如果你也在 怎样代写量子力学Quantum mechanics这个学科遇到相关的难题，请随时右上角联系我们的24/7代写客服。量子力学Quantum mechanics在理论物理学中，量子场论（QFT）是一个结合了经典场论、狭义相对论和量子力学的理论框架。QFT在粒子物理学中用于构建亚原子粒子的物理模型，在凝聚态物理学中用于构建准粒子的模型。
量子力学Quantum mechanics产生于跨越20世纪大部分时间的几代理论物理学家的工作。它的发展始于20世纪20年代对光和电子之间相互作用的描述，最终形成了第一个量子场理论–量子电动力学。随着微扰计算中各种无限性的出现和持续存在，一个主要的理论障碍很快出现了，这个问题直到20世纪50年代随着重正化程序的发明才得以解决。第二个主要障碍是QFT显然无法描述弱相互作用和强相互作用，以至于一些理论家呼吁放弃场论方法。20世纪70年代，规整理论的发展和标准模型的完成导致了量子场论的复兴。
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物理代写|量子力学代写quantum mechanics代考|Classical-to-Classical Channels
It is natural to expect that classical channels are special cases of quantum channels, and indeed, this is the case. To see this, fix an input probability distribution $p_X(x)$ and a classical channel $p_{Y \mid X}(y \mid x)$. Fix an orthonormal basis ${|x\rangle}$ corresponding to the input letters and an orthonormal basis ${|y\rangle}$ corresponding to the output letters. We can then encode the input probability distribution $p_X(x)$ as a density operator $\rho$ of the following form:
$$
\rho=\sum_x p_X(x)|x\rangle\langle x|
$$
Let $\mathcal{N}$ be a quantum channel with the following Kraus operators
$$
\left{\sqrt{p_{Y \mid X}(y \mid x)}|y\rangle\langle x|\right}_{x, y} .
$$
(The fact that these are legitimate Kraus operators follows directly from the fact that $p_{Y \mid X}(y \mid x)$ is a conditional probability distribution.) The quantum channel then has the following action on the input $\rho$ :
$$
\begin{aligned}
\mathcal{N}(\rho) & =\sum_{x, y} \sqrt{p_{Y \mid X}(y \mid x)}|y\rangle\left\langle x\left|\left(\sum_{x^{\prime}} p_X\left(x^{\prime}\right)\left|x^{\prime}\right\rangle\left\langle x^{\prime}\right|\right) \sqrt{p_{Y \mid X}(y \mid x)}\right| x\right\rangle\langle y| \
& =\sum_{x, y, x^{\prime}} p_{Y \mid X}(y \mid x) p_X\left(x^{\prime}\right)\left|\left\langle x^{\prime} \mid x\right\rangle\right|^2|y\rangle\langle y| \
& =\sum_{x, y} p_{Y \mid X}(y \mid x) p_X(x)|y\rangle\langle y| \
& =\sum_y\left(\sum_x p_{Y \mid X}(y \mid x) p_X(x)\right)|y\rangle\langle y| .
\end{aligned}
$$
物理代写|量子力学代写quantum mechanics代考|Classical-to-Quantum Channels
Classical-to-quantum channels, or classical-quantum channels for short, are channels which take classical systems to quantum systems. They thus go one step beyond both classical-to-classical channels and preparation channels. More generally, they make a given quantum system classical and then prepare a quantum state, as discussed in the following definition:
DEFInition 4.6.6 (Classical-Quantum Channel) A classical-quantum channel first measures the input state in a particular orthonormal basis and outputs a density operator conditioned on the result of the measurement. Given an orthonormal basis $\left{|k\rangle_A\right}$ and a set of states $\left{\sigma_B^k\right}$, each of which is in $\mathcal{D}\left(\mathcal{H}_B\right)$, a classical-quantum channel has the following action on an input density operator $\rho_A \in \mathcal{D}\left(\mathcal{H}_A\right):$
$$
\rho_A \rightarrow \sum_k\left\langle\left. k\right|_A \rho_A \mid k\right\rangle_A \sigma_B^k .
$$
Let us see how this comes about, using the definition above. The classicalquantum channel first measures the input state $\rho_A$ in the basis $\left{|k\rangle_A\right}$. Given that the result of the measurement is $k$, the post measurement state is
$$
\frac{|k\rangle\left\langle k\left|\rho_A\right| k\right\rangle\langle k|}{\left\langle k\left|\rho_A\right| k\right\rangle} .
$$
The channel then correlates a density operator $\sigma_B^k$ with the post-measurement state $k$ :
$$
\frac{|k\rangle\left\langle k\left|\rho_A\right| k\right\rangle\langle k|}{\left\langle k\left|\rho_A\right| k\right\rangle} \otimes \sigma_B^k .
$$
量子力学代考
物理代写|量子力学代写quantum mechanics代考|Classical-to-Classical Channels
我们很自然地认为经典通道是量子通道的特殊情况，事实也确实如此。要看到这一点，固定一个输入概率分布$p_X(x)$和一个经典通道$p_{Y \mid X}(y \mid x)$。固定输入字母对应的标准正交基${|x\rangle}$和输出字母对应的标准正交基${|y\rangle}$。然后我们可以将输入概率分布$p_X(x)$编码为如下形式的密度算子$\rho$:
$$
\rho=\sum_x p_X(x)|x\rangle\langle x|
$$
设$\mathcal{N}$为具有以下克劳斯算符的量子信道
$$
\left{\sqrt{p_{Y \mid X}(y \mid x)}|y\rangle\langle x|\right}{x, y} . $$ (这些都是合法的Kraus运算符，这一事实直接源于$p{Y \mid X}(y \mid x)$是一个条件概率分布。)然后量子通道对输入$\rho$有以下动作:
$$
\begin{aligned}
\mathcal{N}(\rho) & =\sum_{x, y} \sqrt{p_{Y \mid X}(y \mid x)}|y\rangle\left\langle x\left|\left(\sum_{x^{\prime}} p_X\left(x^{\prime}\right)\left|x^{\prime}\right\rangle\left\langle x^{\prime}\right|\right) \sqrt{p_{Y \mid X}(y \mid x)}\right| x\right\rangle\langle y| \
& =\sum_{x, y, x^{\prime}} p_{Y \mid X}(y \mid x) p_X\left(x^{\prime}\right)\left|\left\langle x^{\prime} \mid x\right\rangle\right|^2|y\rangle\langle y| \
& =\sum_{x, y} p_{Y \mid X}(y \mid x) p_X(x)|y\rangle\langle y| \
& =\sum_y\left(\sum_x p_{Y \mid X}(y \mid x) p_X(x)\right)|y\rangle\langle y| .
\end{aligned}
$$
物理代写|量子力学代写quantum mechanics代考|Classical-to-Quantum Channels
经典到量子通道，或简称经典量子通道，是将经典系统传输到量子系统的通道。因此，他们超越了古典到古典的渠道和准备渠道。更一般地说，它们使给定的量子系统变得经典，然后制备量子态，如下面的定义所述:
定义4.6.6(经典量子通道)经典量子通道首先以特定的标准正交基测量输入状态，并根据测量结果输出密度算子。给定一个标准正交基$\left{|k\rangle_A\right}$和一组状态$\left{\sigma_B^k\right}$，其中每个都在$\mathcal{D}\left(\mathcal{H}_B\right)$中，经典量子通道对输入密度算子$\rho_A \in \mathcal{D}\left(\mathcal{H}_A\right):$具有以下作用
$$
\rho_A \rightarrow \sum_k\left\langle\left. k\right|_A \rho_A \mid k\right\rangle_A \sigma_B^k .
$$
让我们用上面的定义来看看这是怎么发生的。经典量子通道首先测量基$\left{|k\rangle_A\right}$中的输入状态$\rho_A$。假设测量结果为$k$，则测量后的状态为
$$
\frac{|k\rangle\left\langle k\left|\rho_A\right| k\right\rangle\langle k|}{\left\langle k\left|\rho_A\right| k\right\rangle} .
$$
然后通道将密度算子$\sigma_B^k$与测量后状态$k$关联起来:
$$
\frac{|k\rangle\left\langle k\left|\rho_A\right| k\right\rangle\langle k|}{\left\langle k\left|\rho_A\right| k\right\rangle} \otimes \sigma_B^k .
$$
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