Quantum Probability as Area on Bloch Sphere

two qubit states in z basis

cos

θ

2

ϕ



sin

θ

2

|

ψ

1

>

θ

1

0.836

ϕ

1

2.41

|

ψ

2

>

θ

2

0

ϕ

2

0

purple area / total area = |<

ψ

2

|

ψ

1

>

2

|

= 0.835218

Detailed State and Projector Data…

Qubits (quantum bits) are two-state quantum systems. The quantum state of a qubit can be visualized as a point on the Bloch sphere. For a qubit prepared in a state

|

ψ

1

>

, the probability of measuring the system to be in a second state,

|

ψ

2

>

, can also be visualized on the Bloch sphere. The probability is proportional to the area of the complementary spherical cap obtained by rotating one Bloch vector around the other.