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Zhongguo kexue. Wulixue Lixue Tianwenxue

任意多光子Dicke态的制备

Qing Lin

Published Apr 1, 2014• 1 citation
Publisher

Abstract

Quantum Dicke state belongs to the class of maximally entangled state. Due to its complicated entangled structure and robustness against decoherence, it is the important resource for the investigation of entanglement properties and the creation of quantum network. How to generate Dicke state and apply Dicke state in quantum communication protocol becomes a hot topic in the area of quantum information science. In this paper, we focus on the problem how to create arbitrary multi-photon Dicke state efficiently. The experimental generations and applications of four-photon and six-photon Dicke state had been reported in recent years. However, the generation is not scalable, that is it is difficult to generate Dicke state with more photons only using spontaneous parametric down-conversion and linear optical technology. If assisted with the weak cross-Kerr nonlinearity, it is possible to generate multi-photon Dicke state with some probability. However, it is still impossible to generate Dicke state with arbitrary coefficients, and the success probability decreases exponentially with the increasing of photon number. Here, we use three element gates called c-path gate, merging gate, entangler, which are introduced in former works, to design the generation of Dicke state. Firstly, the deterministic scheme of four-photon Dicke state generation is provided. After that, we modify the former W state generation scheme to be available for arbitrary coefficients W state generation. For the generation of arbitrary Dicke state, we decompose it to be a series of W state generations, with the help of c-path gates and merging gates. This scheme is deterministic and available for arbitrary coefficients. Especially, for some classes of Dicke states generation, the required resources are only polynomial growth with the increasing of photon number. All these features will make the investigation of multi-photon Dickes to be more convenient than the former schemes. In addition, our scheme is theoretically feasible with the current experimental technology.

DOI
10.1360/sspma2013-00052

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Quantum Dicke state belongs to the class of maximally entangled state. Due to its complicated entangled structure and robustness against decoherence, it is the important resource for the investigation of entanglement properties and the creation of quantum network. How to generate Dicke state and apply Dicke state in quantum communication protocol becomes a hot topic in the area of quantum information science. In this paper, we focus on the problem how to create arbitrary multi-photon Dicke state efficiently. The experimental generations and applications of four-photon and six-photon Dicke state had been reported in recent years. However, the generation is not scalable, that is it is difficult to generate Dicke state with more photons only using spontaneous parametric down-conversion and linear optical technology. If assisted with the weak cross-Kerr nonlinearity, it is possible to generate multi-photon Dicke state with some probability. However, it is still impossible to generate Dicke state with arbitrary coefficients, and the success probability decreases exponentially with the increasing of photon number. Here, we use three element gates called c-path gate, merging gate, entangler, which are introduced in former works, to design the generation of Dicke state. Firstly, the deterministic scheme of four-photon Dicke state generation is provided. After that, we modify the former W state generation scheme to be available for arbitrary coefficients W state generation. For the generation of arbitrary Dicke state, we decompose it to be a series of W state generations, with the help of c-path gates and merging gates. This scheme is deterministic and available for arbitrary coefficients. Especially, for some classes of Dicke states generation, the required resources are only polynomial growth with the increasing of photon number. All these features will make the investigation of multi-photon Dickes to be more convenient than the former schemes. In addition, our scheme is theoretically feasible with the current experimental technology.
How to create entanglement is an important problem in quantum information processing. In this paper, we propose an experimental scheme to generate multi-photon W state using c-path gate and merging gate introduced in the former works. Compared with the other linear optical schemes, our scheme is deterministic without post-selection, and then there is no probabilistic problem and no limitation on the use of W state. Moreover, the required resources for generation grow linearly with the number of involved photons, which is obviously better than the polynomial growth with the traditional circuit-based quantum computation. This scheme is deterministic, suitability, and efficient, so it is feasible and suitable for large-scale quantum information processing.
Entanglement is a fundamental feature of quantum mechanics and a key resource for quantum information processing. Among multipartite entangled states, Dicke states ∣Dnk⟩|D_n^k\rangle∣Dnk​⟩ are distinguished by their permutation symmetry, which provides robustness against particle loss and enables applications for quantum communication and computation. Although Dicke states have been realized in various platforms, most optical implementations rely on postselection, which destroys the state upon detection and prevents its further use. A heralded optical scheme is therefore highly desirable. Here, we present a linear-optical heralded scheme for generating arbitrary Dicke states ∣Dnk⟩|D_n^k\rangle∣Dnk​⟩ with 3n+k3n+k3n+k photons through the framework of the linear quantum graph (LQG) picture. By mapping the scheme design into the graph-finding problem, and exploiting the permutation symmetry of Dicke states, we overcome the structural complexity that has hindered previous approaches. Our results provide a resource-efficient pathway toward practical heralded preparation of Dicke states for quantum technologies.
Major efforts in quantum information science are devoted to the development of methods that are superior to the one of classical information processing, for example the quantum computer or quantum simulations. For these purposes, superposition and entangled states are considered a decisive resource. Furthermore, since the early days of quantum mechanics, entanglement has revealed the discrepancy between the quantum mechanical and the everyday life perception of the physical world. This combination of fundamental science and application-oriented research makes the realization, characterization, and application of entanglement a challenge pursued by many researchers. In this work, the observation of entangled states of polarization encoded photonic qubits is pushed forward in two directions: flexibility in state observation and increase in photon rate. To achieve flexibility two different schemes are developed: setup-based and entanglement-based observation of inequivalent multi-photon states. The setup-based scheme relies on multi-photon interference at a polarizing beam splitter with prior polarization manipulations. It allows the observation of a family of important four-photon entangled states. The entanglement-based scheme exploits the rich properties of Dicke states under particle projections or loss in order to obtain inequivalent multi-photon entangled states. The observed states are characterized using the fidelity and entanglement witnesses. An increase in photon rate is crucial to achieve entanglement of higher photon numbers. This holds especially, when photon sources are utilized that emit photons spontaneously. To this end, a new photon source is presented based on a femtosecond ultraviolet enhancement cavity and applied to the observation of the six-photon Dicke state with three excitations. The implemented schemes not only allow the observation of inequivalent types of entanglement, but also the realization of various quantum information tasks. In this work, the four-photon GHZ state has been used in a quantum simulation of a minimal instance of the toric code. This code enables the demonstration of basic properties of anyons, which are quasiparticles distinct from bosons and fermions. Further, the six-photon Dicke state has been applied for quantum metrology: It allows one to estimate a phase shift with a higher precision than by using only classical resources. Altogether, a whole series of experiments for observing inequivalent multi-photon entangled states can now be substituted by a single experimental setup based on the designs developed in this work. In addition to this new approach of photon processing, a novel photon source has been implemented, paving the way to realizations of applications requiring higher photon numbers.
Entanglement lies at the heart of quantum mechanics and challenged the intuition of physicists ever since it was discovered. At the same time, it is a powerful tool that serves as a key resource for quantum communication and quantum computation schemes. Many of these applications rely on multiparticle entanglement, whose description, generation and manipulation became therefore a very active field in theoretical and experimental quantum information science. The goals are here to classify and understand the different types of entanglement, to find new applications and to control and analyze the quantum states experimentally. In this thesis, the experimental observation and analysis of two different types of four-photon polarization entangled states is presented: The cluster state and the symmetric Dicke state with two excitations. For this purpose, experimental setups based on spontaneous parametric down conversion and linear optics with conditional detection were designed. They allowed to observe the cluster state with a fidelity of 74.1 % and the symmetric Dicke state with a fidelity of 84.4 %. The cluster state experiment included the development of a new instrument that is of interest for linear optics quantum logic in general: A probabilistic controlled phase gate that is, due to the simplification of a previous approach, highly stable and can actually be used in multiphoton experiments. The quality of the gate is evaluated by analyzing its entangling capability and by performing full process tomography. The achieved results demonstrate that this device is well suited for implementation in various multiphoton quantum information protocols. In order to study the observed quantum states, efficient analysis tools are introduced. It was possible to verify that essential properties of the ideal states are indeed reproduced in the experiment, among others, the presence of genuine four-partite entanglement. A particular focus is put on the behavior of the states under projective measurements and photon loss. Several new insights in their entanglement structure are revealed and verified experimentally. We further demonstrate properties that are characteristic for the entanglement classes of the states. These can be used to infer the applicability of the observed states for certain distributed quantum communication applications. The presented experiments are generic for the design of setups to observe cluster- and symmetric Dicke states with a higher number of photons. Furthermore, also the efficient non-tomographic methods for state analysis we employ can directly be generalized to experiments with higher qubit numbers, where the reduction of the experimental effort for state analysis is even more crucial.
The generation of a high-dimensional quantum entangled state provides a crucial resource for achieving more complex and diverse quantum information processing tasks. In this paper, we present two deterministic protocols designed for the generation of a four-dimensional two-qudit Bell state and three-qudit Greenberger-Horne-Zeilinger (GHZ) state assisted by cross-Kerr nonlinearity, where the four-dimensional qudit is encoded in the hybrid polarization-spatial state of the single photon to conserve quantum resources and alleviate environmental noise. The proposed protocols for generating a four-dimensional two-qudit Bell state and three-qudit GHZ state are circuit concise, high success, robust fidelity, noise resistant, and resource saving. Moreover, the four-dimensional NNN-qudit (N>3N>3N>3) GHZ states can be generated with the help of the $N\ensuremath{-}1$ generating devices of the four-dimensional Bell state. Consequently, its efficiency and fidelity decay exponentially by a factor of $N\ensuremath{-}1$. Further, the arbitrary high-dimensional qudit-encoded entangled states can be achieved with linear-optics four-dimensional single-qudit XXX gates and ZZZ gates. These protocols offer a reference for further advancements in high-dimensional state generation technology and providing insights for the practical implementations of metrological enhancement, quantum simulation, high-dimensional quantum computation, and quantum error correction.
We propose two interesting methods of generating the four-photon W state. These methods use parametric down-conversion processes, linear optical elements, and commercial photon detectors, which are readily feasible under current technology. They can also be used to generate the three-photon W state, the three-photon Greenberger–Horne–Zeilinger state, and the three-photon maximally entangled photon-number state (a typical photon-number entanglement state) by simply changing some experimental components or their parameters. Moreover, assuming we have photon number-resolving detectors, these methods can develop into methods that generate a general n -photon W state. They are expected to become powerful tools for experimental investigations of multipartite entanglement and its applications to quantum information processing.