  A single photon has many physical degrees of freedom (DOF) that can carry the
state of a high-dimensional quantum system. Nevertheless, only a single DOF is
usually used in any specific demonstration. Furthermore, when more DOF are
being used, they are analyzed and measured one at a time. We introduce a
two-qubit information system, realized by two degrees of freedom of a single
photon: polarization and time. The photon arrival time is divided into two
time-bins representing a qubit, while its polarization state represents a
second qubit. The time difference between the two time-bins is created without
an interferometer at the picosecond scale, which is much smaller than the
detector's response time. The two physically different DOF are analyzed
simultaneously by photon bunching between the analyzed photon and an ancilla
photon. Full two-qubit states encoded in single photons were reconstructed
using quantum state tomography, both when the two DOF were entangled and when
they were not, with fidelities higher than 96%.
