Nondestructive detector for exchange symmetry of photonic qubits

Abstract

We experimentally realize a quantum Fredkin gate and use it for constructing a nondestructive detector of exchange symmetry for qubits. The detector, which discriminates between symmetric and anti-symmetric quantum states of two qubits, allows us to directly measure a purity and overlap of quantum states and implement a quantum state programmable measurement. Furthermore, the nondestructive nature of the detector can be used for analysis of the back-action of the measurements, as well as for realization of nonlinear quantum operations, such as quantum purification and quantum cloning. As a whole, the experiment demonstrates the utility of exchange symmetry measurements and their potential for multi-step characterization and processing of quantum states.