Skip to main content
4 votes
Accepted

Why is a state Gaussian if and only if its covariance matrix satisfies $\boldsymbol\sigma+i\boldsymbol\Omega\ge0$?

From the definition of the covariance matrix, $${\sigma}_{ij}=\left\langle \frac{x_i x_j+ x_j x_i}{2}\right\rangle -\langle x_i\rangle\langle x_j\rangle,$$ where we define $$\boldsymbol{x}=(q_1,p_1,\...
Quantum Mechanic's user avatar
2 votes
Accepted

How to write the covariance matrix of a quantum gaussian state as a function of photon numbers?

Recall that $a=(q+ip)/\sqrt{2}$ in some dimensionless units (Weedbrook might change the units because I think they like $\hbar=2$; I'm using $[q,p]=i$ and $[a,a^\dagger]=1$). We can thus find the ...
Quantum Mechanic's user avatar

Only top scored, non community-wiki answers of a minimum length are eligible