Compare Protocol A & B

Protocol A vs. B Evolution Comparison

p₀⁽¹'¹⁾ 0.05 p₀⁽⁰'¹⁾ 0.05 p₀⁽¹'⁰⁾ 0.02 p₁⁽⁰'⁰⁾ 0.02 p₁⁽⁰'¹⁾ 0.03 p₁⁽¹'⁰⁾ 0.05 Initial F₀ 0.50

Comparing two steady states y expressing \(a,b,a_R,b_R\) in the independent-error model

If we now invoke the independence assumption (mis-read erorr vs back-action error are happening independently of each other), with parameters:

\[ \epsilon_0,\epsilon_1,\quad p_{0\to1},p_{1\to0}, \]

the 2 groups of “four joint probabilities” are:

\[ \begin{array}{l} p_0^{(0,0)}=(1-\epsilon_0)(1-p_{0\to1}),\quad p_0^{(0,1)}=(1-\epsilon_0)p_{0\to1},\\ p_0^{(1,0)}=\epsilon_0(1-p_{0\to1}),\quad\;\;\; p_0^{(1,1)}=\epsilon_0 p_{0\to1},\\[3pt] p_1^{(1,1)}=(1-\epsilon_1)(1-p_{1\to0}),\quad p_1^{(1,0)}=(1-\epsilon_1)p_{1\to0},\\ p_1^{(0,1)}=\epsilon_1(1-p_{1\to0}),\quad\;\;\; p_1^{(0,0)}=\epsilon_1 p_{1\to0}. \end{array} \]

Then:

Protocol A: (post-select on all the \(o=0\))