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
We present two robust quantum key distribution protocols against two kinds of collective noise, following some ideas in quantum dense coding. Three-qubit entangled states are used as quantum information carriers, two of which forming the logical qubit which is invariant with a special type of collective noise. The information is encoded on logical qubits with four unitary operations, which can be read out faithfully with Bell-state analysis on two physical qubits and a single-photon measurement on the other physical qubit, not three-photon joint measurements. Two bits of information are exchanged faithfully and securely by transmitting two physical qubits through a noisy channel. When the losses in the noisy channel is low, these protocols can be used to transmit a secret message directly in principle.
We investigate the relation between the entanglement and the robustness of a
multipartite system to a depolarization noise. We find that the robustness of a
two-qubit system in an arbitrary pure state depends completely on its
entanglement. However, this is not always true in a three-qubit system. There
is a residual effect on the robustness of a three-qubit system in an arbitrary
superposition of Greenberger-Horne-Zeilinger state and W state. Its
entanglement determines the trend of its robustness. However, there is a
splitting on its robustness under the same entanglement. Its robustness not
only has the same periodicity as its three-tangle but also alters with its
three-tangle synchronously. There is also a splitting on the robustness of an
$n$-qubit ($n>3$) system although it is more complicated.Comment: 5 pages, 4 figures; A figure is added, compared with the version
published in Phys. Rev. A 82, 014301 (2010
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