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Optics and Spectroscopy

Qudit-type entanglement of continuous variables via weak cross-Kerr non linearity

S. Ya. Kilin, Alexander B. Mikhalychev

Published Oct 1, 2011• 1 citation
Publisher

Abstract

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.

DOI
10.1134/s0030400x11110154

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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 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.
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.
Entanglement represents an important resource for quantum information processing, but its generation itself requires physical resources that are limited. We propose a scheme for generating a wide class of entangled qudit-type states of optical field modes at sites separated by noisy medium when only weak optical nonlinearities are available at both sites. The protocol is also based on exploiting a weak probe field, transmitted between the sites and used for generation of quantum correlations between two spatially separated field modes. The idea of probabilistic entanglement enhancement by measurement is discussed and a corresponding scheme for measuring the probe field state with linear optics and photodetectors not resolving photon numbers is proposed. It is shown that the protocol is applicable in the case when limited efficiency and dark counts of photodetectors, decoherence, and uncertainty of nonlinear coupling constants are present.
We propose a scheme for generating entanglement of quantum states with continuous variables (coherent states and squeezed vacuum states) of electromagnetical fields. The scheme involves cross-Kerr nonlinearity. It was shown that the cross-Kerr nonlinearity required for generating the superposition and entanglement of squeezed vacuum states is smaller than that required for coherent states. It was also found that the fidelity monotonously decreases with both the increase of the amplitude of the input coherent field and the increase of the deviation of the nonlinear phase shift from π.