The error probability of quantum nondemolition detection of a vacuum/one-photon qubit is shown to increase from 0 to 1/2 as the post-interaction fidelity increases from 2/3 to 1.
Kerr effect cross-phase-modulation between signal and probe beams has been proposed and demonstrated as a means for quantum nondemolition (QND) measurement of the signal beam's photon number by homodyne detection of the probe beam. Recently, such QND measurements have been suggested as providing a new route to photonic quantum computation. For a signal-beam qubit, whose computational basis is the vacuum and one-photon states, the QND detector's error probability is shown to be determined by the qubit fidelity after the cross-phase-modulation interaction, with the former increasing from 0 to 21 as the latter increases from 32 to 1. This relationship is shown to hold regardless of the probe beam's input state. It also applies, without modification, when the cross-phase-modulation interaction is replaced with a more general unitary transformation.
The multimode quantum fluctuations of colliding solitons are investigated. Strong mutual quantum correlations appear in their intensity spectrum as the solitons approach each other in the collision. The leaving solitons erase the interpulse correlations. These transient correlations are induced by cross phase modulation, whereas the intrapulse correlations are due to self phase modulation. As a possible application a direct detection quantum-nondemolition (QND) measurement of the photon number is proposed. It shows a performance better than a collision induced phase-shift QND measurement.