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.
We derive sampling functions for estimation of quantum state fidelity with Schrodinger cat-like states, which are defined as superpositions of two coherent states with opposite amplitudes. We also provide sampling functions for fidelity with squeezed
Fock states that can approximate the cat-like states and can be generated from Gaussian squeezed states by conditional photon subtraction. The fidelities can be determined by averaging the sampling functions over quadrature statistics measured by homodyne detection. The sampling functions are designed such that they can compensate for losses and inefficient homodyning provided that the overall efficiency exceeds certain threshold. The fidelity with an odd coherent state and the fidelity with a squeezed odd Fock state provide convenient witnesses of negativity of Wigner function of the measured state. The negativity of Wigner function at the origin of phase space is certified if any of these fidelities exceeds 0.5. Finally, we discuss the possibility of reducing the statistical uncertainty of the fidelity estimates by a suitable choice of the dependence of the number of quadrature samples on the relative phase shift between local oscillator and signal beam.
We present a linear-optical implementation of a class of two-qubit partial SWAP gates for polarization states of photons. Different gate operations, including the SWAP and entangling square root of SWAP, can be obtained by changing a classical contro
l parameter -- namely the path difference in the interferometer. Reconstruction of output states, full process tomography and evaluation of entanglement of formation prove very good performance of the gates.
