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For any quantum state, we have a unique density matrix $\rho$. For any $\rho$, we can do the Wigner transformation to get a unique Wigner function $P(x,p)$. For any Wigner function $P(x,p)$, we can do the Weyl transformation to get back the unique $\rho$. If the construction of the Wigner function from $\rho$ was not unique, then it would not be possible to ...


5

What is non-classicality? I'm not sure if there's a universally accepted definition, but the way that I'd define it is: if all possible outcomes of experiments on a particular quantum system can be described by a probability distribution, then the system is classical. Otherwise, it is non-classical. In alternative terminology, for a classical system, people ...


3

You mean something like $$W_{G}(\mathbf{r}) =\frac{2^{n}}{\pi^{n} \sqrt{\operatorname{Det} \sigma}} \mathrm{e}^{-(\mathbf{r}-\overline{\mathbf{r}})^{\top} \boldsymbol{\sigma}^{-1}(\mathbf{r}-\overline{\mathbf{r}})},$$ where $W_{G}(\mathbf{r})$ is the Wigner function corresponding to a Gaussian state, $\mathbf{\sigma}$ its covariance matrix, and $\overline{r}$...


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