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arXiv:1210.2015 · Physical Review A

Atomic and photonic entanglement concentration via photonic Faraday rotation

Zhao-Hui Peng, Jian Zou, Xiaojuan Liu, Yongjun Xiao, Le‐Man Kuang

Published Sep 7, 2012• 65 citations
arXivHTMLPDF

Abstract

We propose two alternative entanglement concentration protocols (ECPs) using the Faraday rotation of photonic polarization. Through the single-photon input-output process in cavity QED, it is shown that the maximally entangled atomic (photonic) state can be extracted from two partially entangled states. The distinct feature of our protocols is that we can concentrate both atomic and photonic entangled states via photonic Faraday rotation, and thus they may be universal and useful for entanglement concentration in the experiment. Furthermore, as photonic Faraday rotation works in low-$Q$ cavities and only involves virtual excitation of atoms, our ECPs are insensitive to both cavity decay and atomic spontaneous emission.

DOI
10.1103/physreva.86.034305

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We propose two alternative entanglement concentration protocols (ECPs) using the Faraday rotation of photonic polarization. Through the single-photon input-output process in cavity QED, it is shown that the maximally entangled atomic (photonic) state can be extracted from two partially entangled states. The distinct feature of our protocols is that we can concentrate both atomic and photonic entangled states via photonic Faraday rotation, and thus they may be universal and useful for entanglement concentration in the experiment. Furthermore, as photonic Faraday rotation works in low-QQQ cavities and only involves virtual excitation of atoms, our ECPs are insensitive to both cavity decay and atomic spontaneous emission.
By utilizing Faraday rotation of photons, we present a highly efficient protocol for entanglement concentration of atomic Bell states, which departs from the conventional method of sequential interactions between the auxiliary photon and two optical cavities. Instead, the simultaneous interaction of the auxiliary photon with two atomic cavities is involved in order to significantly reduce the time requirement for achieving atomic Bell state entanglement concentration. By employing iterative applications of the protocol for entanglement concentration, the discarded states can be repeatedly concentrated, efficiently increasing the probability of success. Furthermore, our entanglement concentration protocols (ECPs) operate in low-Q cavities, which are easier to implement in practical applications than high-Q cavities. Finally, it can be generalized to an N -atom GHZ states entanglement concentration protocol.
We put forward an optimal entanglement concentration protocol (ECP) for recovering an arbitrary less-entangled multi-photon Greenberger–Horne–Zeilinger (GHZ) state into the maximally entangled GHZ state based on the photonic Faraday rotation in low-quality ( Q ) cavity. In the ECP, only one pair of less-entangled multi-photon GHZ state and one auxiliary photon are required, and the concentration task can be realized by local operations. Moreover, our ECP can be used repeatedly to further concentrate the discarded items of conventional ECPs, which can increase its success probability largely. Under the practical imperfect detection condition, our protocol can still work with relatively high success probability. This ECP has application potential in current and future quantum communication.
A recent paper (Phys. Rev. A \textbf{86}, 034305 (2012)) proposed an entanglement concentration protocol (ECP) for distilling one pair of maximally entangled multi-photon Greenberger-Horne-Zeilinger (GHZ) state from two pairs of less-entangled multi-photon states with the photonic Faraday rotation. In this paper, we put forward an improved ECP for arbitrary less-entangled multi-photon GHZ state. In the ECP, we only require one pair of less-entangled multi-photon state and one auxiliary photon, and the whole concentration process only requires local operations. Moreover, our ECP can be used repeatedly to further concentrate the less-entangled multi-photon state and obtain a higher success probability. If consider the practical operation and imperfect detection, our protocol is more efficient. This ECP may be useful in current quantum information processing.
We propose a scheme for deterministically teleporting a pure quantum state, making use of the Faraday rotation of photonic polarization in cavity QED system. Based on the single-photon input-output process regarding cavities, the scheme works well even in low-Q cavities. Since only virtual excitation of the atoms is involved, it is also insensitive to atomic spontaneous emission. Besides, the CNOT operation replaced by the Faraday rotation is not needed in the scheme, which could greatly relax the experimental difficulty.
Based on the input-output relation in low-Q cavities, we propose a feasible scheme to prepare remotely a single-atom state via photonic Faraday rotation, and then the scheme is generalized to the case of remote preparation of a two-atom entangled state. Our results show that when the coefficients of the initial atomic state to be prepared are real, both remote preparation of the single-atom state and that of the two-atom entangled state can be achieved deterministically by selecting appropriate parameters of the systems for the interactions among the atom, polarized single-photon pulse, and cavity field. Compared with the existing schemes for remote preparation of atomic states, in our scheme photons are used as flying qubits to transmit quantum information, which is suitable indeed to achieve a long-distance atomic state preparation in principle. Due to the fact that the information of atomic state is encoded in two degenerate ground-state levels of a -type three-level atom confined in a unilateral dissipative cavity, and that the atoms are only virtually excited, our schemes are insensitive to both cavity decay and atomic spontaneous emission. Besides, the two schemes we proposed do not need two- or multi-particle orthogonal measurements, only product-state measurements are involved, as well as they work in low-Q regime and do not require a strong coupling condition between the atoms and the optical cavities, which greatly reduce the experimental difficulty.
We propose two optimal entanglement concentration protocols (ECPs) for arbitrary single-photon multi-mode W state and multi-photon polarization W state, respectively. In both ECPs, we only require one pair of partially entangled W state, and do not consume any auxiliary photon. Both ECPs are based on the linear optics which can be easily realized. On the other hand, the concentrated maximally entangled states can be remained, which are quite different from the previous ECPs. Moreover, for the concentration of the arbitrary single-photon N-mode W state or N-mode polarization W state, the total success probability is equal to Nth the modulus square of the Schmidt coefficient of the smallest magnitude. It makes both ECPs optimal than all the previous ECPs. Our ECPs may be useful in current quantum communication fields.