Several schemes have been proposed to extend Quantum Key Distribution
protocols aiming at improving their security or at providing new physical
substrates for qubit implementation. We present a toolbox to jointly create,
manipulate and measure qubits stored in polarization and transverse-modes
degrees of freedom of single photons. The toolbox includes local operations on
single qubits, controlled operations between the two qubits and projective
measurements over a wide variety of non-local bases in the four dimensional
space of states. We describe how to implement the toolbox to perform an
extended version of the BB84 protocol for this Hilbert space (ideally
transmitting two key bits per photon). We present the experimental
implementation of the measurement scheme both in the regimes of intense light
beams and with single photons. Thus, we show the feasibility of implementing
the protocol providing an interesting example of a new method for quantum
information processing using the polarization and transverse modes of light as
qubits.Comment: 9 pages, 7 figures, 5 table
