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Journal of the Optical Society of America B

Multiphoton Knill-Laflamme-Milburn states generated by nonlinear optics

Cai‐Peng Shen, Xiaofei Gu, Qi Guo, Xiaoyu Zhu, Shi‐Lei Su, Erjun Liang

Published Mar 5, 2018• 19 citations

Abstract

The Knill-Laflamme-Milburn (KLM) entangled state, proposed by Knill et al. in Nature409, 46 (2001)NATUAS0028-083610.1038/35051009, has unique advantages for linear optics quantum information processing tasks, because it is able to decrease the error rate. In this paper, we propose scalable schemes to generate the multi-qubit KLM entangled states with single-photon resources and weak cross-Kerr nonlinearity theoretically. We first construct the two-qubit KLM state, through which the three- and other n-qubit KLM states are generated. For the schemes using weak cross-Kerr nonlinearity, P homodyne measurement has a higher success rate than X homodyne measurement but with narrow applications since |αeiθ⟩ and |αe−iθ⟩ are distinguished from each other, which is undesirable for most of the entanglement generation schemes. To avoid this disadvantage, Jin et al. [Phys. Rev. A75, 054302 (2007)PLRAAN1050-294710.1103/PhysRevA.75.054302] introduced the coherent state superposition (CSS), c(|α⟩+|−α⟩), to generate a Greenberger-Horne-Zeilinger state but with a rapid oscillation term, which needs to be ignored. Through designing the optical path uniquely and choosing the phase of cross-Kerr nonlinearity suitably, our P homodyne measurement and CSS probe mode-based schemes to generate the KLM state avoid the needless term. The present scalable schemes have high total success probabilities, high fidelities even in consideration of decoherence, and may find potential applications in the future with the further development of nonlinear optics.

DOI: 10.1364/josab.35.000694

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A specific class of partially entangled states known as Knill-Laflamme-Milburn states (or KLM states) has been proved to be useful in relation to quantum information processing [Knill et al., Nature 409, 46 (2001)]. Although the usage of such states is widely investigated, considerably less effort has been invested into experimentally accessible preparation schemes. This paper discusses the possibility to employ a tunable controlled phase gate to generate an arbitrary Knill-Laflamme-Milburn state. In the first part, the idea of using the controlled phase gate is explained on the case of two-qubit KLM states. Optimization of the proposed scheme is then discussed for the framework of linear optics. Subsequent generalization of the scheme to arbitrary n-qubit KLM state is derived in the second part of this paper.

Abstract The protocol for the compact generation of the two-photon four-dimensional spatial-mode partially entangled Knill–Laflamme–Milburn (KLM) state is proposed. The two-photon entanglement shared among four spatially distinct optical modes can be generated from three concurrent spontaneous parametric down-conversion processes by using the multiple quasi-phase-matching technique. The scheme for the concentration of the two-photon four-dimensional spatial-mode partially entangled KLM state is also proposed. By using quantum non-destructive detection and local operation, the two-photon maximally entangled KLM state can be obtained and used as an entangled quantum channel in quantum communication.

We report an experimental preparation of the so-called Knill-Laflamme-Milburn states (KLM states) that have been known to have interesting properties related to quantum information processing. Our experiment has demonstrated successful preparation of entangled two-photon four-mode KLM states using spontaneous parametric down-conversion as a source of entangled photon pairs, linear optical components, and avalanche photodiodes for single-photon detection. We have verified the successful generation of KLM states by complete quantum state tomography.

Abstract In the process of quantum information processing, decoherence effect caused by the coupling between system and its environment will no doubt lead to the error of quantum information stored in the system. To decrease the influence of decoherence effect, decoherence‐free subspace (DFS) is introduced. In this work, several schemes to convert the polarized‐entangled Knill–Laflamme–Milburn (KLM) states into Greenberger–Horne–Zeilinger (GHZ) states in DFS by using the weak cross‐Kerr nonlinearity are proposed. Numerical analysis shows that the proposed schemes have high fidelity and success probability. Due to the unique applications of multi‐qubit quantum entangled states in quantum information processing and the robust feature of DFS, the proposed schemes may play positive roles in the future development of quantum communication and quantum information processing tasks.