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Part 3 of 3 Part Series

The Essence of Quantum Computing
Part 3 of 3 Part Series

Note that while entanglement results in a synchronous state for the two particles, the converse is not necessarily true. When a measurement is made on one of the entangled particles, both will collapse simultaneously. According to our model, the particles will collapse to the state they are in at the instant of measurement (such as τ1 or τ2 in Figure 13.3), which is in accord with postulate 3. We do not know how Nature might accomplish the required synchronization. It is, of course, clear that this interpretation cannot violate the uncertainty principle since Postulate 3 is not violated. Everything rests entirely on the notion of external observations because without it there are no means to ascribe a physical interpretation. We now use the teleportation algorithm (see Section 10.6 in Part II) to elucidate the interpretation.

Alice wishes to teleport a qubit, labelled by subscript 1, of unknown state |Φ〉 = α|01〉 + β|11〉, to Bob. In addition, there is an entangled pair of auxiliary qubits designated by subscripts 2 and 3 in the state
|x〉 = (|0213〉 – |1203〉)/√2. Alice holds the qubit with subscript 2 in addition to the one with subscript 1 while Bob holds the qubit with subscript 3. Thus, the initial state of the three-qubit system is (see Figure 13.4a where the qubit subscripts (in this and subsequent Figures 13.4b and 13.4c) have been omitted since they can be inferred from their position in the state |…〉) given by

eq9

Alice now applies the Cnot gate (with qubit 2 as the target) to the qubits held by her. This changes the state of the three-qubit system to (see Figure 13.4b)

eq10

Next, Alice applies the Hadamard gate to qubit 1 which puts the three-qubit system in the state shown in Figure 13.4c.

eq11

img4

Figure 13.4a Initial state |ψ0〉 of the teleportation system.

img5

Figure 13.4b State |ψ1〉 of the teleportation system after Cnot operation.

img6

Figure 13.4c State |ψ2〉 of the teleportation system after Hadamard operation.

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