Two-photon tomography using on-chip quantum walks

We present an approach to quantum tomography based on first expanding a quantum state across extra degrees of freedom and then exploiting the introduced sparsity to perform reconstruction. We formulate its application to photonic circuits and show that measured spatial photon correlations at the output of a specially tailored discrete-continuous quantum walk can enable full reconstruction of any two-photon spatially entangled and mixed state at the input. This approach does not require any tunable elements, so it is well suited for integration with on-chip superconducting photon detectors. (C) 2016 Optical Society of America