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arXiv:1108.1006 · Journal of Physics B Atomic Molecular and Optical Physics

Preparation of Knill–Laflamme–Milburn states using a tunable controlled phase gate

Karel Lemr

Published Aug 30, 2011• 15 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1088/0953-4075/44/19/195501

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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.
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.
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.
Controlled-phase (CP) gates with an arbitrary phase, which play an irreplaceable role in quantum computation and quantum information processing, are constructed between two neutral-atom qubits by using the Rydberg antiblockade regime. The phases needed for the CP gates are induced by the collective excitation of the pair of atoms. Numerical simulations show that high-fidelity CP gates can be obtained. In addition, the optimization of the scheme is given to enhance the robustness against the control error. As applications, we study in detail the preparation of n-qubit Knill–Laflamme–Milburn (KLM) states and a cluster state based on the Rydberg CP gates. The high-fidelity KLM states and cluster state can be obtained with the current physical parameters.
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.
Quantum information science addresses how uniquely quantum mechanical phenomena such as superposition and entanglement can enhance communication, information processing, and precision measurement. Photons are appealing for their low-noise, light-speed transmission and ease of manipulation using conventional optical components. However, the lack of highly efficient optical Kerr nonlinearities at the single photon level was a major obstacle. In a breakthrough, Knill, Laflamme, and Milburn (KLM) showed that such an efficient nonlinearity can be achieved using only linear optical elements, auxiliary photons, and measurement [Knill E, Laflamme R, Milburn GJ (2001) Nature 409:46-52]. KLM proposed a heralded controlled-NOT (CNOT) gate for scalable quantum computation using a photonic quantum circuit to combine two such nonlinear elements. Here we experimentally demonstrate a KLM CNOT gate. We developed a stable architecture to realize the required four-photon network of nested multiple interferometers based on a displaced-Sagnac interferometer and several partially polarizing beamsplitters. This result confirms the first step in the original KLM "recipe" for all-optical quantum computation, and should be useful for on-demand entanglement generation and purification. Optical quantum circuits combining giant optical nonlinearities may find wide applications in quantum information processing, communication, and sensing.
The Knill-Laflamme-Milburn (KLM) states have been proved to be a useful resource for quantum information processing [Nature409, 46 (2001)]. For atomic KLM states, several schemes have been put forward based on the time-dependent unitary dynamics, but the dissipative generation of these states has not been reported. This work discusses the possibility for creating different forms of bipartite KLM states in neutral atom system, where the spontaneous emission of excited Rydberg states, combined with the Rydberg antiblockade mechanism, is actively exploited to engineer a steady KLM state from an arbitrary initial state. The numerical simulation of the master equation signifies that a fidelity above 99% is available with the current experimental parameters.