Quantum state tomography of undetected photons

The measurement of quantum states is one of the most important problems in quantum mechanics. We introduce a quantum state tomography technique in which the state of a qubit is reconstructed, while the qubit remains undetected. The key ingredients are (i) employing an additional qubit, (ii) aligning the undetected qubit with a known reference state by using path identity, and (iii) measuring the additional qubit to reconstruct the undetected qubit state. We establish theoretically and demonstrate experimentally the method with photonic polarization states. The principle underlying our method could also be applied to quantum entities other than photons.