Chapter 4, Qubit Conspiracy Theories

1. q1 is 1, q0 is 0.
2. You can demonstrate that writing in the form is impossible. Here’s how:

Assume (to the contrary) that . Then, .

But since , either or .

In the first case, must be 0 instead of 1. In the second case, must be 0 instead of 1. Either way, things don’t work out.



4. from qiskit import QuantumCircuit
   circ = QuantumCircuit(2)
   circ.h(0)
   circ.cnot(0, 1)
   circ.x(1)
   circ.z(1)
   display(circ.draw('latex', initial_state=True))

The resulting sphere looks like this:



The |01⟩ qubit’s phase is , and the |10⟩ qubit’s phase is 0.

5. 
6. There are eight ways to assign up-or-down arrows to the three measuring directions on the left. For the six ways that resemble the scenario in Figure 4.35, the probability of disagreement is . For the remaining two ways, the probability of disagreement is 1 (see...