Formalisms (in fidelity calculation for quantum teleportation)

[ssampak]

Hi, I am trying to read a paper about quantum teleportation and got stuck with calculating the fidelity of the mixed(noisy) channel.

Fidelity F := < $$\Phi^{(-)}_{12} | \rho_{1} \otimes \rho_{23} | \Phi^{(-)}_{12}$$ >

where $$\rho_{1} = | \phi_{1} > < \phi_{1} |$$
and $$\rho_{23} = t | \Phi^{(+)}_{23}><\Phi^{(+)}_{23}| + (1-t) | \Phi^{(-)}_{23}><\Phi^{(-)}_{23}|$$

$$|\phi_{1}> = a|0_{1}> + b|1_{1}>$$
$$|\Phi^{(\pm)}_{23}> = 1/sqrt{2} (|00_{23}> \pm |11_{23}>)$$

Am I doing wrong if terms like < 0_{1} | 1_{3} > appear?
Then, if right what do I have to do with those? If wrong please give me the right way.

 

[azntoon]

No, you are not doing anything wrong. The terms < 0_{1} | 1_{3} > may appear in the calculation of the fidelity. In this case, since the two states being compared are orthogonal, the value of such a term will be zero, so you can simply ignore it and carry on with the calculation.