Hi, I am trying to read a paper about quantum teleportation and got stuck with calculating the fidelity of the mixed(noisy) channel.(adsbygoogle = window.adsbygoogle || []).push({});

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

where [tex]\rho_{1} = | \phi_{1} > < \phi_{1} | [/tex]

and [tex] \rho_{23} = t | \Phi^{(+)}_{23}><\Phi^{(+)}_{23}| + (1-t) | \Phi^{(-)}_{23}><\Phi^{(-)}_{23}| [/tex]

[tex] |\phi_{1}> = a|0_{1}> + b|1_{1}> [/tex]

[tex] |\Phi^{(\pm)}_{23}> = 1/sqrt{2} (|00_{23}> \pm |11_{23}>) [/tex]

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.

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# Formalisms (in fidelity calculation for quantum teleportation)

Can you offer guidance or do you also need help?

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