# Photon and qubit representation

The photon spin-1 has two states, $$\pm\hbar$$, just like the spin qubit ($$\pm\frac{\hbar}{2}$$).

From a quantum information point of view, they can encode the same amount of data.

However, I am confused about the usual qubit representation:

$$$$|q\rangle = \cos\frac{\theta}{2}|0\rangle + e^{i\gamma}\sin\frac{\theta}{2}|1\rangle. \tag{1}$$$$

The $$\frac{1}{2}$$ factor comes from the spin operators:

$$$$S_{x,y,z} = \frac{\hbar}{2}\sigma_{x,y,z}$$$$ where $$\sigma_x, \sigma_y, \sigma_z$$ are the Pauli matrices.

They imply that a full rotation needs $$\theta=4\pi$$ and a bit flip (from 0 to 1) needs a $$2\pi$$ rotation.

But for the photon, a full rotation (for polarization) only need $$2\pi$$.

So, is the usual qubit representation (1) valid for photons? can the photon spin state be represented on the Bloch sphere? I sometimes heard that the right representation for the photon is the Poincaré sphere.

• Can you write an equation like (1) for the Poincaré sphere? I do not think so... Commented Mar 15 at 12:51