Loss tolerant quantum state tomography by number-resolving measurements without approximate displacements

We introduce a quantum state tomography technique to reconstruct the density matrix of an arbitrary quantum state by experimentally determining the Wigner function overlap, or the fidelity, between the unknown state and a set of tomographically complete coherent states. Each fidelity is determined by a parity measurement from number-resolving statistics on only a single mode of the output field after an interference between each probing coherent state and the unknown state. We demonstrate that the state can be accurately reconstructed following an arbitrary well-calibrated loss, and that this reconstruction is robust to noise. Unlike conventional continuous variable state tomography methods, our method utilizes computationally efficient semidefinite programming (SDP).