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In general it is a lot more boring than you'd think. The two patterns are some complex-valued functions $\psi_{1,2}(z)$ on the screen which you only see in absolute value, $|\psi_{1,2}(z)|^2$ being the actual pattern seen. Typically for example you might have $$\psi_\pm(z) = {(2\pi\sigma^2)}^{1/4}\exp\left[\frac{(z \pm \mu)^2}{4\sigma^2}\right] e^{i k (x ...


The covariance matrix is a kind of a description of a quantum state that is an alternative to a density matrix or a wavefunction. So calculation of it implies that you know a particular state you are dealing with in other representation (density matrix, wavefunction, Q/W/P-function) then you can calculate all the expectations. For example for a coherent ...


The most general description of a quantum system is given by a density matrix $\rho$. It has dimensions of $N \times N$, where $N$ is the number of degrees of freedom of the system: 2 for a 2 level quantum system (qubit), 3 for 3-level etc. But often we deal with the systems that have infinite number of degrees of freedom. Such systems are quantum harmonic ...


A Gaussian state is a ground or thermal state of a (bosonic or fermionic) Hamiltonian which is quadratic in the creation and annihiliation operators. Those states are fully characterized by expectation values of quadratic operators, and thus $4N^2$ parameters for $N$ fermions or bosons.

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