A quantum analog of the fundamental classical NOT gate is a quantum gate that would transform any input qubit state onto an orthogonal state. Intriguingly, this universal NOT gate is forbidden by the laws of quantum physics. This striking phenomenon
has far-reaching implications concerning quantum information processing and encoding information about directions and reference frames into quantum states. It also triggers the question under what conditions the preparation of quantum states orthogonal to input states becomes possible. Here we report on experimental demonstration of orthogonalization of partly unknown single- and two-qubit quantum states. A state orthogonal to an input state is conditionally prepared by quantum filtering, and the only required information about the input state is a mean value of a single arbitrary operator. We show that perfect orthogonalization of partly unknown two-qubit entangled states can be performed by applying the quantum filter to one of the qubits only.
We present a systematic comparison of different methods of fidelity estimation of a linear optical quantum controlled-Z gate implemented by two-photon interference on a partially polarizing beam splitter. We have utilized a linear fidelity estimator
based on the Monte Carlo sampling technique as well as a non-linear estimator based on maximum likelihood reconstruction of a full quantum process matrix. In addition, we have also evaluated lower bound on quantum gate fidelity determined by average quantum state fidelities for two mutually unbiased bases. In order to probe various regimes of operation of the gate we have introduced a tunable delay line between the two photons. This allowed us to move from high-fidelity operation to a regime where the photons become distinguishable and the success probability of the scheme significantly depends on input state. We discuss in detail possible systematic effects that could influence the gate fidelity estimation.
