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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 equality $$a^\dagger a=(q-ip)(q+ip)/2=[q^2+p^2+i(qp-pq)]/2=\frac{q^2+p^2-1}{2}.$$ This relates the total number of photons to the trace of your matrix $\sigma$. ...


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QML researcher at Xanadu here. Our X-series chip produce entangled states by squeezing light and then combining it at beam splitters: those 'cables' are waveguides in a chip, which when they are close enough they allow tunnelling between them and effectively couple those two modes. Note that the squeezing is necessary in this case (for example, had we used ...


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