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The Wigner function of the thermal state is given as $W(\alpha)=\frac{1}{\pi(\langle n\rangle+ \frac{1}{2})} \exp \left( -\frac{|\alpha|^2}{\langle n\rangle+\frac{1}{2}} \right)$ The source is Quantum optics, the author is Girish S. Agarwal


Energy loss by photons occurs in a dielectric medium when the photons interact with the atoms of which the dielectric is made. This interaction does not normally result in a red-shift of the photons, but rather an attenuation of a beam of photons due to photons being absorbed. Depending on the nature of the material and the energy of the photons, the ...


I'm assuming your input photon has a known polarization (say horizontal). You won't see interference, because the polarizers act as a "which-path" measuring device. If you erase the polarization information, the interference pattern will appear.


In general, degeneracy in quantum mechanics means that there are at least two states that have indistinguishable energy. In the case of a degenerate photon pair, the two photons have will the same frequency (as E = $\hbar$ $\omega$). This is, of course, oversimplifying things slightly. The above describes the case when the photons are each in a single mode....


The photon pair (obtained in a spontaneous parametric down conversion WITHOUT post-selection) keeps the same filter angle, reducing crosstalk in quantum optic networks, therefore increasing channel manipulation.


After searching I find these "closing operators" defined by the authors correspond to particular sets of operators mentioned in a part (on quantum regression theorem) of the book Statistical methods in quantum optics 1.


This is done in several papers, e.g. here: The relevant portion is Lemma 1. Given a state $\rho$ with covariance matrix in block form $$ \gamma_{\rho}=\begin{pmatrix}{} A & B \\ B^T & C \end{pmatrix} $$ the covariance matrix after a measurement after a projection onto the pure Gaussian state with ...

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