Questions tagged [quasiprobability-distributions]

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Is there a simple way to obtain the Quantum Fisher Information (QFI) from a Wigner function? (or any other quasiprobability distribution?)

In theory the Wigner function $W(q,p)$ contains all the same information as the density matrix $\rho$ associated with it, so it's definitely possible to write the QFI $\mathcal F_Q$ in terms of the ...
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Wigner function in relation to real space

The Wigner function is a quasi-probability distribution because it can have values of $x$ from -1,0,+1. As it is orthogonal to the $x,p$ plane can this be represented as a dipole moment along the $z$ ...
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Converting the complex Wigner function to its real form in terms of the quadrature operators

I noticed something that bugged me recently, the Wigner function which is defined for one mode in the complex plane as $$W(\alpha)=\frac{1}{\pi^2}\int e^{\lambda\alpha^*-\lambda^*\alpha} \operatorname{...
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Computing $\frac{1}{\pi^{2}} \int_{\mathbb{C}} \exp(\lambda\alpha^{*}-\lambda^{*}\alpha)\exp(-|\lambda|^{2}/2)d^{2}\lambda$

This came up when attempting to do a routine calculation of Wigner function of the vacuum state $$ \frac{1}{\pi^{2}} \int_{\mathbb{C}} \exp(\lambda\alpha^{*}-\lambda^{*}\alpha-|\lambda|^{2}/2)d^{2}\...
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Can the lifetime of a broken covalent bond be calculated?

According to a paper (molecular dynamic simulation) published in 2018,(https://www.scirp.org/journal/paperinformation.aspx?paperid=83351) the Maxwell-Boltzman distribution is also valid for the number ...
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What does it mean for $P$ functions to be "more singular than a delta"?

Consider the Glauber-Sudarshan $P$ representation of a state $\rho$, which is the function $\mathbb C\ni\alpha\mapsto P_\rho(\alpha)\in\mathbb R$ such that $$\rho = \int d^2\alpha \, P_\rho(\alpha) |\...
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Understanding the relationship between Phase Space Distributions (Wigner vs Glauber-Sudarshan P vs Husimi Q)

I am moving into a new field and after thorough literature research need help appreciating what is out there. In the continuos variable formulation of optical state space. (Quantum mechanical/Optical) ...
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What is the physical interpretation of the density matrix in a double continuous basis $|\alpha\rangle$, $|\beta\rangle$?

(a) Any textbook gives the interpretation of the density matrix in a single continuous basis $|\alpha\rangle$: The diagonal elements $\rho(\alpha, \alpha) = \langle \alpha |\hat{\rho}| \alpha \...
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An example of a quantum system for which Wigner function transitions to negative values

I want to check my understanding of the Wigner transform and try to understand why and how exactly the probabilistic interpretation drops down as the function goes to zero and then to negative values ...
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