Previous analyses of conditional ${\phi }_{nl}$-phase gates for photonic qubits that treat cross-phase modulation (XPM) in a causal, multimode, quantum field setting suggest that a large ($\sim$$\pi$ rad) nonlinear phase shift is always accompanied by fidelity-degrading noise [J. H. Shapiro, Phys. Rev. A 73, 062305 (2006); J. Gea-Banacloche, Phys. Rev. A 81, 043823 (2010)]. Using an atomic $\vee$ system to model an XPM medium, we present a conditional phase gate that, for sufficiently small nonzero ${\phi }_{nl}$, has high fidelity. The gate is made cascadable by using a special measurement, i.e., principal-mode projection, to exploit the quantum Zeno effect and preclude the accumulation of fidelity-degrading departures from the principal-mode Hilbert space when both control and target photons illuminate the gate. The nonlinearity of the $\vee$ system we study is too weak for this particular implementation to be practical. Nevertheless, the idea of cascading through principal-mode projection is of potential use to overcome fidelity-degrading noise for a wide variety of nonlinear optical primitive gates.

• Received 4 March 2012

DOI:https://doi.org/10.1103/PhysRevA.87.042325