spin state normalisation

[Mengjia He]

Hi, Prof. Kuprov,

I find in some examples in Spinach, you use the following step to normalize a state: rho=rho/norm(full(rho),2).

As we know, norm(rho, 2) given the max value of svd(rho), but as quantum mechanics habit, a normalized state should be <rho|rho>=1.

So, can we doing normalization by dividing the Frobenius norm, i.e., rho=rho/norm(full(rho),'fro') ?

[kuprov]

That depends on the formalism - in Liouville space, rho is a vector, and therefore it's 2-norm is the usual root-sum-abs-square. You can easily prove that when you stretch a matrix into a vector column-wise, the 2-norm of the resulting vector is equal to the Frobenius norm of the original matrix. In Hilbert space, yes, the correct norm is the Frobenius norm.