Questions tagged [quasiprobability-distributions]
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Phase distribution of coherent states
I am studying the phase distribution for coherent states, as is defined in quantum optics. (See, for example, Introductory Quantum Optics by Gerry and Knight, pages 46–48).
In this situation, we seek ...
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Distributions "more singular than a Dirac delta" must have negativity
I am looking at properties of the Glauber P-functions, which are distributions (in the sense of a dirac delta) on the complex plane, normalized so that $\int_{\mathbb{C}} d^2 \alpha P(\alpha) = 1$. On ...
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Is it possible to relate the expectation values of an operator w.r.t. two different density matrices if the matrices are related up to a displacement?
I'm trying to derive a general relationship between the expectation values of two different operators with respect to some unspecified state $E_{j}(\lambda)=\mathrm{Tr}[\rho \hat{O}_{j}(\lambda)]$ (...
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Do we actually need negative probabilities in quantum mechanics?
I was reading this thread and I'm a bit confused. The answer says negative probabilities can account for destructive wave interference and the events cancelling out. But if events just cancel out, ...
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Is there a way to find the superposition of two Wigner functions without finding their density operators?
Say I have two Wigner functions $W_1(x,p)$ and $W_2(x,p)$ representing pure states on optical phase space, and I want to know what the Wigner function of their superposition $W_{1+2}(x,p)$ looks like (...
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Intuitively, why does Quantum Mechanics involve a sum over all possibilities?
I understand that one can just mathematically derive the path integral from the Schrodinger equation. I'm looking for an intuitive explanation in contrast with classical mechanics.
Consider a ...
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Is there a relationship between the phase space path integral and phase space quantum mechanics?
I understand that they're, in the end, related because they're the same theory. But is there a closer relationship because both are theories of probability distributions on phase space?
I also ...
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The first non-classical property of field state
In quantum optics, the first non-classical property of the field is squeezing.
The reason we say non-classical is that the some of the quasiprobability distribution functions become negative in some ...
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An equation for Wigner's quasi-probability distribution?
I learned that Moyal's evolution equation is the equation for the time-evolution of Wigner's quasi-probability distribution. However, I couldn't say I perfectly understand the meaning of this ...
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Non-uniqueness of Glauber-Sudarshan $P$-function
For a state $\rho$ acting on single bosonic mode with coherent states $|\alpha\rangle$, one can always define a $P$-function to furnish a diagonal representation of the state in the coherent-state ...
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Question about Glauber-Sudarshan $P$ representation
I'm reading Scully's 'Quantum Optics'. I've got some question about the Glauber-Sudarshan $P$ representation.
It's straight forward that
$$
P(\alpha) = \frac{e^{\vert \alpha \vert ^2}}{\pi^2} \int \...
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How can I show that the negative region of Wigner quasi-probability distribution is small enough than $h$?
Wigner quasi-probability distribution is the main tools used in the formulation of Quantum mechanics on phase space which is equivalent to usual formulations. This distribution can have negative ...
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Is there a simple way to obtain the Quantum Fisher Information (QFI) from a Wigner function? (or any other quasiprobability distribution?)
In theory the Wigner function $W(q,p)$ contains all the same information as the density matrix $\rho$ associated with it, so it's definitely possible to write the QFI $\mathcal F_Q$ in terms of the ...
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Wigner function in relation to real space
The Wigner function is a quasi-probability distribution because it can have values of $x$ from -1,0,+1. As it is orthogonal to the $x,p$ plane can this be represented as a dipole moment along the $z$ ...
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Converting the complex Wigner function to its real form in terms of the quadrature operators
I noticed something that bugged me recently, the Wigner function which is defined for one mode in the complex plane as
$$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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