Quantum Computing

1.
Suppose the Bell state 1/
√
2 (|00 > +|11 >) is measured in {|+ >, |− >} basis. What
is the measured output?
2. √
Suppose Alice and Bob initially share the Bell state 1/ 2 (|01 > +|10 >) and Alice has
another qubit |Ψ >= a|0 > +b|1 >. Explain how Alice can teleport her qubit to Bob.
3.Design a full adder quantum circuit (you may use Toffoli gates).
4.Show that the the column vectors of the 2
n dimensional Hadamard matrix
(i.e., tensor product of n H’s) are orthonormal.