What do the Bell states mean physically?
The state of Q 1 that we want to teleport, we write as:
With a probability of | C 0 | 2 a vertical polarization measurement would give "0" and a probability of | C 1 | 2 would come out "1".
For this state we want four transformations U 1 , U 2 , U 3 and U 4 define that change the state slightly. We will need these transformations later:
Let us now consider the state that describes all three quanta. Such a state can be written as a special form of product between the states of the individual quanta.
In our case of three quanta Q 1 , Q H and Q 2 does this mean:
The states of the quanta Q 2 and Q H are now linked to one another via a quantum long-range relationship in such a way that the measurement of the polarization "1" of Q 2 always to the measurement "0" of Q H leads or vice versa. More precisely, the two quanta are prepared in such a way that they are in the first of the following four so-called Bell states:
The state of all three quanta can be written as follows:
Together with the transformations from equations 2 to 5, we now have all the ingredients to simply rewrite the state of our overall system. There is no witchcraft behind this, just a little mathematical transformation work:
So the unknown state has moved from the first position to the third. If we now carry out a Bell measurement on the first two quanta, one of the four Bell states is assumed. We then only have to carry out the corresponding transformation U 1 , U 2 , U 3 or U 4 apply to the third quant. And the state of the quant is teleported!
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