A two-state quantum system is called a qubit. A qubit can be realized by a photon which has two different polarization states and which correspond to polarization along the vertical and horizontal axes, respectively. The ability to precisely and reliably manipulate qubits is key to the advent of large-scale quantum computing
A linearly polarized photon aligned with angle can be split into its and components with amplitudes corresponding to the projection of the wave on the measurement axis. These states are orthogonal, so a pure photon has no component, and vice versa:
One way to manipulate a photon qubit is with polarization filters. Each filter measures and absorbs all photons in the state, while all others pass through. Consider a series of three linear polarization filters, each rotated by an angle of and respectively, with respect to the polarization direction.
What is the probability that a photon passes all three polarizing filters and emerges as a photon?