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Commit 8d57eeb

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committedJan 19, 2023
Fixed typo that would cause incorrect Latex redering
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‎docs/source/whitepaper/5-density-matrix.ipynb

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"metadata": {},
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"In this framework though, the output of a channel acting on $\\vert{\\psi}\\rangle$ , i.e.\n",
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"$\n",
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"\\mathcal{E} ( \\vert{\\psi}\\rangle\\langle{\\psi}\\vert) = \\sum_i K_i \\vert{\\psi}\\rangle\\langle{\\psi}\\vert K_i^ \\dagger\n",
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"$\n",
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"$\\mathcal{E} ( \\vert{\\psi}\\rangle\\langle{\\psi}\\vert) = \\sum_i K_i \\vert{\\psi}\\rangle\\langle{\\psi}\\vert K_i^ \\dagger$\n",
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"is viewed as an ensemble of states $\\frac{K_i\\vert{\\psi}\\rangle}{\\sqrt{\\langle{\\psi}\\vert K_i^\\dagger K_i \\vert{\\psi}\\rangle}}$ that each occur with probability $p_i = \\langle{\\psi}\\vert K_i^\\dagger K_i \\vert{\\psi}\\rangle$. Thus, the code above stochastically produces the output of a single qubit initialized in state $\\vert{\\psi}\\rangle=\\frac{\\vert{0}\\rangle+\\vert{1}\\rangle}{\\sqrt{2}}$ being passed through a phase damping channel with parameter $\\gamma=0.5$. \n",
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"\n",
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"The Monte Carlo simulation of channels where the Kraus operators are all unitary matrices (up to a constant factor) can be handled with additional efficiency by using ``unitary_kraus`` instead of ``general_kraus``."
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"nbformat": 4,
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‎docs/source/whitepaper/5-density-matrix_cn.ipynb

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"不过,在这个框架中,作用于 $\\vert{\\psi}\\rangle$ 的通道的输出,即\n",
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"$\n",
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"\\mathcal{E} ( \\vert{\\psi}\\rangle\\langle{\\psi}\\vert) = \\sum_i K_i \\vert{\\psi}\\rangle\\langle{\\psi}\\vert K_i^ \\dagger\n",
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"$\n",
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"$\\mathcal{E} ( \\vert{\\psi}\\rangle\\langle{\\psi}\\vert) = \\sum_i K_i \\vert{\\psi}\\rangle\\langle{\\psi}\\vert K_i^ \\dagger$\n",
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"被视为状态的集合 $\\frac{K_i\\vert{\\psi}\\rangle}{\\sqrt{\\langle{\\psi}\\vert K_i^\\dagger K_i \\vert{\\psi}\\rangle}}$\n",
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"每个发生的概率为 $p_i = \\langle{\\psi}\\vert K_i^\\dagger K_i \\vert{\\psi}\\rangle$.\n",
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"因此,上面的代码随机产生在状态 $\\vert{\\psi}\\rangle=\\frac{\\vert{0}\\rangle+\\vert{1}\\rangle}{\\sqrt{2} }$\n",
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"nbformat": 4,
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