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Conditional quantum optical processes enable a wide range of technologiesfrom generation of highly non-classical states to implementation of quantumlogic operations. The process fidelity that can be achieved in a realisticimplementation depends on a number of system parameters. Here we experimentallyexamine Fock-state filtration, a canonical example of a broad class ofconditional quantum operations acting on a single optical field mode. Thisoperation is based upon interference of the mode to be manipulated with anauxiliary single-photon state at a beam splitter, resulting in the entanglementof the two output modes. A conditional projective measurement onto a singlephoton at one output mode heralds the success of the process. This operation,which implements a measurement-induced nonlinearity, is capable of suppressingparticular photon-number probability amplitudes of an arbitrary quantum state.We employ coherent-state process tomography to determine the precise operationrealized in our experiment. To identify the key sources of experimentalimperfection, we develop a model of the process and identify three maincontributions that significantly hamper its efficacy. The reconstructed tensoris compared with a model of the process taking into account sources ofexperimental imperfection with fidelity better than 0.95. This enables us toidentify three key challenges to overcome in realizing a filter with highfidelity - namely the single-photon nature of the auxiliary state, high-modeoverlap, and the need for number resolving detection when heralding. Theresults show that the filter does indeed exhibit a nonlinear response as afunction of input photon number and preserves the phase relation between Focklayers of the output state, providing promise for future applications.

Characterization of conditional state-engineering quantum processes by coherent state quantum process tomography