')\n", "axes.set_xlabel(\"$t$\", fontsize=18)\n", "axes.set_ylabel(\"Logarithmic negativity\", fontsize=18)\n", "fig.tight_layout()" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stderr", "text": [ "/usr/local/lib/python3.4/dist-packages/qutip/continuous_variables.py:287: RuntimeWarning: invalid value encountered in sqrt\n", " nu_ = sigma / 2 - np.sqrt(sigma ** 2 - 4 * np.linalg.det(V)) / 2\n" ] }, { "metadata": {}, "output_type": "display_data", "png": 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lFHJExPUuXoTXXjPhZudO2LDB7FJcq5bVlYnI1bp396pbVg6vrnJnWl0l4qYu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\n", "text": [ "" ] } ], "prompt_number": 45 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Software versions:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "from qutip.ipynbtools import version_table\n", "\n", "version_table()" ], "language": "python", "metadata": {}, "outputs": [ { "html": [ "
SoftwareVersion
Cython0.20.1post0
matplotlib1.3.1
QuTiP3.0.0.dev-5a88aa8
OSposix [linux]
SciPy0.13.3
IPython2.0.0
Numpy1.8.1
Python3.4.1 (default, Jun 9 2014, 17:34:49) \n", "[GCC 4.8.3]
Thu Jun 26 14:44:43 2014 JST
" ], "metadata": {}, "output_type": "pyout", "prompt_number": 46, "text": [ "" ] } ], "prompt_number": 46 } ], "metadata": {} } ] }