HW8 - Exercise 2 (b) (normalization of teleported states)

HW8 - Exercise 2 (b) (normalization of teleported states)

by Guifré Sánchez i Serra -
Number of replies: 2

Hi, part (b) in Exercise 2 of HW8 asks us explain what are the teleported states that Bob gets when the protocol is completed, and to compare with the initial state |φ⟩. In this "corrupted" teleportation situation, when Bob receives, say, bits 01, and applies the X unitary to his qubit, what he will obtain will not be, in general, of the form K(|φ⟩ + something else), although when we do the projection without normalizing, we obtain something of the stated form. My question is whether we have to work with Bob's normalized state or not. Because without normalization, the comparison with the initial state |φ⟩ is more direct and, to some extent, gives more intuition about what's happening.

Thanks very much. 

In reply to Guifré Sánchez i Serra

Re: HW8 - Exercise 2 (b) (normalization of teleported states)

by Nicolas Macris -
Hi,
I am not sure I understand your question. Any state can be written as K(| phi > + something else). In particular Bob's teleported normalized state is of this form. If you do all computations you will get K and the "something else". When delta--> 0 this state tends to | phi >.

This being said if you dont want to normalize your final result this is ok but in any case since we ask you to compute the probability you automatically get the normalization.

I am not sure I have answered your question though.

N.M
In reply to Nicolas Macris

Re: HW8 - Exercise 2 (b) (normalization of teleported states)

by Guifré Sánchez i Serra -
Hi,

Thanks for the answer. What I wanted to say is that the comparison is much more direct if we consider Bob's state to be of the form |phi> + A|k>, with k = 0,1, but in this case, we don't have it normalized. In any case, considering the normalization is also important when talking about the difference between the "corrupted" teleported states and the "ideal" teleported states.