# Can a qubit be in the inside of the Bloch Sphere?

Can qubit be inside Bloch Sphere, i.e. its length is less than 1?
If yes, how we represent that state since we have only parameter for angles and not the length (norm) of the vector?

• – glS Jan 16 at 12:11

$$\rho=q|\psi\rangle\langle\psi| + (1-q)|\phi\rangle\langle\phi|$$ where $$|\psi\rangle$$ and $$|\phi\rangle$$ are pure states with vectors $$\overset{\rightarrow}{r_{\psi}}$$ and $$\overset{\rightarrow}{r_{\phi}}$$ on Bloch sphere, and $$0; then the vector $$\overset{\rightarrow}{r_{\rho}}=q\overset{\rightarrow}{r_{\psi}}+(1-q)\overset{\rightarrow}{r_{\phi}}$$ inside Bloch sphere represents mixed state with density matrix $$\rho$$. Geometrically, $$\overset{\rightarrow}{r_{\rho}}$$ is a point on the line connecting points $$\overset{\rightarrow}{r_{\psi}}$$ and $$\overset{\rightarrow}{r_{\phi}}$$