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Journal of the Optical Society of America B

Entanglement generation with coherent states using cross-Kerr nonlinearity

Si Yu Song, Shuhao Wang, Guo Fu Xu, Gui Lu Long

Published Aug 15, 2013• 11 citations
Publisher

Abstract

We propose methods for generating Bell-type entangled coherent states for quantum information processing. The protocols are completed using linear optical elements, single-photon detectors, and cross-Kerr nonlinearity. We investigate the decoherence effect on our protocols; photon loss is found to affect only the probability, not the fidelity, of the generation process. The entanglement of the generated entangled states is also analyzed using concurrence. Finally, the feasibility of our scheme is discussed using the continuous-time cross-phase modulation model. In the weak nonlinearity region, on the condition that θ2|αp|2∼1, θ≪1, and σ2≪1, our scheme is applicable theoretically.

DOI
10.1364/josab.30.002393

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High-dimensional entangled states have attracted attention because of their strong nonlocality and powerful capability for quantum information processing. By the methods presented in this paper, arbitrary forms-entangled qudits including symmetric and asymmetric forms could be generated with weak cross-Kerr nonlinearity. These schemes are heralded by the use of single-photon detectors. If all the detectors do not register any single photons, the generation is a success with the probability 1/nM determined by dimension n and partite M. Furthermore, these schemes work well even with the common photon number nonresolving detectors; therefore they are feasible with the current experimental technology.
Weak cross-Kerr nonlinearities between single photons and coherent states are the basis for many applications in quantum-information processing. These nonlinearities have so far mainly been discussed in terms of highly idealized single-mode models. We develop a general theory of the interaction between continuous-mode photonic pulses and apply it to the case of a single photon interacting with a coherent state. We quantitatively study the validity of the usual single-mode approximation using the concepts of fidelity and conditional phase. We show that high fidelities, nonzero conditional phases, and high photon numbers are compatible, under conditions where the pulses fully pass through each other and where unwanted transverse-mode effects are suppressed.
With the assistance of weak cross-Kerr nonlinearities, we present a preparation scheme of four-photon polarization-entangled decoherence-free states, which can be used to construct the minimal optical decoherence-free subspaces where a logical qubit is fully protected against collective decoherence. To complete the preparation task, one spatial entanglement process, two polarization entanglement processes, and one detecting process are applied. The fulfillments of the above processes are contributed by a cross-Kerr nonlinear interaction between the signal photons and a coherent state via Kerr media. Exploiting the available single-photon resource and simple linear optics elements, this scheme is feasible and desirable to be extended to the construction of multiphoton decoherence-free states against the collective decoherence.
We propose a protocol for creating arbitrary qudit state (including entangled states) with arbitrary dimensionality in continuous variable system using weak cross-Kerr nonlinearity, linear beamsplitters, detectors not resolving photon numbers, and sources of coherent states. The equation for unique determination of the used coherent states amplitudes is found. The protocol is applicable for creating entangled states at distances of 100 km using cross-Kerr nonlinearity χ ≥ χ min ≃ 0.01 and optical fiber quantum channel.
We propose an effective protocol for preparation of four-photon polarization-entangled decoherence-free states with quantum nondemolition detectors. The protocol is based on optical elements, single polarization photons, and cross-Kerr nonlinearity, which are feasible with existing experimental technology. Compared with previous protocols, the present one is to replace the entangled-state resources with much simpler single-photon resources and has a higher success probability. All these advantages make this protocol more efficient and more convenient than others in the applications in quantum communication.