# 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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