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Zhongguo kexue. Wulixue Lixue Tianwenxue

任意多体高维偏振纠缠态的有效制备

Qing Lin

Published Jul 1, 2012• 1 citation
Publisher

Abstract

Quantum entanglement plays a crucial role in the area of quantum information processing, which was widely used in various quantum information tasks. With the development of quantum information, more and more attentions are paid to high dimensional quantum state and entangled state, since higher dimension means stronger nonlocality, which enables securer and more powerful quantum information processing. Thereafter, how to create entangled qudits efficiently is worth discussed, which is the motivation of this paper. Based on the technique of cross phase modulation, we firstly introduce a single-photon qudit (n-dimension) encoded by spatial mode as ancilla, and then let it interact with n pairs of Bell states in the Kerr medias respectively. Finally, the arbitrary two-partite polarized entangled qudits could be generated after the multi-photon interference. This approach could be directly generalized to the generaion of arbitrary multi-partite polarized entangled qudits. The interactions between an ancilla single-photon qudit and n multi-photon GHZ states, associated with multi-photon interference, will yield the desired arbitrary multi-partite polarized entangled qudits. Except of the inevitable multi-photon interference, which is used to generate polarized qudit from single photons, all the generation processes are deterministic, therefore the generation efficiency is higher than the former proposals. In addition, using quantum nondemolition detection module to preserve two cases that all the single photons appear in the same spatial mode, the success probability of multi-photon interference, i.e., the generation of entangled qudits could be increased. Furthermore, the generated multi-partite polarized entangled qudits are flexible, whose coefficients could be adjusted flexibly by the single-photon unitary operations used in the generation of single-photon qudit. Thanks to this flexibility, it is convenient for the research of the property of entangled qudits and the many-body problem.

DOI
10.1360/132012-281

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In quantum information processing, quantum entanglement plays a very important role with special physical property, which makes the quantum information have many new characteristics that the classical information do not have, and provides a new physical resource in the transmission and processing of information. Compared with classical bit, quantum entanglement, especially the high dimensional quantum entanglement (i.e., entangled qudit), has a large information storage space and good security confidentiality, which means stronger nonlocality and much more powerful capability in quantum information processing. In this sense, here we focus on the topic of polarized entangled qudit generation, especially the asymmetric entangled qutrit generation, which hasnt been discussed before. The initial states could be an entangled photon pair and two single photons. Using two qubus beams as ancilla, and based on the cross phase modulation, the initial quantum states could be projected into different subspaces, which include the desired one. Finally, through the bi-photon Hong-Ou-Mandel interference, the asymmetric entangled qutrit could be generated. This scheme is heralded by the detection results of three ideal photon number non-resolving detectors (PNNDs). If neither of the three ideal PNNDs registers photons, the generation is successful; otherwise, any click appearing on one of the three ideal PNNDs means the failure of the generation. The corresponding success probability of maximally entangled qutrit generation is 3/64, which is relatively small. However, the success probability could be increased to 3/8 by using the special photon detectors, associated with the quantum non- demolition detectors (QNDs) replacing the ideal PNNDs. The more efficient scheme is still heralded, so the generated entangled qutrit could be used flexibly in the quantum information processing.
How to generate and manipulate high dimensional quantum state is a hot topic in the area of quantum information processing. In the optical system, based on the technique of linear optics and cross phase modulation, we consider the realization of universal unitary operation of single partite polarization encoded qudit. Firstly, we introduce the spatially encoded qudit as ancilla, and the entangler of polarization encoded qudit and spatially encoded qudit as core element. After that, the realization of a special unitary operation for single qutrit is discussed by one entangler and the Fourier transformation performed on the spatially encoded qutrit by a linear optical multi-port interferometer (LOMI). The corresponding success probability could be high, but this scheme is only available for a special type of unitary operations and cannot be developed to realize higher dimensional unitary operation. For general qudit universal unitary operation realization, we use qutrit unitary operation as example. The polarization encoded qutrit could be transformed to spatially encoded qutrit by one entangler and the measurement of polarization encoded qutrit, associated with the measurement results are used to control the transmission factors of mirrors placed on the spatial modes of spatially encoded qutrit. Then the desired universal unitary operation is performed on spatially encoded qutrit by a LOMI. Finally, one more entangler, a LOMI implementing Fourier transformation to spatially encoded qutrit, the measurement of spatially encoded qutrit and the phase shifts controlled by the measurement results through classical feed-forward will complete the realization of qutrit unitary operation. This approach could be developed for general case. By two entanglers, one LOMI for Fourier transformation of spatially encoded qudit and the measurement of polarization encoded qudit associated with its results are used to control the transmission factors of mirrors, the bi-directional mapping between polarization and spatially encoded qudits could be realized. Therefore, the universal unitary operation for general qudit could be realized by one more LOMI performed on the ancilla spatially encoded qutrit. In principle, our scheme is available for general single partite polarization encoded qudit and is feasible with the current experimental technology.
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.
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.
In this paper, we provide a simple but powerful module to generate entangled qudits. This module, assisted with cross-Kerr nonlinearity, is flexible for generation of entangled qudits with arbitrary dimensions. Since the generation is still probabilistic, we modify the simple module in order to increase efficiency and save resources. With the modified module, the input independent qudits could be transformed into different entangled forms, which include the possible maximal entangled form and the less entangled forms. The corresponding total success probability could reach 1.
Entanglement in high-dimensional systems plays a vital role in quantum information processing (QIP), as it extends the available Hilbert space, supports the manipulation of more intricate information, and broadens the scope of implementable quantum operations. In the paper, we present a deterministic scheme for the four-dimensional two-qudit Bell entangled state analysis for the four-photon system in the polarization degree of freedom, resorting to the weak cross-Kerr nonlinearity and some linear optical components. In our scheme, the analysis of four-dimensional Bell entangled state is constructed by three-photon Toffoli gate and quantum nondemolition detectors (QND 1 and QND 2 ). By phase shifts of the coherent beams, the 16 orthogonal four-dimensional two-qudit Bell states can be completely distinguished from each other. The proposal can be extended to the four-dimensional three-qudit entangled state analysis and n -qudit entangled state analysis. In addition, our deterministic scheme for high-dimensional entangled state analysis can be applied to high-dimensional quantum teleportation, including both uncontrolled and controlled quantum teleportation protocols. Moreover, our scheme can achieve high fidelity and efficiency, further broadening its applicability in high-dimensional QIP.