Q-salto

$n=$

This might take a while

linear symlog

$M$

$M'$

$\tilde{M}$

$T'$

$T'^{-1}$

$\tilde{T}$

$\tilde{T}^{-1}$

$\tilde{T}'$

$\tilde{T}'^{-1}$

$\mathbf{a}[\rho]$

$\mathbf{b}[\rho]$

$\mathbf{a'}[\rho]$

$\mathbf{b'}[\rho]$

$\mathbf{\tilde{a}}[\rho]$

$\mathbf{\tilde{b}}[\rho]$

Hover over a matrix entry to preview its value:

$$ a_j[\rho] = \frac{1}{2^n} \sum_{|P|=j} \mathrm{Tr}[\rho P]^2 $$

$$ b_j[\rho] = \frac{1}{2^n} \sum_{|P|=j} \mathrm{Tr}[\rho P\rho P] $$

$$ a'_j[\rho] = \frac{1}{\binom{n}{j}} \sum_{\substack{S\subseteq \{1,\dots,n\}\\|S|=j}} \mathrm{Tr}[\rho_S^2] $$

$$ b'_j[\rho] = \frac{1}{\binom{n}{j}} \sum_{\substack{S\subseteq \{1,\dots,n\}\\|S|=n-j}} \mathrm{Tr}[\rho_S^2] $$

$$ a''_j[\rho] = \frac{1}{2^n} \sum_{|P|=j} \mathrm{Tr}[\rho P \tilde{\rho} P] $$

$$ b''_j[\rho] = \frac{(-1)^{(n-j)}}{2^n} \sum_{|P|=j} \mathrm{Tr}[\rho P \tilde{\rho} P] $$