{
 "cells": [
  {
   "cell_type": "markdown",
   "source": [
    "# Entanglement Generation"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "A useful feature of ZPGenerator is that it can also provide the state of the source conditioned on time-integrated detection outcomes, in addition to raw detection probability. This is allows the package to be used to study protocols that encode quantum information in the state of the source. In this tutorial, we will explore the conditional states feature in order to estimate the quality of photon-mediated entanglement generation between spin qubits situated in spatially-separated emitters. Following the structure of [[S. C. Wein et al., Phys. Rev. A 102, 033701 (2020)](https://journals.aps.org/pra/abstract/10.1103/PhysRevA.102.033701)], we will delve into three different protocols each based on a different encoding in the pulse of light: (1) photon-number encoding, (2) time-bin encoding, (3) and polarization encoding. To demonstrate these protocols, we will use the Source.trion() source type, which is introduced in the third section of the [Quantum Dots](quantum_dots.ipynb) tutorial."
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "## Photon-number encoding"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "This scheme for generating entanglement between remote spin qubits relies on first entangling the spin degree of freedom with the number of emitted photons (either 0 or 1). In other words, the goal is to produce a state of the form $|\\psi\\rangle = (|\\downarrow\\rangle |0\\rangle + |\\uparrow\\rangle |1\\rangle)/\\sqrt{2}$ from each of two different emitters. The pulse of light is then sent through a beam splitter that is monitored by photon-number resolving detectors. If exactly one detector detects exactly one photon, then the which-path information of the incoming photon is erased and the two spin qubits are projected onto a maximally entangled Bell state. Let's set up this experiment using ZPGenerator."
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "outputs": [],
   "source": [
    "from zpgenerator import *\n",
    "import numpy as np\n",
    "import qutip  as qt\n",
    "import matplotlib.pyplot as plt"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2024-02-09T13:51:04.227239Z",
     "start_time": "2024-02-09T13:51:03.820419Z"
    }
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "First thing to do is create our trion quantum dot source. By default, the trion initial state is a maximally mixed state between the spin up anda spin down states. To produce entanglement, we can initialize our trion into a superposition state. A more realistic simulation might explicitly simulate this state preparation step, as was shown in the [Quantum Dots](quantum_dots.ipynb) tutorial."
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "outputs": [],
   "source": [
    "trion = Source.trion()\n",
    "trion.initial_state = (trion.states['|spin_up>'] + trion.states['|spin_down>']) / np.sqrt(2)"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2024-02-09T13:51:04.309335Z",
     "start_time": "2024-02-09T13:51:03.835446Z"
    }
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "To produce the entangled state, we can drive our source with a $\\pi$ pulse to excite the $|\\uparrow\\rangle$ state so that it produces an R-polarized photon. To ensure this behaviour, we can update the default parameters of the source so that the excitation and collection angles are both circularly polarized."
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "outputs": [],
   "source": [
    "trion.update_default_parameters({'theta': np.pi/4, 'phi': -np.pi/2, # excitation polarization: right circular polarized.\n",
    "                                 'theta_c': np.pi/4, 'phi_c': -np.pi/2, # collect polarization: right mode 0 (left for mode 1)\n",
    "                                 'area': np.pi})  # pulse area of pi to bring the spin up state fully to the trion state"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2024-02-09T13:51:04.310403Z",
     "start_time": "2024-02-09T13:51:03.847495Z"
    }
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "Now that we have created our source, we can build our optical setup using the Processor class. Recall that the trion source has two emission modes: a right-polarized emission and a left-polarized emission by default. So, we can add our trion source to modes 0 and 2 of our processor, so that the polarization assignment will be: 0 - Right, 1 - Left, 2 - Right, 3 - Left."
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "outputs": [],
   "source": [
    "p = Processor() // ([0, 2], trion)"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2024-02-09T13:51:04.311269Z",
     "start_time": "2024-02-09T13:51:03.861814Z"
    }
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "We can check to ensure that our excitation and collection parameters are correct by seeing if modes 0 and 2 each show a probability of 1/2 to emit a photon while modes 1 and 3 are empty."
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mode 0\n",
      "Number  | Probability\n",
      "0       | 0.50000\n",
      "1       | 0.50000\n",
      "2       | 0.00000\n",
      "\n",
      "Mode 1\n",
      "Warning: no light detected in mode 1, g2 1 cannot be defined.\n",
      "Number  | Probability\n",
      "0       | 1.00000\n",
      "1       | 0.00000\n",
      "2       | 0.00000\n",
      "\n",
      "Mode 2\n",
      "Number  | Probability\n",
      "0       | 0.50000\n",
      "1       | 0.50000\n",
      "2       | 0.00000\n",
      "\n",
      "Mode 3\n",
      "Warning: no light detected in mode 3, g2 3 cannot be defined.\n",
      "Number  | Probability\n",
      "0       | 1.00000\n",
      "1       | 0.00000\n",
      "2       | 0.00000\n",
      "\n"
     ]
    }
   ],
   "source": [
    "for m in range(4):\n",
    "    print('Mode ' + str(m))\n",
    "    p.photon_statistics(port=m, truncation=2).display()"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2024-02-09T13:51:04.340888Z",
     "start_time": "2024-02-09T13:51:03.876577Z"
    }
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "To generate entanglement between the two emitters, we must pass the emission from modes 0 and 2 through each input of a balanced beamsplitter. To do this, we can permute the modes so that modes 0 and 2 are beside each other, then add our beamsplitter. Let's also add a beam splitter on the orthogonal polarization mode and permute the modes back, so that the entire component can represent a single beam splitter serving as an entangling circuit."
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "outputs": [],
   "source": [
    "entangling_circuit = Circuit.perm([0, 2, 1, 3]) // (0, Circuit.bs()) // (2, Circuit.bs()) // Circuit.perm([0, 2, 1, 3])\n",
    "detectors = ([0, 2], Detector.pnr(2))\n",
    "p = p // entangling_circuit // detectors"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2024-02-09T13:51:04.340983Z",
     "start_time": "2024-02-09T13:51:04.156732Z"
    }
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "Now that we have defined our optical setup, we can simulate all the conditional states of the processor using the conditional_states() method of the Processor class. This produces a dictionary of Qobj density operators that represent the unnormalized state of the two trion sources conditioned on the photo-detection pattern represented by the dictionary key of a tuple of integers. Please see the [QuTiP Documentation](https://qutip.org/docs/latest/) for more information about Qobj objects."
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "Notice that, since the final time is by default much longer than the system emission timescale, all the conditional states have negligible population in the source excited state. Since we care only about the spin qubit in the ground state, we can take a partial trace of our states to eliminate the excited state manifolds. This can be done using QuTiP's ptrace function, or we can simply specify the desired subspaces when simulating the conditional states using the 'select' keyword, which simply applies the ptrace function before returning the results. In this case, note that the first index of the trion source labels the $|g\\rangle$, $|e\\rangle$ states while the second index of the trion source is the spin qubit. Adding the two sources to the processor concatenates these spaces, so that the desired subspace is the second and fourth indices (labeled 1 and 3). After tracing out the excited states, we can then ask for the state associated with the detection outcome (1, 0), where we observed exactly one photon at the first detector and zero photons at the second. If everything goes well, this should be an entangled state."
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "outputs": [
    {
     "data": {
      "text/plain": "Quantum object: dims = [[2, 2], [2, 2]], shape = (4, 4), type = oper, isherm = True\nQobj data =\n[[0.   +0.j    0.   +0.j    0.   +0.j    0.   +0.j   ]\n [0.   +0.j    0.125+0.j    0.   -0.125j 0.   +0.j   ]\n [0.   +0.j    0.   +0.125j 0.125+0.j    0.   +0.j   ]\n [0.   +0.j    0.   +0.j    0.   +0.j    0.   +0.j   ]]",
      "text/latex": "Quantum object: dims = [[2, 2], [2, 2]], shape = (4, 4), type = oper, isherm = True $ \\\\ \\left(\\begin{matrix}0.0 & 0.0 & 0.0 & 0.0\\\\0.0 & 0.125 & -0.125j & 0.0\\\\0.0 & 0.125j & 0.125 & 0.0\\\\0.0 & 0.0 & 0.0 & 0.0\\\\\\end{matrix}\\right)$"
     },
     "execution_count": 98,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "states = p.conditional_states(select=[1, 3])\n",
    "states[1, 0].tidyup(1e-6)"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2024-02-09T13:51:04.374552Z",
     "start_time": "2024-02-09T13:51:04.168206Z"
    }
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "Indeed, we can see that we have an entangled state. However, the density operator is not normalized because the probability of outcome (1, 0) is not unity. We can simply re-normalize this operator by its trace and then use QuTiP's concurrence function to check how entangled it is."
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "outputs": [
    {
     "data": {
      "text/plain": "0.9999999925450656"
     },
     "execution_count": 99,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qt.concurrence(states[1, 0] / states[1, 0].tr())"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2024-02-09T13:51:04.374799Z",
     "start_time": "2024-02-09T13:51:04.370026Z"
    }
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "As we can see, the entanglement concurrence of the spin qubit state is unity within precision of the simulation (default 6 digits), given that the outcome (1, 0) was observed. However, note that the efficiency of our setup defaults to 100%, meaning that no photons are lost. Having a protocol that is robust against loss is extremely important since it is extremely difficult to eliminate loss entirely. Let's create a new optical setup that has some loss in between the sources and the entangling circuit."
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "outputs": [],
   "source": [
    "p_num = Processor() // ([0, 2], trion) // Circuit.loss(modes=4, name='transmission') // entangling_circuit // detectors\n",
    "\n",
    "transmission_list = np.linspace(0.01, 1, 20)\n",
    "state_list = [p_num.conditional_states(parameters={'transmission/efficiency': eff}, select=[1, 3]) for eff in transmission_list]"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2024-02-09T13:51:08.333150Z",
     "start_time": "2024-02-09T13:51:04.386847Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "outputs": [
    {
     "data": {
      "text/plain": "<Figure size 640x480 with 1 Axes>",
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "efficiency_list = [abs(2 * states[1, 0].tr()) for states in state_list]  # multiply by 2 for both successful outcomes (assuming symmetry)\n",
    "concurrence_list = [qt.concurrence(states[1, 0] / states[1, 0].tr()) for states in state_list]\n",
    "plt.plot(transmission_list, efficiency_list, label='Efficiency')\n",
    "plt.plot(transmission_list, concurrence_list, label='Concurrence')\n",
    "plt.xlabel('Transmission efficiency')\n",
    "plt.ylabel('Figure of Merit')\n",
    "plt.legend()\n",
    "plt.show()"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2024-02-09T13:51:08.425355Z",
     "start_time": "2024-02-09T13:51:08.336588Z"
    }
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "From this plot, we can see that the entanglement concurrence of the resulting state rapidly degrades with a decreasing transmission efficiency, along with the total efficiency of the protocol. The reason why this happens is that if both trion emitters produce a photon (i.e. end up in the $|\\uparrow\\rangle|\\uparrow\\rangle$ state), a single lost photon can result in a (1, 0) outcome and cause infidelity. To compensate for this problem, the solution is to reduce the probability the trions produce photons by biasing the initial state to be in the $|\\downarrow\\rangle$ state. That is, we make the initial state $|\\psi\\rangle =  \\sin(\\vartheta)|\\uparrow\\rangle + \\cos(\\vartheta)|\\downarrow\\rangle$ where $\\vartheta$ is close to 0 when transmission efficiency is small."
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "outputs": [],
   "source": [
    "angles = np.linspace(0.01, 0.5, 20)\n",
    "state_list = []\n",
    "trion_num = trion  # since we will modify this object and overwrite it later, let's rename it\n",
    "for theta in angles:\n",
    "    trion_num.initial_state = np.sin(theta * np.pi) * trion.states['|spin_up>'] + np.cos(theta * np.pi) * trion.states['|spin_down>']\n",
    "    state_list.append(p_num.conditional_states(parameters={'transmission/efficiency': 0.5}, select=[1, 3]))"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2024-02-09T13:51:12.141119Z",
     "start_time": "2024-02-09T13:51:08.426870Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "outputs": [
    {
     "data": {
      "text/plain": "<Figure size 640x480 with 1 Axes>",
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "efficiency_list = [abs(2 * states[0, 1].tr()) for states in state_list]\n",
    "concurrence_list = [qt.concurrence(states[0, 1]/states[0, 1].tr()) for states in state_list]\n",
    "plt.plot(angles, efficiency_list, label='Efficiency')\n",
    "plt.plot(angles, concurrence_list, label='Concurrence')\n",
    "plt.xlabel('Superposition angle, $\\\\vartheta$ ($\\pi$)')\n",
    "plt.ylabel('Figure of Merit')\n",
    "plt.ylim([0, 1.01])\n",
    "plt.xlim([0, 0.5])\n",
    "plt.legend()\n",
    "plt.show()"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2024-02-09T13:51:12.222894Z",
     "start_time": "2024-02-09T13:51:12.146773Z"
    }
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "Now we can see that, by reducing the probability of producing light, we can sacrifice efficiency to arbitrarily bring the concurrence near unity in this idealized scenario. Although it may seem counterintuitive, it turns out that this encoding can provide a significant efficiency advantage over the other two encodings despite having to sacrifice emission probability to achieve high fidelity entanglement [[S. C. Wein et al., Phys. Rev. A 102, 033701 (2020)](https://journals.aps.org/pra/abstract/10.1103/PhysRevA.102.033701), [S. L. N. Hermans et al., New J. Phys. 25, 013011 (2023)](https://iopscience.iop.org/article/10.1088/1367-2630/acb004/meta)]."
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "## Time-bin encoding"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "As we saw in the previous example, the photon-number encoding is sensitive to loss. In addition, it is a method that is sensitive to phase instability in the photon routing. One approach to combat these downsides was proposed by S. D. Barrett and P. Kok in 2005 [[S. D. Barrett and P. Kok, Phys. Rev. A 71, 060310(R) (2005)](https://journals.aps.org/pra/abstract/10.1103/PhysRevA.71.060310)]. This method uses the emission time bin to encode the quantum information rather than the number of emitted photons, and it was famously implemented in the first demonstration of a loop-hole free Bell inequality violation [[B. Hensen et al., Nature 526, 682-686 (2015)](https://www.nature.com/articles/nature15759)].\n",
    "\n",
    "The time-bin encoding follows very similarly to the photon-number encoding. However, instead of ending the protocol after the detection of a single photon, the spin state of both sources are flipped and then the photon-number protocol is repeated a second time. If a single photon is detected both before and after the spin flip, this implies that no photons were lost and the spin states are projected onto a maximally entangled state regardless of losses. In addition, the flip-and-repeat approach creates a symmetry so that exactly one photon must have travelled from each source, which naturally eliminates any phase instability.\n",
    "\n",
    "To demonstrate this scheme, we will use the same trion source as in the previous section. However, this time we will give a more complicated pulse sequence that will attempt two photon-number encoding protocols separated by a spin flip. This will require us to modify our source to add a control on the spin qubit. To make things easier, we can also use the operators available from the TrionEmitter object contained in the trion source."
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "outputs": [],
   "source": [
    "# make a sequence of two dirac pulses with different names so that we can modify their parameters independently\n",
    "excitation_sequence = Pulse(name='excitation')\n",
    "excitation_sequence.add(Pulse.dirac(parameters={'delay': 0}, name='first'))\n",
    "excitation_sequence.add(Pulse.dirac(parameters={'delay': 20}, name='second'))\n",
    "\n",
    "# create the catalogue trion source component using the excitation sequence\n",
    "trion = Source.trion(pulse=excitation_sequence)\n",
    "\n",
    "# we can extract the emitter object contained in the source component to modify it\n",
    "emitter = trion.elements['_TrionEmitter']\n",
    "\n",
    "# using the Control class method 'drive', we create a new control object to drive a specified transition of the emitter using a dirac pulse\n",
    "spin_control = Control.drive(pulse=Pulse.dirac(parameters={'delay': 18}, name='spin control'),\n",
    "                             transition=emitter.states['|spin_down>'] * emitter.states['|spin_up>'].dag())\n",
    "emitter.add(spin_control)\n",
    "\n",
    "# as before, we initialize the trion into a superposition state, and specify the default excitation parameters\n",
    "trion.initial_state = (trion.states['|spin_up>'] + trion.states['|spin_down>']) / np.sqrt(2)\n",
    "trion.update_default_parameters({'theta': np.pi/4, 'phi': -np.pi/2, 'theta_c': np.pi/4, 'phi_c': -np.pi/2})"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2024-02-09T13:51:12.238413Z",
     "start_time": "2024-02-09T13:51:12.226745Z"
    }
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "Now that we have our source, we can build our processor as we did in the previous section. Before doing that, we must construct the detector needed to monitor two time bins of the same spatial mode. This can be done using the partition class method of the Detector class. Please see [Detectors](detectors.ipynb) for more information about this detector type. Since we expect at most two photons overall using this pulse sequence, we can specify a photon number resolution of 2. To help distinguish the photon indices, we can also make an argument to name the detector."
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "outputs": [],
   "source": [
    "time_bin_detector = lambda name: Detector.partition(['excitation/first/delay', 'excitation/second/delay'], # first bin goes from the first pulse to the second, the second bin goes from the second pulse to infinity\n",
    "                                                    parameters={'excitation/first/delay': 0, 'excitation/second/delay': 20},  # default parameters to match previous defaults\n",
    "                                                    resolution=2,\n",
    "                                                    name=name)"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2024-02-09T13:51:12.262609Z",
     "start_time": "2024-02-09T13:51:12.241330Z"
    }
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "To make sure our source and detectors are configured correctly, we can ensure that we get 1/2 probability of seeing a photon in the first time bin and 1/2 probability of seeing a photon in the second time bin."
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['detector bin 0', 'detector bin 1']\n",
      "Pattern | Probability\n",
      "1 0     | 0.50000\n",
      "0 1     | 0.50000\n",
      "\n"
     ]
    }
   ],
   "source": [
    "p = Processor() // trion // time_bin_detector('detector')\n",
    "print(p.bin_labels)\n",
    "p.probs().display()"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2024-02-09T13:51:12.386843Z",
     "start_time": "2024-02-09T13:51:12.243470Z"
    }
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "Now that we have verified that our source and detectors are operating correctly, we can build the entanglement setup. To distinguish time bins in each spatial mode, we can name the detectors 'left' and 'right' that are monitoring modes 0 and 1, respectively."
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 107,
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['left bin 0', 'left bin 1', 'right bin 0', 'right bin 1']\n",
      "Pattern | Probability\n",
      "2 0 0 0 | 0.12500\n",
      "1 1 0 0 | 0.12500\n",
      "0 2 0 0 | 0.12500\n",
      "0 1 1 0 | 0.12500\n",
      "0 0 2 0 | 0.12500\n",
      "1 0 0 1 | 0.12500\n",
      "0 0 1 1 | 0.12500\n",
      "0 0 0 2 | 0.12500\n",
      "\n"
     ]
    }
   ],
   "source": [
    "p = Processor() // ([0, 2], trion) // entangling_circuit // (0, time_bin_detector('left')) // (2, time_bin_detector('right'))\n",
    "print(p.bin_labels)\n",
    "p.probs().display()"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2024-02-09T13:51:13.232516Z",
     "start_time": "2024-02-09T13:51:12.399708Z"
    }
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "We can now see all the detection outcomes expected of the scheme in the ideal case. Notice that we always observe exactly two photons, and importantly it is the two-photon outcomes that now herald the successful projection of the spins onto an entangled state. This means that loss or number-resolving limitations cannot cause errors. Notice also that we never observe outcomes like (1, 0, 1, 0,) and (0, 1, 0, 1), since these are eliminated due to perfect Hong-Ou-Mandel interference between photons from the two sources. Once we start adding imperfections, like decoherence, these cases can appear.\n",
    "\n",
    "Now that we have verified our outcome probabilities are correct, let's take a look at the entanglement concurrence of the spin state of the source conditioned on each outcome."
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 108,
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(0, 0, 0, 2) 0\n",
      "(0, 2, 0, 0) 0\n",
      "(0, 0, 1, 1) 0.9999882077603706\n",
      "(0, 1, 1, 0) 0.9999973704435464\n",
      "(0, 0, 2, 0) 0\n",
      "(1, 0, 0, 1) 0.9999973775122543\n",
      "(1, 1, 0, 0) 0.9999882133082519\n",
      "(2, 0, 0, 0) 0\n"
     ]
    }
   ],
   "source": [
    "states = p.conditional_states(select=[1, 3])\n",
    "for pattern, state in states.items():\n",
    "    print(pattern, qt.concurrence(state / state.tr()))"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2024-02-09T13:51:13.869756Z",
     "start_time": "2024-02-09T13:51:13.233991Z"
    }
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "As expected, if we observe exactly one photon in both the first time bin (in either spatial mode) and exactly one photon in the second time bin (in either spatial mode), we generate a maximally entangled spin state up to the simulation precision. Now, as before, we can test how robust the scheme is to transmission losses."
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 109,
   "outputs": [],
   "source": [
    "p_time = Processor() // ([0, 2], trion) // Circuit.loss(modes=4, name='transmission') // entangling_circuit // (0, time_bin_detector('left')) // (2, time_bin_detector('right'))\n",
    "transmission_list = np.linspace(0.01, 1, 20)\n",
    "state_list = [p_time.conditional_states(parameters={'transmission/efficiency': eff}, select=[1, 3]) for eff in transmission_list]"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2024-02-09T13:51:30.470614Z",
     "start_time": "2024-02-09T13:51:13.886006Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "outputs": [
    {
     "data": {
      "text/plain": "<Figure size 640x480 with 1 Axes>",
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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "efficiency_list = [abs(4 * states[1, 1, 0, 0].tr()) for states in state_list] # multiply by 4 for all successful outcomes (assuming symmetry)\n",
    "concurrence_list = [qt.concurrence(states[1, 1, 0, 0] / states[1, 1, 0, 0].tr()) for states in state_list]\n",
    "plt.plot(transmission_list, efficiency_list, label='Efficiency')\n",
    "plt.plot(transmission_list, concurrence_list, label='Concurrence')\n",
    "plt.xlabel('Transmission efficiency')\n",
    "plt.ylabel('Figure of Merit')\n",
    "plt.legend()\n",
    "plt.show()"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2024-02-09T13:51:30.592422Z",
     "start_time": "2024-02-09T13:51:30.474678Z"
    }
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "As we can see, the concurrence produced using time-bin encoding is completely robust against losses. However, notably the protocol efficiency degrades much quicker than seen in the photon-number encoding. This is because it relies on the successful transmission of two photons rather than one."
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "## Polarization encoding"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "The final encoding we will explore is the polarization of light. Using the same trion source, we can exploit the fact that there are two orthogonally-polarized transitions that connect the ground-state spin doublet to the excited-state trion doublet. Instead of targeting just the R-polarized transition, we can instead excite both R and L polarized transition by using an H-polarized pulse. Then, if we begin with a spin superposition state $|\\psi\\rangle = (|\\downarrow\\rangle + |\\uparrow\\rangle)/\\sqrt{2}$, after the trion state decays back to the ground state we will be left with the spin-polarization entangled state: $|\\psi\\rangle = (|\\downarrow\\rangle|L\\rangle| + |\\uparrow\\rangle|R\\rangle)/\\sqrt{2}$. By interfering two such states on a beam splitter and monitoring the subsequent polarization at the output, we can identify that the case where we detect exactly one R and one L polarized photon will project the emitters onto a maximally entangled spin state.\n",
    "\n",
    "The setup for this experiment is slightly less complicated than the time-bin encoding since we do not need to add a spin control pulse or create time bin detectors. Instead, we only need to use all 4 modes of our processor and configure the excitation pulse appropriately."
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 111,
   "outputs": [],
   "source": [
    "trion = Source.trion()\n",
    "trion.initial_state = (trion.states['|spin_up>'] + trion.states['|spin_down>']) / np.sqrt(2)\n",
    "trion.update_default_parameters({'theta': 0, 'phi': 0, # excitation polarization: horizontally  polarized.\n",
    "                                 'theta_c': np.pi/4, 'phi_c': -np.pi/2, # collect polarization: right mode 0 (left for mode 1)\n",
    "                                 'area': np.sqrt(2) * np.pi})  # pulse area of sqrt(2)*pi to bring both spin up and spin down state fully to the trion state"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2024-02-09T13:51:30.606677Z",
     "start_time": "2024-02-09T13:51:30.594228Z"
    }
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "With our source configured, we can construct the setup. This time, we must add a detector for each spatial mode and each polarization for 4 detectors total."
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 112,
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Pattern | Probability\n",
      "2 0 0 0 | 0.12500\n",
      "0 0 2 0 | 0.12500\n",
      "1 1 0 0 | 0.12500\n",
      "0 1 1 0 | 0.12500\n",
      "0 2 0 0 | 0.12500\n",
      "1 0 0 1 | 0.12500\n",
      "0 0 1 1 | 0.12500\n",
      "0 0 0 2 | 0.12500\n",
      "\n"
     ]
    }
   ],
   "source": [
    "p_pol = Processor() // ([0, 2], trion) // Circuit.loss(modes=4, name='transmission') // entangling_circuit // (list(range(4)), Detector.pnr(resolution=2))\n",
    "p_pol.probs().display()"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2024-02-09T13:51:31.781699Z",
     "start_time": "2024-02-09T13:51:30.631073Z"
    }
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "Since our source modes are ordered (L, R), and the circuit does not permute them, the outputs of the processor are labelled following (L, R, L, R). We can always label the bins explicitly to be sure, or it is often possible to deduce the right labels by through experimental observation. Similar to the time-bin encoding, we can see that we only observe two-photon outputs, and since we expect to generate entanglement heralded by one of these, this protocol is also robust against loss. Let's confirm that we find entanglement."
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 113,
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(0, 0, 0, 2) 0\n",
      "(0, 0, 1, 1) 0.9999993017264965\n",
      "(0, 0, 2, 0) 0\n",
      "(0, 1, 1, 0) 0.9999954728823505\n",
      "(0, 2, 0, 0) 0\n",
      "(1, 0, 0, 1) 0.9999925262768165\n",
      "(1, 1, 0, 0) 0.9999987846232194\n",
      "(2, 0, 0, 0) 0\n"
     ]
    }
   ],
   "source": [
    "states = p_pol.conditional_states(select=[1, 3])\n",
    "for pattern, state in states.items():\n",
    "    print(pattern, qt.concurrence(state / state.tr()))"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2024-02-09T13:51:32.861010Z",
     "start_time": "2024-02-09T13:51:31.795839Z"
    }
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "As anticipated, we find a maximally entangled spin state when we observe an L and R photon. As with the other two schemes, we can"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 114,
   "outputs": [
    {
     "data": {
      "text/plain": "<Figure size 640x480 with 1 Axes>",
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "transmission_list = np.linspace(0.01, 1, 20)\n",
    "state_list = [p_pol.conditional_states(parameters={'transmission/efficiency': eff}, select=[1, 3]) for eff in transmission_list]\n",
    "efficiency_list = [abs(4 * states[1, 1, 0, 0].tr()) for states in state_list] # multiply by 4 for all successful outcomes (assuming symmetry)\n",
    "concurrence_list = [qt.concurrence(states[1, 1, 0, 0] / states[1, 1, 0, 0].tr()) for states in state_list]\n",
    "plt.plot(transmission_list, efficiency_list, label='Efficiency')\n",
    "plt.plot(transmission_list, concurrence_list, label='Concurrence')\n",
    "plt.xlabel('Transmission efficiency')\n",
    "plt.ylabel('Figure of Merit')\n",
    "plt.legend()\n",
    "plt.show()"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2024-02-09T13:51:56.036911Z",
     "start_time": "2024-02-09T13:51:32.864321Z"
    }
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "Unsurprisingly, since this protocol is also a two-photon protocol, it has an identical dependence on loss as the time-bin encoding."
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "## Comparison\n"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "Now that we have constructed the processors implementing each of the three protocols, and tested their basic features, we are in a good position to compare them. Since we already discussed losses, let's now take a look at emitter pure dephasing. Since the TrionEmitter class already has this parameter built in, all we need to do is modify it when running our protocol.\n",
    "\n",
    "First thing we need to do is reset the initial state of the trion emitters in the photon-number encoding processor because we had modified it before."
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 115,
   "outputs": [],
   "source": [
    "trion_num.initial_state = (trion.states['|spin_up>'] + trion.states['|spin_down>']) / np.sqrt(2)"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2024-02-09T13:51:56.037031Z",
     "start_time": "2024-02-09T13:51:56.031703Z"
    }
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "Now, let's find out how the concurrence depends on emitter pure dephasing for each protocol. Let's also compute the associated single-photon indistinguishability for the same dephasing rate."
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 116,
   "outputs": [],
   "source": [
    "dephasing_rates = np.linspace(0, 1, 10)\n",
    "hom_list = []\n",
    "concurrence_list_num = []\n",
    "concurrence_list_time = []\n",
    "concurrence_list_pol = []\n",
    "for rate in dephasing_rates:\n",
    "    hom_list.append(trion.hom(parameters={'dephasing': rate})['M'])\n",
    "\n",
    "    state = p_num.conditional_states(parameters={'dephasing': rate}, select=[1, 3])[1, 0]\n",
    "    concurrence_list_num.append(qt.concurrence(state / state.tr()))\n",
    "\n",
    "    state = p_time.conditional_states(parameters={'dephasing': rate}, select=[1, 3])[1, 1, 0, 0]\n",
    "    concurrence_list_time.append(qt.concurrence(state / state.tr()))\n",
    "\n",
    "    state = p_pol.conditional_states(parameters={'dephasing': rate}, select=[1, 3])[1, 1, 0, 0]\n",
    "    concurrence_list_pol.append(qt.concurrence(state / state.tr()))"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2024-02-09T13:52:23.767375Z",
     "start_time": "2024-02-09T13:51:56.035432Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 117,
   "outputs": [
    {
     "data": {
      "text/plain": "<Figure size 640x480 with 1 Axes>",
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(hom_list, concurrence_list_num, label='Number encoding', color='tab:orange')\n",
    "plt.plot(hom_list, concurrence_list_time, label='Time-bin encoding', color='tab:green')\n",
    "plt.plot(hom_list, concurrence_list_pol, label='Polarization encoding', color='tab:blue', linestyle='dashed')\n",
    "plt.xlabel('Indistinguishability')\n",
    "plt.ylabel('Entanglement Concurrence')\n",
    "plt.legend()\n",
    "plt.show()"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2024-02-09T13:52:23.861766Z",
     "start_time": "2024-02-09T13:52:23.780354Z"
    }
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "Interestingly, we can clearly see that the time-bin encoding suffers substantially more from emitter pure dephasing than the other two protocols. This is because each source undergoes two excitation-decay cycles. The photon-number encoding only requires a single excitation that produces on average 1/2 of a photon, while the polarization encoding only requires a single excitation that produces on average 1 photon. So, although the number encoding and the polarization encoding use a different number of photons in total, it is the number of emitter cycles-not the total number of photons-that determines the susceptibility to emitter dephasing."
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "markdown",
   "source": [],
   "metadata": {
    "collapsed": false
   }
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}