Multipartite entanglement purification with quantum nondemolition detectors

Abstract

We present a scheme for multipartite entanglement purification of quantum systems in a Greenberger-Horne-Zeilinger state with quantum nondemolition detectors (QNDs). This scheme does not require the controlled-not gates which cannot be implemented perfectly with linear optical elements at present, but QNDs based on cross-Kerr nonlinearities. It works with two steps, i.e., the bit-flipping error correction and the phase-flipping error correction. These two steps can be iterated perfectly with parity checks and simple single-photon measurements. This scheme does not require the parties to possess sophisticated single photon detectors. These features maybe make this scheme more efficient and feasible than others in practical applications.PACS numbers: 03.67.Pp Quantum error correction and other methods for protection against decoherence -03.67.Hk Quantum communication

Efficient multipartite entanglement purification with the entanglement link from a subspace

“…By far, there have been several interesting EPPs [25][26][27][28][29][30][31][32] focusing on entangled two-photon systems, while there are only two EPPs for multipartite photon systems [35,36] and an EPP for multipartite electronic systems [37] with charge detection. In 1998, Murao et al [35] proposed a multipartite entanglement purification protocol (MEPP) to purify multipartite quantum systems in a Greenberger-Horne-Zeilinger (GHZ) with CNOT gates, following some ideas in the EPP by Bennett et al [25].…”

“…In 1998, Murao et al [35] proposed a multipartite entanglement purification protocol (MEPP) to purify multipartite quantum systems in a Greenberger-Horne-Zeilinger (GHZ) with CNOT gates, following some ideas in the EPP by Bennett et al [25]. In 2009, a MEPP based on cross-Kerr nonlinearities was proposed [36]. In this protocol, the cross-Kerr nonlinearity is used to construct a nondestructive quantum nondemolition detector (QND) [38] which has the functions of both a parity-check gate and a photon-number detector.…”

“…One is our conventional MEPP with which the parties can obtain a high-fidelity N -photon ensemble directly, similar to the conventional MEPP with controlled-not gates [35], but it doubles the efficiency of the MEPP with cross-Kerr nonlinearity in Ref. [36] and the MEPP for electronic systems [37]. The other is our recycling MEPP in which the entanglement link is used to produce some N -photon entangled systems from subspaces.…”

“…The other is our recycling MEPP in which the entanglement link is used to produce some N -photon entangled systems from subspaces. That is, the parties in quantum communication first distil some entangled N ′ -photon subsystems (2 ≤ N ′ < N ) from the cross-combinations which are just the discarded instances in the conventional MEPPs [35][36][37], and then they produce some N -photon entangled systems with entanglement link. It is interesting to show that the entangled N ′ -photon subsystems are obtained efficiently by measuring the potential photons with bit-flip errors in the two cross-combinations of two N -photon states.…”

“…Moreover, the present MEPP works by replacing parity-check detectors with CNOT gates. With these two parts, the present MEPP has a higher efficiency than all other conventional MEPPs [35][36][37].…”