Make A, B
H A
CNOT A, B
The above code will produce
The above state is a "Bell Pair" or "The Einstein-Podolsky-Rosen (EPR) Pair", or "Maximally Entangled Pair"
There are many maximally entangled pair of qubits, but the above is the most famous one. Although isn't a way to quantify how "entangled" a pair is, but the |MEP\rangle is definitely as most entangled as a pair can be.
Property of MEP:
doing an unitrary operation M with real amplitude on one bit is the same as doing the inverse operation M^\dagger on the other.
doing an unitrary operation M with real amplitude twice on different qubits will cancel out the effect.
any rotation of individual bits of |MEP\rangle is still a |MEP\rangle (only joint operations can get the state out of |MEP\rangle)
measuring any bits in |MEP\rangle will give \frac{1}{2} chance of being 1 and \frac{1}{2} chance of being 0.
We saw, in one homework, that you can hide one extra bit of information in the amplitude. Sending one of the qubit in |MEP\rangle can convey 2 classical bits of information.
We use the fact that Alice doing operation M on a joined state is the same as Bob doing operation M^\dagger on the joined state. So we can transmit information by "helping" Bob to do certain operation.
Sending 1 classical bit after preparing |MEP\rangle can convey 1 qubit of information. Here is how we do it:
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