基于原子—腔—光纤系统的纠缠态制备和远程量子逻辑门实现方案
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摘要
就腔量子电动力学而言,随着腔中耦合原子的增多,由于原子间的交叉相互作用,使得对原子自身和原子与腔相互作用的操纵变得越来越困难,所以单个腔中可以耦合的原子数目是有物理限制的。但是,一台实用的量子计算机必然包含很多量子比特,并且它的能力会随着所包含量子比特数目的增多而增强。因此人们提出了分布量子计算的方案。它通过量子传输线连接多个空间分离的包含少数量子比特的处理器组成网络来实现量子计算。制备分离子系统间共享的纠缠和构建远程量子逻辑门是实现分布量子计算的核心问题。另一方面,近来在实验上已经能够实现囚禁在光学腔中的单个原子控制、原子与腔及光纤与腔的强耦合。因此,原子-腔-光纤耦合系统逐渐引起了人们的重视,提出了许多基于此类系统完成量子信息处理的方案。本文以此类系统作为研究对象,提出一些制备远程两比特共享纠缠态、多比特W态和三比特Greenberger-Horne-Zeilinger(GHZ)态、实现远程两比特量子控制相位门和交换门、及远程三比特量子控制Z门的理论方案。本文的主要工作包括以下内容：
1.基于通过光纤连接的三个腔分别与三个原子耦合组成的系统,提出一种通过绝热演化制备远程两比特共享纠缠态的方案。并把它推广到制备多体W态的情况。此外,基于此系统可以通过信息分发实现量子信息共享。这些结果有助于对量子网络和量子密码学方面的研究。并且,这些方案是易于操作的,因为在完成方案的整个过程中只需调节驱动原子的经典场。
2.基于通过光纤连接的单原子-腔和双原子-腔耦合组成的系统。提出分别通过控制相互作用时间和绝热演化确定性地制备远程三原子共享GHZ态的方案。并且研究原子自发辐射和腔与光纤的光子泄漏等消相干过程带来的影响。结果表明,即使在考虑消相干的情况下,这些方案也能够以比较高的保真度实现。
3.基于通过光纤连接的两个腔分别与经典光驱动的两个二能级原子耦合组成的系统,提出实现远程两比特量子逻辑门的方案。研究发现,当腔场频率和原子跃迁频率间存在失谐时,在经典场的辅助下可以实现远程两比特量子控制相位门和交换门。此外,分析腔场和光纤的耗散等导致的消相干对此方案的影响；并通过引入八型原子有效地抑制原子自发辐射的影响。
4.基于通过光纤连接的三个腔分别与三个Λ型原子耦合组成的系统,提出实现远程三比特量子控制Z门的方案。并研究一些消相干过程如原子的自发辐射及光纤和腔的光子泄漏等带来的影响。结果表明,即使在考虑消相干的情况下此方案也能以较高的保真度实现。此结果可以推广到由光纤连接的N个腔分别与N个Λ型原子耦合的情况,进而实现远程N比特量子控制Z门。
As for the cavity quantum electrodynamics, with the increase in the number of the atomic qubits, the manipulations not only on qubit-cavity interaction but also on qubits themselves become difficult. Because some unexpected crossing interactions from qubits which are temporarily out of consideration, might arise and thus influence or spoil the useful interactions. Therefore, there are physical limitations on the number of atomic qubits in a quantum cavity. However, a practical quantum computer involves a large number of qubits, inevitably. And the power of the quantum computer increases as the mumber of qubits increases. Therefore, distributed quantum computing is introduced. It is thought of as a network of spatially separated local processors that contain only a few qubits and are connected via quantum transmission lines. Two of the key problems in the realization of distributed quantum computing are to implement the remote quantum logical gates and prepare the entanglement among the distant nodes. On the other hand, the control of single atom trapped in optical cavities and the perfect fiber-cavity coupling via microfabrication have been realized in experiment. The system, consisting of atoms separately trapped in distant cavities coupled by optical fibers, is very promising for the generation of entanglement shared by distant subsystems and implementing the remote quantum logical gates. And many schemes based on this system for the implementation of quantum information process have been proposed. In this paper, we consider this system and propose some schemes for the generation of entanglement and implementation of the quantum logical gates. Significant new results are shown as following.
1. A scheme, based on the system composed of three atoms separately trapped in three cavities coupled by optical fibres, for entangling two distant atoms via adiabatic passage is proposed. It is found that the multi-particle W entangled state can also be generated. Moreover, the quantum information sharing can be implemented using this system. These results may be helpful for the implementation of quantum network and useful in quantum cryptography. And this scheme is convenient to operate since only the laser fields applied to the atoms need to be adjusted to accomplish the processes.
2. A system composed of a single-atom-trapped cavity and a remote two-atom-trapped cavity connected by the optical fibre is considered. It is shown that a shared Greenberger-Horne-Zeilinger (GHZ) state of the three atoms can be deterministically generated by controlling the time of interaction or via the adiabatic passage based on this system. The influence of various decoherence processes such as spontaneous emission and photon loss on the fidelity is also investigated. It is found that these schemes can be realized with high fidelity even when these decoherence processes are considered.
3. A scheme, based on the two two-level atoms resonantly driven by the classical field separately trapped in two cavities coupled by an optical fibre, for the implementation of remote two-qubit gates is investigated. It is found that the quantum controlled-phase and swap gates can be achieved with the assistance of classical field when there are detunings of the coupling quantum fields. Moreover, the influence of the dissipation of the cavities and the optical fibre is analyzed while the spontaneous emission of the atoms can be effectively suppressed by introducing the∧-type atoms.
4. A scheme for implementing the three-qubit controlled-Z gate with three atoms separately trapped in three distant cavities coupled by the optical fibres is proposed. The influence of various decoherence processes, such as spontaneous emission of the atoms and photon leakage of the cavities and the optical fibres, on the fidelity is also investigated. It is found that the gate can be implemented with high fidelity even when these decoherence processes are considered. This scheme can be extended to the implementation of remote N-qubit controlled-Z gate with N atoms separately trapped in N distant cavities coupled by the optical fibres.
1.基于通过光纤连接的三个腔分别与三个原子耦合组成的系统,提出一种通过绝热演化制备远程两比特共享纠缠态的方案。并把它推广到制备多体W态的情况。此外,基于此系统可以通过信息分发实现量子信息共享。这些结果有助于对量子网络和量子密码学方面的研究。并且,这些方案是易于操作的,因为在完成方案的整个过程中只需调节驱动原子的经典场。
2.基于通过光纤连接的单原子-腔和双原子-腔耦合组成的系统。提出分别通过控制相互作用时间和绝热演化确定性地制备远程三原子共享GHZ态的方案。并且研究原子自发辐射和腔与光纤的光子泄漏等消相干过程带来的影响。结果表明,即使在考虑消相干的情况下,这些方案也能够以比较高的保真度实现。
3.基于通过光纤连接的两个腔分别与经典光驱动的两个二能级原子耦合组成的系统,提出实现远程两比特量子逻辑门的方案。研究发现,当腔场频率和原子跃迁频率间存在失谐时,在经典场的辅助下可以实现远程两比特量子控制相位门和交换门。此外,分析腔场和光纤的耗散等导致的消相干对此方案的影响；并通过引入八型原子有效地抑制原子自发辐射的影响。
4.基于通过光纤连接的三个腔分别与三个Λ型原子耦合组成的系统,提出实现远程三比特量子控制Z门的方案。并研究一些消相干过程如原子的自发辐射及光纤和腔的光子泄漏等带来的影响。结果表明,即使在考虑消相干的情况下此方案也能以较高的保真度实现。此结果可以推广到由光纤连接的N个腔分别与N个Λ型原子耦合的情况,进而实现远程N比特量子控制Z门。
As for the cavity quantum electrodynamics, with the increase in the number of the atomic qubits, the manipulations not only on qubit-cavity interaction but also on qubits themselves become difficult. Because some unexpected crossing interactions from qubits which are temporarily out of consideration, might arise and thus influence or spoil the useful interactions. Therefore, there are physical limitations on the number of atomic qubits in a quantum cavity. However, a practical quantum computer involves a large number of qubits, inevitably. And the power of the quantum computer increases as the mumber of qubits increases. Therefore, distributed quantum computing is introduced. It is thought of as a network of spatially separated local processors that contain only a few qubits and are connected via quantum transmission lines. Two of the key problems in the realization of distributed quantum computing are to implement the remote quantum logical gates and prepare the entanglement among the distant nodes. On the other hand, the control of single atom trapped in optical cavities and the perfect fiber-cavity coupling via microfabrication have been realized in experiment. The system, consisting of atoms separately trapped in distant cavities coupled by optical fibers, is very promising for the generation of entanglement shared by distant subsystems and implementing the remote quantum logical gates. And many schemes based on this system for the implementation of quantum information process have been proposed. In this paper, we consider this system and propose some schemes for the generation of entanglement and implementation of the quantum logical gates. Significant new results are shown as following.
1. A scheme, based on the system composed of three atoms separately trapped in three cavities coupled by optical fibres, for entangling two distant atoms via adiabatic passage is proposed. It is found that the multi-particle W entangled state can also be generated. Moreover, the quantum information sharing can be implemented using this system. These results may be helpful for the implementation of quantum network and useful in quantum cryptography. And this scheme is convenient to operate since only the laser fields applied to the atoms need to be adjusted to accomplish the processes.
2. A system composed of a single-atom-trapped cavity and a remote two-atom-trapped cavity connected by the optical fibre is considered. It is shown that a shared Greenberger-Horne-Zeilinger (GHZ) state of the three atoms can be deterministically generated by controlling the time of interaction or via the adiabatic passage based on this system. The influence of various decoherence processes such as spontaneous emission and photon loss on the fidelity is also investigated. It is found that these schemes can be realized with high fidelity even when these decoherence processes are considered.
3. A scheme, based on the two two-level atoms resonantly driven by the classical field separately trapped in two cavities coupled by an optical fibre, for the implementation of remote two-qubit gates is investigated. It is found that the quantum controlled-phase and swap gates can be achieved with the assistance of classical field when there are detunings of the coupling quantum fields. Moreover, the influence of the dissipation of the cavities and the optical fibre is analyzed while the spontaneous emission of the atoms can be effectively suppressed by introducing the∧-type atoms.
4. A scheme for implementing the three-qubit controlled-Z gate with three atoms separately trapped in three distant cavities coupled by the optical fibres is proposed. The influence of various decoherence processes, such as spontaneous emission of the atoms and photon leakage of the cavities and the optical fibres, on the fidelity is also investigated. It is found that the gate can be implemented with high fidelity even when these decoherence processes are considered. This scheme can be extended to the implementation of remote N-qubit controlled-Z gate with N atoms separately trapped in N distant cavities coupled by the optical fibres.
引文
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