Measurement of the Overlap between Quantum States with the Use of Coherently Addressed Teleportation

We will show how to measure the overlap between photon polarization states with the use of linear optics and postselection only. Our scheme is based on quantum teleportation and succeeds with the probability of 8 1 . PACS number(s): 03.67.-a Many concepts of quantum information processing have been first implemented with the use of linear optics. Among them there are e.g. quantum teleportation [1], dense coding [2], quantum cryptography (e.g. [3, 4]). These schemes use polarization degrees of freedom of single photons for encoding qubits. Unfortunately, linear optics does not allow to perform arbitrary two-qubit operations in a deterministic way. However, it was shown theoretically [5, 6] as well as experimentally [7, 8] that it is possible to achieve this aim in a nondeterministic way. The main idea is to use quantum measurement as a source of nonlinearity. For example, one can construct CNOT gate which succeeds with the probability of 4 / 1 [9]. As well known