Deterministic and cascadable conditional phase gate for photonic qubits

Previous analyses of conditional φNL-phase gates for photonic qubits that treat crossphase modulation (XPM) in a causal, multimode, quantum field setting suggest that a large (∼π 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 V-system to model an XPM medium, we present a conditional phase gate that, for sufficiently small nonzero φNL, has high fidelity. The gate is made cascadable by using a special measurement, 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 V-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.