Simple questions

This is a forum for simple QI questions - don't be shy!

Quadrature operators and Hermite polynomials

Hello everyone. I have the following problem.

I have The Hamiltonian of the 1D Harmonic Oscillator (hbar=m=w=1)

H= x^2+p^2

with the known solutions

psi(x)=exp(-x^2/2)*H_n(x)

where H_n are the Hermite polynomials of order n.

If I change the variables for the following ones (quadrature operators)

s=cos(y) x + sin(y) p
t=sin(y) x + cos(y) p

Entanglement, Causality and Local Realism

I have been walking around with the notion that "quantum entanglement implies a causal relationship due to the states having a shared history". I am now not so
sure that even fits into any interpretation of QM. To be honest, I'm not even sure what I am saying as the whole subject seems to be just out of my reach.

Quantum minimization

Hello everyone. I looking for information about minimization of functions with quantum computer. I mean, if I have a multidimensional function f(x0,x1,...xD) and I want to kown if there is any quantum algorithm or simulator for finding the values of (x0,x1,..,xD) that minimize it.

In the classical algorithm the minimization time scales linearly with the dimension D and I want to find a procedure with a lower scaling.

Do you known any reference?

Thank you very much.

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