Quantum computation using weak nonlinearities: Robustness against decoherence

Abstract

We investigate decoherence effects in the recently suggested quantum computation scheme using weak nonlinearities, strong probe coherent fields, detection and feedforward methods. It is shown that in the weak-nonlinearity-based quantum gates, decoherence in nonlinear media can be made arbitrarily small simply by using arbitrarily strong probe fields, if photon number resolving detection is used. On the contrary, we find that homodyne detection with feedforward is not appropriate for this scheme because in this case decoherence rapidly increases as the probe field gets larger.

Efficient Concentration Protocols for the Single-Photon Entanglement State with Polarization Feature

“…In the practical applications, the cross-Kerr nonlinearity has been regarded as a controversial topic for a long time [92,93]. The reason is that during the homodyne detection process, the Frontiers in Physics | www.frontiersin.orgdecoherence is inevitable, which may cause the qubit states to degrade to the mixed states [94,95]. On the other hand, the natural cross-Kerr nonlinearity is weak so that it is difficult to determine the phase shift due to the impossible discrimination of two overlapping coherent states in homodyne detection [96].…”

“…On the other hand, the natural cross-Kerr nonlinearity is weak so that it is difficult to determine the phase shift due to the impossible discrimination of two overlapping coherent states in homodyne detection [96]. Fortunately, according to Jeong [94], the decoherence can be extremely reduced simply by an arbitrary strong coherent state associated with a displacement D(−α) performed on the coherent state. Moreover, several theoretical works have proved that with the help of weak measurement, it is possible for the phase shift to reach an observable value [82-85, 97, 98].…”

Concurrence Measurement for the Two-Qubit Optical and Atomic States

“…There are two main reasons. First, during the homodyne detection process, the qubit states may degrade to the mixed states [108][109][110][111][112]. Second, the natural cross-Kerr nonlinearity is extremely weak, which makes it difficult to discriminate two overlapping coherent states in homodyne detection.…”

“…On the other hand, in current technology, it is quite a controversial assumption to obtain a clean cross-Kerr nonlinearity [113,114]. Fortunately, according to [108], we can make the decoherence extremely weak, simply by an arbitrary strong coherent state associated with a displacement D (−α) performed on the coherent state. Meanwhile, with the help of weak measurement, it is possible to obtain an observable cross-Kerr phase shift with amplification [115].…”

Quantum Fourier transform of polarization photons mediated by weak cross-Kerr nonlinearity

“…3 and 4. Referring to [61], we set the intensity of the probe coherent state to be α 1.0 × 10 4 , which corresponds to weak decoherence effect by exploiting photon-number measurement.…”