{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Boson Bunching\n", "\n", "A prominent example of boson bunching is the Hong-Ou-Mandel effect, where the bunching of two photons arises from a destructive quantum interference between the trajectories where they both either cross a beam splitter or are reflected. This effect takes its roots in the indistinguishability of identical photons. You can read more about it [[1]](#references).\n", "More generally one can send in $n$ photons into an optical interferometer via $m$ modes and one then measures in which modes the photons are ending up.\n", "For the example discussed here there are 7 photons sent into 7 modes and we are interested in the probability that all 7 photons end up in the first two modes. The interferometer is described by an unitary matrix and the incoming photons can be fully indistinguishable, fully distinguishable or partially distinguishable.\n", "\n", "## Introduction\n", "\n", "The paper [[2]](#references) shows that, unlike in the Hong-Ou-Mandel effect, bunching gets maximized with partially distinguishable photons. This disproofs the following conjecture:\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "### Conjecture 1\n", "(Generalized Bunching). Consider any input state of classically correlated photons. For any linear interferometer\n", "$\\hat{U}$ and any nontrivial subset $\\mathcal{K}$ of output modes, the probability that all photons are found in $\\mathcal{K}$ is maximal if the photons are (perfectly) indistinguishable. \n", "\n", "Evidence for this conjecture was given [[3]](#references)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The probability for such a case is given by:\n", "$$\n", "P_n(S) = perm(H \\odot S^T)\n", "$$\n", "where $n$ is the number of input photons, $S$ the distinguishability matrix and $H$ a matrix which depends on $\\hat{U}$ and $\\mathcal{K}$. The symbol $\\odot$ is the elementwise multiplication.\n", "\n", "The distinguishability matrix $S$ is defined by:\n", "$$ S_{ij} = $$ \n", "where $ tuple:\n", " # first two orthonormal vectors from which the Unitary matrix for the circuit is built\n", " v1 = np.zeros(n, dtype='complex_')\n", " v1[0] = 1\n", " v1[1] = 0\n", " for i in range(2, n):\n", " v1[i] = 1/math.sqrt(2)\n", "\n", " v2 = np.zeros(n, dtype='complex_')\n", " v2[0] = 0\n", " v2[1] = 1\n", " for i in range(2, n):\n", " v2[i] = np.conj(w**(i-2))/math.sqrt(2)\n", "\n", " return v1, v2 # these are the complex conjugate of the first two rows of the matrix M for n=7\n", "\n", "def normalize(vector: np.ndarray) -> np.ndarray:\n", " return vector / np.linalg.norm(vector)\n", "\n", "\n", "def make_unitary(n: int, w: complex) -> np.matrix:\n", " vector1, vector2 = create_vectors(n, w)\n", " orthonormal_basis = [normalize(vector1), normalize(vector2)]\n", " for _ in range(n-2):\n", " # Create a random n-dimensional complex vector\n", " random_vector = np.random.rand(n) + 1j*np.random.rand(n)\n", " # Subtract projections onto existing basis vectors to make it orthogonal\n", " for basis_vector in orthonormal_basis:\n", " random_vector -= np.vdot(basis_vector,\n", " random_vector) * basis_vector\n", " # Normalize the orthogonal vector to make it orthonormal\n", " orthonormal_basis.append(normalize(random_vector))\n", " # Define the unitary matrix from the calculated vectors\n", " mat = []\n", " for i in range(n):\n", " mat.append(orthonormal_basis[i])\n", " unitary_matrix = np.matrix(mat)\n", "\n", " return unitary_matrix\n", "\n", "unitary_matrix = make_unitary(n, w)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Building the Circuit\n", "\n", "Now that we have the unitary matrix we can use perceval to create a circuit from it. We do this by decomposing the unitary into Mach-Zender Interferometers. This gives us a 7 modes interferometer." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "image/svg+xml": [ "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "Φ=4.671018\n", "\n", "\n", "Φ=5.344707\n", "\n", "\n", "Φ=3.463949\n", "\n", "\n", "Φ=3.554204\n", "\n", "\n", "Φ=0.269035\n", "\n", "\n", "Φ=3.923696\n", "\n", "\n", "Φ=4.247596\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "Rx\n", "\n", "\n", "Φ=1.519525\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "Rx\n", "\n", "\n", "Φ=0.53838\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "Rx\n", "\n", "\n", "Φ=4.317761\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "Rx\n", "\n", "\n", "Φ=2.52884\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "Rx\n", "\n", "\n", "Φ=5.843819\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "Rx\n", "\n", "\n", "Φ=3.469752\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "Rx\n", "\n", "\n", "Φ=0.546012\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "Rx\n", "\n", "\n", "Φ=1.220482\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "Rx\n", "\n", "\n", "Φ=1.420609\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "Rx\n", "\n", "\n", "Φ=1.087897\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "Rx\n", "\n", "\n", "Φ=2.241685\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "Rx\n", "\n", "\n", "Φ=3.46322\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "Rx\n", "\n", "\n", "Φ=0.646221\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "Rx\n", "\n", "\n", "Φ=4.966345\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "Rx\n", "\n", "\n", "Φ=5.548939\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "Rx\n", "\n", "\n", "Φ=5.336294\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "Rx\n", "\n", "\n", "Φ=4.730925\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "Rx\n", "\n", "\n", "Φ=0.307159\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "Rx\n", "\n", "\n", "Φ=2.272413\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "Rx\n", "\n", "\n", "Φ=5.635176\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "Rx\n", "\n", "\n", "Φ=0.40874\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "Rx\n", "\n", "\n", "Φ=5.453475\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "Rx\n", "\n", "\n", "Φ=5.289967\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "Rx\n", "\n", "\n", "Φ=4.152004\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "Rx\n", "\n", "\n", "Φ=5.124207\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "Rx\n", "\n", "\n", "Φ=3.030306\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "Rx\n", "\n", "\n", "Φ=4.134838\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "Rx\n", "\n", "\n", "Φ=5.7987\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "Rx\n", "\n", "\n", "Φ=5.4546\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "Rx\n", "\n", "\n", "Φ=1.142738\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "Rx\n", "\n", "\n", "Φ=5.51816\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "Rx\n", "\n", "\n", "Φ=6.155096\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "Rx\n", "\n", "\n", "Φ=0.878151\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "Rx\n", "\n", "\n", "Φ=3.325585\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "Rx\n", "\n", "\n", "Φ=5.098012\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "Rx\n", "\n", "\n", "Φ=3.267043\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "Rx\n", "\n", "\n", "Φ=0.772848\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "Rx\n", "\n", "\n", "Φ=3.661129\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "Rx\n", "\n", "\n", "Φ=5.094331\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "Rx\n", "\n", "\n", "Φ=3.197166\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "Rx\n", "\n", "\n", "Φ=3*pi/2\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "Rx\n", "\n", "\n", "Φ=7*pi/5\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "0\n", "1\n", "2\n", "3\n", "4\n", "5\n", "6\n", "0\n", "1\n", "2\n", "3\n", "4\n", "5\n", "6\n", "" ], "text/plain": [ "" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# building Mach-Zender Interferometer block of the circuit\n", "mzi = pcvl.catalog[\"mzi phase last\"].build_circuit(\n", " phi_a=pcvl.Parameter(\"φ_a\"), phi_b=pcvl.Parameter(\"φ_b\"))\n", "# convert Unitary matrix into perceval language\n", "unitary = pcvl.Matrix(unitary_matrix)\n", "# create circuit\n", "circuit_rand = pcvl.Circuit.decomposition(unitary, mzi,\n", " phase_shifter_fn=pcvl.PS,\n", " shape=pcvl.InterferometerShape.TRIANGLE)\n", "\n", "pcvl.pdisplay(circuit_rand, recursive=True)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Inputting photons of different degrees of distinguishability\n", "\n", "Now that we have the circuit which represents the correct unitary matrix and therefore the correct $H$ from the conjecture, we need to feed in the right photons following the distinguishably matrix $S=A$. In the [[2]](#references) the input photons are described via polarization. In this simulation it is not specified how the photons are distinguishable. The first two photons are fully distinguishable. The other five photons are each a linear combination of the first two photons and form an equally spaced star shape when drawn on the Bloch sphere. \n", "\n", "\n", "\n", "![Blochsphere](../_static/img/Blochsphere.png)\n", "\n", "Here one can see the two fully distinguishable photons with red arrows and the five linear combinations in the equator plane." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "def create_inputs(n: int, w: complex) -> tuple:\n", " # make a list of fully distinguishable photons of the form |{a:i}> that means we give the photon an attribute a with value i\n", " states_dist = []\n", " for i in range(1, n+1):\n", " x = \"|{{a:{}}}>\".format(i)\n", " states_dist.append(pcvl.StateVector(x))\n", " # make a list of all input photons which are superpositions of |{a:1}> and |{a:2}>\n", " # start with the pure states |{a:1}> and |{a:2}>\n", " states_par_dist = [states_dist[0], states_dist[1]]\n", " for i in range(2, n):\n", " x = states_par_dist[0] + states_par_dist[1] * \\\n", " w**(i-2) # add the states |{a:1}> + w^(i-2)|{a:2}>\n", " states_par_dist.append(x)\n", " # Input states\n", " # initialise the variables\n", " indistinguishable_photons = []\n", " partially_distinguishable_photons = 1\n", " distinguishable_photons = 1\n", " # fill the states\n", " for i in range(n):\n", " indistinguishable_photons.append(1) # gives the state |1,1, ... , 1>\n", " partially_distinguishable_photons = partially_distinguishable_photons * \\\n", " states_par_dist[i]\n", " distinguishable_photons = distinguishable_photons * \\\n", " states_dist[i] # gives the state |{a:1},{a:2}, ... ,{a:n}>\n", " return pcvl.BasicState(indistinguishable_photons), partially_distinguishable_photons, distinguishable_photons\n", "\n", "\n", "# indistinguishable photons, partially distinguishable photons, fully distinguishable photons respectively\n", "indistinguishable_photons, partially_distinguishable_photons, distinguishable_photons = create_inputs(\n", " n, w)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To see if photon bunching gets amplified for partially distiguishable photons we need to compare it to the case of indistinguishable photons and for interest we are also comparing it to fully distinguishable photons. We are expecting that the probability for partially distinguishable photons will be highest followed by the indistinguishable photons and fully distinguishable photons having the lowest probability." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "# simulating boson sampling\n", "processor = pcvl.Processor(\"SLOS\")\n", "processor.set_circuit(circuit_rand)\n", "simulator = pcvl.SimulatorFactory().build(processor)" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "The probability for all 7 indistinguishable photons ending up in the first two modes is: 0.699 %\n", "The probability for all 7 distinguishable photons ending up in the first two modes is: 0.016 %\n", "The probability for all 7 partially distinguishable photons ending up in the first two modes is: 0.751 %\n" ] } ], "source": [ "def calc_prob(distinguishable_type, n: int, simulator) -> tuple:\n", " def reverse(lst):\n", " new_lst = lst[::-1]\n", " return new_lst\n", " # initialize the probabilities\n", " probability_photons = 0\n", " probability_distribution_photons = []\n", " # summing over all cases where all photons end up in only two modes\n", " # range over half the distribution because of symmetry\n", " for i in range(math.ceil((n+1)/2)):\n", " probability = simulator.probability(\n", " distinguishable_type, pcvl.BasicState([i, n-i]+[0] * (n-2)))\n", " probability_distribution_photons.append(probability)\n", " probability_photons += probability\n", " X = []\n", " for i in range(math.ceil((n+1)/2), n+1):\n", " X.append(probability_distribution_photons[i-math.ceil((n+1)/2)])\n", " probability_photons += probability_distribution_photons[i-math.ceil(\n", " (n+1)/2)]\n", " probability_distribution_photons = probability_distribution_photons + \\\n", " reverse(X)\n", " for i in range(n+1):\n", " if probability_photons != 0:\n", " probability_distribution_photons[i] = probability_distribution_photons[i] / \\\n", " probability_photons\n", "\n", " return probability_distribution_photons, probability_photons\n", "\n", "\n", "# Save the Probabilities so we don't have to run the CalcProb function multiple times\n", "probability_distribution_indistinguishable, probability_indistinguishable = calc_prob(\n", " indistinguishable_photons, n, simulator)\n", "probability_distribution_distinguishable, probability_distinguishable = calc_prob(\n", " distinguishable_photons, n, simulator) # high runtime\n", "probability_distribution_partially_distinguishable, probability_partially_distinguishable = calc_prob(\n", " partially_distinguishable_photons, n, simulator) # high runtime\n", "\n", "print(\n", " f\"The probability for all {n} indistinguishable photons ending up in the first two modes is: {probability_indistinguishable*100:.3f} %\")\n", "print(\n", " f\"The probability for all {n} distinguishable photons ending up in the first two modes is: {probability_distinguishable*100:.3f} %\")\n", "print(\n", " f\"The probability for all {n} partially distinguishable photons ending up in the first two modes is: {probability_partially_distinguishable*100:.3f} %\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "From the results above we can clearly see that the implemented partial distinguishablity amplified the bunching probability from 0.699% to 0,751%. This however does not proof that our set up gives the maximum bunching probability. As it only disproofs the conjecture with a counter example." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Plotting the results" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The first plot shows two-mode bunching probabilities for the three different scenarios. Here we can see the results match our expectations.\n", "\n", "The second plot shows the photon-number probability distribution for the first two output modes. The distributions are normalized, i.e., the probabilities are conditioned on events where all 7 photons end up in the first two modes (two-mode bunching events). This plot is interesting because it shows that the shape of the distribution of indistinguishable photons is very different to the shape of the distributions of partially and fully distinguishable photons." ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def plot(n: int, probability_distribution_indistinguishable, probability_indistinguishable, probability_distribution_partially_distinguishable, probability_partially_distinguishable, probability_distribution_distinguishable, probability_distinguishable):\n", " X = []\n", " for i in range(n+1):\n", " # creates a list of all possible tuple such that a+b=n for tuple (a,b)\n", " X.append(\"({},{})\".format(i, n-i))\n", " output_modes = X\n", " colours = ['#58c4e1', '#946cba', '#383e48'] # light blue, purple and gray\n", "\n", " def add_labels(x, y):\n", " for i in range(len(x)):\n", " if y[i] > 0.0005:\n", " plt.text(i, y[i]/2, round(y[i], 5), ha='center', color='white')\n", " else:\n", " plt.text(i, 1.25*y[i], round(y[i], 5), ha='center')\n", " cases = [\"indistinguishable\",\n", " \"partially distinguishable\", \"distinguishable\"]\n", " probabilities = [probability_indistinguishable,\n", " probability_partially_distinguishable, probability_distinguishable]\n", " plt.bar(cases, probabilities, color=colours)\n", " plt.ylabel('probability')\n", " plt.title(\"Comparing the total bunching probabilities for {} photons\".format(n))\n", " add_labels(cases, probabilities)\n", " plt.show()\n", "\n", " plt.scatter(output_modes, probability_distribution_indistinguishable,\n", " label='indistinguishable', color=colours[0])\n", " plt.scatter(output_modes, probability_distribution_partially_distinguishable,\n", " label='partially distinguishable', color=colours[1])\n", " plt.scatter(output_modes, probability_distribution_distinguishable,\n", " label='distinguishable', color=colours[2])\n", " plt.ylabel('probability')\n", " plt.xlabel('number of photons in first two modes')\n", " plt.title(\"Normalized bunching distributions\")\n", " plt.legend()\n", " plt.show()\n", "\n", "\n", "plot(n, probability_distribution_indistinguishable, probability_indistinguishable, probability_distribution_partially_distinguishable,\n", " probability_partially_distinguishable, probability_distribution_distinguishable, probability_distinguishable)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To see the that this set up only works for at least 7 photons we can compare the cases of 4,5,6 and 7 photons. You can see this if you run the above for n = 4,5 and 6. Running it for 8 or higher values for n will take a long time.\n", "\n", "#### For 8 photons the following holds:\n", "\n", "The probability for all 8 indistinguishable photon ending up in the first two modes is: 0.240 %\n", "\n", "The probability for all 8 distinguishable photon ending up in the first two modes is: 0.002 %\n", "\n", "The probability for all 8 partially distinguishable photon ending up in the first two modes is: 0.294 %\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## References" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "[1]\n", "Agata M. Branczyk, Hong-Ou-Mandel Interference (2017) in arXiv:1711.00080 (http://arxiv.org/abs/1711.00080)\n", "\n", "[2]\n", "Benoit Seron, Leonardo Novo and Nicolas J. Cerf, Boson bunching is not maximized by indistinguishable particles (2022) in arXiv:2203.01306 (https://arxiv.org/abs/2203.01306)\n", "\n", "[3]\n", "V. S. Shchesnovich, Universality of Generalized Bunching and Efficient Assessment of Boson Sampling (2016) in arXiv:1509.01561 (https://arxiv.org/abs/1509.01561)\n", "\n", "[4]\n", "Stephen W. Drury, A counterexample to a question of Bapat and Sunder (2016) in Electronic Journal of Linear Algebra **Vol 31** 69-70 (https://journals.uwyo.edu/index.php/ela/article/view/1631/1631)\n" ] } ], "metadata": { "language_info": { "name": "python" } }, "nbformat": 4, "nbformat_minor": 2 }