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arXiv:quant-ph/0108063 · Physical Review Letters

Polarization Entanglement Purification using Spatial Entanglement

Christoph Simon, Jian-Wei Pan

Published Dec 2, 2002• 307 citations
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Abstract

We present a scheme for entanglement purification with linear optics that works for currently available parametric down-conversion sources, in contrast to a previous scheme [J. W. Pan, Nature (London) 410, 1067 (2001)]] that relied on ideal single-pair sources. The present scheme makes use of spatial entanglement in order to purify polarization entanglement. Surprisingly, spatial entanglement as an additional resource also leads to a substantial improvement in entanglement output compared to the previous scheme.

DOI
10.1103/physrevlett.89.257901

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We present a scheme for entanglement purification with linear optics that works for currently available parametric down-conversion sources, in contrast to a previous scheme [J. W. Pan, Nature (London) 410, 1067 (2001)]] that relied on ideal single-pair sources. The present scheme makes use of spatial entanglement in order to purify polarization entanglement. Surprisingly, spatial entanglement as an additional resource also leads to a substantial improvement in entanglement output compared to the previous scheme.
We present a one-step deterministic entanglement purification protocol with linear optics and postselection. Compared with the Simon-Pan protocol [C. Simon and J. W. Pan, Phys. Rev. Lett. 89, 257901 (2002)], this one-step protocol has some advantages. First, it can obtain a maximally entangled pair from each photon pair with only one step, instead of improving the fidelity of less-entangled photon pairs by performing the entanglement purification process repeatedly in other protocols. Second, it works in a deterministic way, not a probabilistic one, which greatly reduces the number of entanglement resources needed. Third, it does not require the polarization state be entangled; only spatial entanglement is needed. Moreover, it is feasible with current techniques [J. W. Pan, S. Gasparonl, R. Ursin, G. Weihs, and A. Zellinger, Nature (London) 423, 417 (2003)]. All these advantages make this one-step protocol more convenient than others in quantum-communication applications.
We propose a scheme to purify entanglement of two atoms from not-too-impure entangled states by checking the parity of the two atoms through the cavity input-output process. As the parity check is made by measurement on single-photon polarization, which would not affect the entanglement of the two atoms, our scheme has the successful probability double of that in a previous well-known scheme with linear optical elements [Nature (London) 410 (2001) 1067], and is insensitive to the photon loss and the detection inefficiency. Experimental feasibility of our scheme with current technology is discussed.
We present a way for entanglement purification based on two parametric down-conversion (PDC) sources with cross-Kerr nonlinearities. It is comprised of two processes. The first one is a primary entanglement purification protocol for PDC sources with nondestructive quantum nondemolition (QND) detectors by transferring the spatial entanglement of photon pairs to their polarization. In this time, the QND detectors act as the role of controlled-NOT (CNOT) gates. Also they can distinguish the photon number of the spatial modes, which provides a good way for the next process to purify the entanglement of the photon pairs kept more. In the second process for entanglement purification, new QND detectors are designed to act as the role of CNOT gates. This protocol has the advantage of high yield and it requires neither CNOT gates based on linear optical elements nor sophisticated single-photon detectors, which makes it more convenient in practical applications.
The protocol using spatial entanglement to purify polarization entanglement by entanglement transformation between different degrees of freedom in a realistic environment is elaborated. Our analyses show that the bit-flip error can be completely purified, but the pure maximally entangled state can not be obtained ultimately if the spatial entanglement is impure. The fidelity of the purified state is decided by the spatial entanglement. Furthermore, this protocol can also be extended to purify the multi-particle Greenberg—Horne—Zeilinger (GHZ) state. It is presented that the spatial entanglement can be served as another source to improve the quality of entanglement.