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Fixed image paths and added further minor refinements
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glpatcern committed Nov 13, 2024
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16 changes: 8 additions & 8 deletions notebooks/Bell inequalities/1. Bell-Wigner inequality.ipynb
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"id": "8e80bb9f",
"metadata": {},
"source": [
"# Lecture 9.1: Bell-Wigner inequality\n",
"# 1. Bell-Wigner inequality\n",
"\n",
"<center><img src=\"../figures/qibo_mascotte/qibo_bell_wigner.png\" alt=\"drawing\" width=\"400\"/></center>\n",
"<center><strong>Fig. 9.1:</strong> Qibo, Bell and Wigner discussing about inequalities at CERN [DALL-E].</center>\n",
"<center><img src=\"../../figures/qibo_mascotte/qibo_bell_wigner.png\" alt=\"drawing\" width=\"400\"/></center>\n",
"<center>Qibo, Bell and Wigner discussing about inequalities at CERN [DALL-E].</center>\n",
"\n",
"### Introduction\n",
"\n",
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"\n",
"$$Q^W = P(\\hat{a}+,\\hat{b}+) - P(\\hat{a}+,\\hat{c}+) - P(\\hat{c}+,\\hat{b}+),$$\n",
"\n",
"where, as an example, with $P(\\hat{a}+,\\hat{b}+)$ we mean the probability of measuring particles A and B as +1.\n",
"where, as an example, with $P(\\hat{a}+,\\hat{b}+)$ we mean the probability of measuring both particles in the state $|1\\rangle$.\n",
"\n",
"In the case of local hidden (LH) variables, the inequality reads:\n",
"\n",
"$$Q^W_{LH} \\le 0$$\n",
"\n",
"We will show how to prepare a quantum state where the $Q^W$ quantity violates the assumptions of locality as discussed in the paper.\n",
"\n",
"In the [next notebook](https://github.com/qiboteam/qiboedu/tree/main/notebooks/Bell64_inequality.ipynb), we turn to the original Bell inequality.\n",
"In the [next notebook](./Bell64_inequality.ipynb), we turn to the original Bell inequality.\n",
"\n",
"### Setup\n",
"\n",
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"name": "stderr",
"output_type": "stream",
"text": [
"[Qibo 0.2.14|INFO|2024-11-12 15:08:02]: Using numpy backend on /CPU:0\n"
"[Qibo 0.2.13|INFO|2024-11-13 14:25:38]: Using numpy backend on /CPU:0\n"
]
}
],
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"lastKernelId": null
},
"kernelspec": {
"display_name": "Python 3 (ipykernel)",
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
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"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.10.0"
"version": "3.11.9"
}
},
"nbformat": 4,
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14 changes: 7 additions & 7 deletions notebooks/Bell inequalities/2. Bell64 inequality.ipynb
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"id": "8e80bb9f",
"metadata": {},
"source": [
"# Lecture 9.2: Bell inequality\n",
"# 2. Original Bell inequality\n",
"\n",
"<center><img src=\"../figures/qibo_mascotte/qibo_bell.png\" alt=\"drawing\" width=\"400\"/></center>\n",
"<center><strong>Fig. 9.2:</strong> Qibo and Bell discussing about inequalities at CERN [DALL-E].</center>\n",
"<center><img src=\"../../figures/qibo_mascotte/qibo_bell.png\" alt=\"drawing\" width=\"400\"/></center>\n",
"<center>Qibo and Bell discussing about inequalities at CERN [DALL-E].</center>\n",
"\n",
"### Introduction\n",
"\n",
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"\n",
"We will show that in a Qibo quantum circuit the inequality is violated in the case of entangled particles.\n",
"\n",
"In the [third notebook](https://github.com/qiboteam/qiboedu/tree/main/notebooks/CHSH_inequality.ipynb), we turn to the popular CHSH inequality.\n",
"In the [third notebook](./CHSH_inequality.ipynb), we turn to the popular CHSH inequality.\n",
"\n",
"\n",
"### Setup\n",
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"source": [
"### Plots\n",
"\n",
"Here we plot the obtained values of $Q^B$."
"Here we plot the obtained values of $Q^B$ using a dedicated plotscript which can be found in `qiboedu.scripts.plotscripts`."
]
},
{
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"lastKernelId": null
},
"kernelspec": {
"display_name": "Python 3 (ipykernel)",
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
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"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.10.0"
"version": "3.11.9"
}
},
"nbformat": 4,
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36 changes: 19 additions & 17 deletions notebooks/Bell inequalities/3. CHSH inequality.ipynb
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"id": "8e80bb9f",
"metadata": {},
"source": [
"# Lecture 9.3: Clauser-Horne-Shimony-Holt (CHSH) inequality\n",
"# 3. Clauser-Horne-Shimony-Holt (CHSH) inequality\n",
"\n",
"<center><img src=\"../figures/qibo_mascotte/qibo_chsh.png\" alt=\"drawing\" width=\"400\"/></center>\n",
"<center><strong>Fig. 9.3:</strong> Qibo discussing with Clauser, Horne, Shimony and Holt about inequalities at CERN [DALL-E].</center>\n",
"<center><img src=\"../../figures/qibo_mascotte/qibo_chsh.png\" alt=\"drawing\" width=\"400\"/></center>\n",
"<center>Qibo discussing with Clauser, Horne, Shimony and Holt about inequalities at CERN [DALL-E].</center>\n",
"\n",
"### Introduction\n",
"\n",
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"\n",
"We will show that in a Qibo quantum circuit the inequality is violated in the case of entangled particles with specific measurement angles.\n",
"\n",
"See also the [first notebook](https://github.com/qiboteam/qiboedu/tree/main/notebooks/Bell-Wigner_inequality.ipynb) for the most basic Bell-Wigner inequality.\n",
"See also the [first notebook](./Bell-Wigner_inequality.ipynb) for the most basic Bell-Wigner inequality.\n",
"\n",
"\n",
"### Setup\n",
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"cell_type": "code",
"execution_count": 4,
"id": "cde5f91f",
"metadata": {},
"metadata": {
"scrolled": true
},
"outputs": [
{
"name": "stdout",
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"print('Completed in %.1f seconds' % (time.time() - tstart))"
]
},
{
"cell_type": "markdown",
"id": "33b6a787",
"metadata": {},
"source": [
"### Plots\n",
"\n",
"Here we plot the obtained values of $Q^S$ using a dedicated plotscript which can be found in `qiboedu.scripts.plotscripts`."
]
},
{
"cell_type": "code",
"execution_count": 5,
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")"
]
},
{
"cell_type": "markdown",
"id": "2868a281",
"metadata": {},
"source": [
"### Plots\n",
"\n",
"Here we plot the obtained values of $Q^S$ using multiple parametric lines and common `matplotlib` primitives."
]
},
{
"cell_type": "markdown",
"id": "058a8ae5",
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"lastKernelId": null
},
"kernelspec": {
"display_name": "Python 3 (ipykernel)",
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
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"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.10.0"
"version": "3.11.9"
}
},
"nbformat": 4,
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