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Distillation of the Greenberger-Horne-Zeilinger state from arbitrary tripartite states

Yi-Na Mo, Chuan‐Feng Li, Guang‐Can Guo

We present a method of distillation of Greenberger-Horne-Zeilinger states from arbitrary tripartite pure states by local operations and classical communication. We go further to discuss the various results we get and calculate the efficiency of the protocol.

Physical Review AJan 4, 20022 citations

Distilling a Greenberger-Horne-Zeilinger State From an Arbitrary Pure State of Three Qubits

Li-Xiang Cen, Shun-Jin Wang

We present a general algorithm to achieve local operators which can produce the GHZ state for an arbitrary given three-qubit state. Thus the distillation process of the state can be realized optimally. The algorithm is shown to be sufficient for the three-qubit state on account of the fact that any state for which this distillation algorithm is invalid cannot be distilled to the GHZ state by any local actions. Moreover, an analytical result of distillation operations is achieved for the general state of three qubits.We present a general algorithm to achieve local operators which can produce the GHZ state for an arbitrary given three-qubit state. Thus the distillation process of the state can be realized optimally. The algorithm is shown to be sufficient for the three-qubit state on account of the fact that any state for which this distillation algorithm is invalid cannot be distilled to the GHZ state by any local actions. Moreover, an analytical result of distillation operations is achieved for the general state of three qubits.

arXiv:quant-ph/0012022Dec 5, 20000 citations

Necessary and sufficient fully separable criterion and entanglement of three-qubit Greenberger–Horne–Zeilinger diagonal states

Xiaoyu Chen, Li-zhen Jiang, Ping Yu +1 more

Quantum Information ProcessingMay 3, 201513 citations

Four qubits can be entangled in nine different ways

Frank Verstraete, Jeroen Dehaene, Bart De Moor +1 more

We consider a single copy of a pure four-partite state of qubits and investigate its behavior under the action of stochastic local quantum operations assisted by classical communication (SLOCC). This leads to a complete classification of all different classes of pure states of four qubits. It is shown that there exist nine families of states corresponding to nine different ways of entangling four qubits. The states in the generic family give rise to Greenberger-Horne-Zeilinger-like entanglement. The other ones contain essentially two-or three-qubit entanglement distributed among the four parties. The concept of concurrence and 3-tangle is generalized to the case of mixed states of four qubits, giving rise to a seven-parameter family of entanglement monotones. Finally, the SLOCC operations maximizing all these entanglement monotones are derived, yielding the optimal single-copy distillation protocol.We consider a single copy of a pure four-partite state of qubits and investigate its behavior under the action of stochastic local quantum operations assisted by classical communication (SLOCC). This leads to a complete classification of all different classes of pure states of four qubits. It is shown that there exist nine families of states corresponding to nine different ways of entangling four qubits. The states in the generic family give rise to Greenberger-Horne-Zeilinger-like entanglement. The other ones contain essentially two-or three-qubit entanglement distributed among the four parties. The concept of concurrence and 3-tangle is generalized to the case of mixed states of four qubits, giving rise to a seven-parameter family of entanglement monotones. Finally, the SLOCC operations maximizing all these entanglement monotones are derived, yielding the optimal single-copy distillation protocol.

arXiv:quant-ph/0109033Physical Review AApr 25, 2002661 citations

Invariants-based shortcuts for fast generating Greenberger-Horne-Zeilinger state among three superconducting qubits

徐晶, 于琳, 吴金雷 +1 more

中国物理B：英文版Jan 1, 20170 citations

Distillation of Greenberger-Horne-Zeilinger States by Selective Information Manipulation

Oliver Cohen, Todd A. Brun

Methods for distilling Greenberger-Horne-Zeilinger (GHZ) states from arbitrary entangled tripartite pure states are described. These techniques work for virtually any input state. Each technique has two stages which we call primary and secondary distillations. Primary distillation produces a GHZ state with some probability, so that when applied to an ensemble of systems a certain percentage is discarded. Secondary distillation produces further GHZs from the discarded systems. These protocols are developed with the help of an approach to quantum information theory based on absolutely selective information, which has other potential applications.Methods for distilling Greenberger-Horne-Zeilinger (GHZ) states from arbitrary entangled tripartite pure states are described. These techniques work for virtually any input state. Each technique has two stages which we call primary and secondary distillations. Primary distillation produces a GHZ state with some probability, so that when applied to an ensemble of systems a certain percentage is discarded. Secondary distillation produces further GHZs from the discarded systems. These protocols are developed with the help of an approach to quantum information theory based on absolutely selective information, which has other potential applications.

arXiv:quant-ph/0001084Physical Review LettersJun 19, 200026 citations

Optimal Distillation of a Greenberger-Horne-Zeilinger State

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Optimal Distillation of a Greenberger-Horne-Zeilinger State

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