  The field of quantum information has been growing fast over the past decade.
Optical quantum computation, based on the concepts of KLM and cluster states,
has witnessed experimental realizations of larger and more complex systems in
terms of photon number. Quantum optical systems, which offer long coherence
times and easy manipulation of single qubits, allow us to probe quantum
properties of the light itself and of the physical systems around it. Recently,
a linear scheme for quantum computing, relying on the bosonic nature of
particles, has been proposed and realized experimentally with photons. The
ability to efficiently measure superpositions of quantum states consisting of
several photons is essential to the characterization of such systems. In fact,
the entire field of quantum information completely relies on the ability to
recover quantum states from measurements. However, the characterization of
quantum states requires many measurements, and often necessitates complicated
measurements schemes; for example, characterizing qubits requires measurements.
Here, we utilize structure, inherent to physically interesting quantum states
of light, in order to reduce the complexity in the recovery of a quantum state.
In particular, we devise a method enabling the recovery of three-photon quantum
states from only two-fold correlation measurements in a single setting. The
ability to take two-fold coincidences instead of three-fold offers the recovery
of the quantum states in far less measurements and in a considerably higher
SNR, because detection of two-photon events is much more likely than that of
three-photon ones. The concept suggested here paves the way to further ideas on
structure-based super resolution in quantum state tomography, such as
recovering a quantum state in an unknown basis in a single setup and recovering
the state of several photons without number resolving detectors.
