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Laser Physics Letters

Generation of an arbitrary logic W state with cross-Kerr nonlinearities

Hao Zheng, Lan Zhou, Wei Zhong, Yu‐Bo Sheng

Published Oct 9, 2020• 3 citations
Publisher

Abstract

Abstract Environmental noise is a big obstacle in quantum communication and computation. Quantum error code (QEC) technology can resist the photon transmission loss and decoherence error caused by the environmental noise and has great application potential in future quantum communication and computation fields. The generation of logic qubits or logic entanglement is the important first step of the QEC. The logic W state, which replaces each physical qubit in a physical W state with a logic qubit, may be highly robust against photon loss and errors, so that it may have big application potential. In this paper, we propose an efficient scheme to generate an arbitrary logic W state with the help of cross-Kerr nonlinearities. Our protocol only requires a physical W state and some auxiliary single photons, and can deterministically generate a general logic W state based on the homodyne measurement results. Our logic W state generation protocol may be useful in future quantum information processing based on the logic W state.

DOI
10.1088/1612-202x/abb601

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Abstract Environmental noise is a big obstacle in quantum communication and computation. Quantum error code (QEC) technology can resist the photon transmission loss and decoherence error caused by the environmental noise and has great application potential in future quantum communication and computation fields. The generation of logic qubits or logic entanglement is the important first step of the QEC. The logic W state, which replaces each physical qubit in a physical W state with a logic qubit, may be highly robust against photon loss and errors, so that it may have big application potential. In this paper, we propose an efficient scheme to generate an arbitrary logic W state with the help of cross-Kerr nonlinearities. Our protocol only requires a physical W state and some auxiliary single photons, and can deterministically generate a general logic W state based on the homodyne measurement results. Our logic W state generation protocol may be useful in future quantum information processing based on the logic W state.
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.
Logic-qubit entanglement has attracted much attention in both quantum communication and quantum computation. Here, we present an efficient protocol to distill the logic-qubit entanglement with the help of cross-Kerr nonlinearity. This protocol not only can purify the logic bit-flip error and logic phase-flip error, but also can correct the physical bit-flip error completely. We use cross-Kerr nonlinearity to construct quantum nondemolition detectors. Our distillation protocol for logic-qubit entanglement may be useful for the practical applications in quantum information, especially in long-distance quantum communication.
Abstract We propose a theoretical protocol for preparing four-photon polarization entangled decoherence-free states, which are immune to the collective noise. With the assistance of the cross-Kerr nonlinearities, a two-photon spatial entanglement gate, two controlled-NOT gates, a four-photon polarization entanglement gate are inserted into the circuit, where X homodyne measurements are aptly applied. Combined with some swap gates and simple linear optical elements, four-photon polarization entangled decoherence-free states which can be utilized to represent two logical qubits, |0〉L and |1〉L are achieved at the output ports of the circuit. This generation scheme may be implemented with current experimental techniques.
The decoherence effect caused by the coupling between the system and the environment undoubtedly leads to the errors in efficient implementations of two (or three) qubit logical gates in quantum information processing. Fortunately, decoherence-free subspace (DFS) introduced can effectively decrease the influence of decoherence effect. In this paper, we propose some schemes for setting up a family of quantum control gates, including controlled-NOT (CNOT), Toffoli, and Fredkin gates for two or three logical qubits by means of cross-Kerr nonlinearities in DFS. These three logical gates require neither complicated quantum computational circuits nor auxiliary photons (or entangled states). The success probabilities of three logical gates are approximate 1 by performing the corresponding classical feed-forward operations based on the different measuring results of the X-homodyne detectors, and their fidelities are robust against the photon loss with the current technology. The proposed logical gates rely on only simple linear-optics elements, available single-qubit operations, and mature measurement methods, making our proposed gates be feasible and efficient in practical applications.
Abstract The concatenated Greenberger–Horne–Zeilinger (C-GHZ) state is a new kind of logic-qubit entangled state, which may have extensive applications in future quantum communication. In this letter, we propose a protocol for constructing an arbitrary C-GHZ state with single photons. We exploit the cross-Kerr nonlinearity for this purpose. This protocol has some advantages over previous protocols. First, it only requires two kinds of cross-Kerr nonlinearities to generate single phase shifts ± θ . Second, it is not necessary to use sophisticated m -photon Toffoli gates. Third, this protocol is deterministic and can be used to generate an arbitrary C-GHZ state. This protocol may be useful in future quantum information processing based on the C-GHZ state.
Relying on weak cross-Kerr nonlinearities, we propose a nearly deterministic generation scheme of the three-photon polarization-entangled perfect WWW state which can be applied to the perfect teleportation of an unknown single-photon state and has robust entanglement against the loss of one photon of them. Three photons entangle together by virtue of the bus function of the coherent state serving as the intermediate among them. In the scheme, three processes are executed successively and two kinds of modules are inserted into the circuit, where the homodyne measurement and the photon number measurement are aptly performed. By means of classical feedforward techniques, single-photon unitary transformation operations are performed on the corresponding photons based on the obtained measurement outcomes, by which the generation efficiency of the perfect WWW state aims to nearly unity. Moreover, some currently available optical elements are applied in the generation process, which offer facilities for the practical implementation.