Photon polarization ($|\psi ⟩=\alpha |H⟩+\beta |V⟩$)

For a photon in a fixed spatial mode, the two transverse photon polarizations span a qubit space. A pure photon polarization state is $\alpha |H⟩+\beta |V⟩$ with $|\alpha {|}^2+|\beta {|}^2=1$, and a general state is a two-dimensional density matrix. Its Bloch vector gives the normalized Stokes parameters. Polarization-dependent path separation can correlate this internal degree of freedom with a path qubit.

// Target: quantum-error-correction.bigb

The quantum state associated with the two transverse polarization degrees of freedom of a photon in a specified propagation mode. In a horizontal-vertical basis, a pure state is $\alpha |H⟩+\beta |V⟩$ with $|\alpha {|}^2+|\beta {|}^2=1$; a density matrix also describes mixtures. Linear polarizers test real combinations of these basis states, while phase-sensitive elements allow elliptical and circular polarization measurements.