2006
DOI: 10.1103/physreva.74.052331
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Classification of multipartite entanglement containing infinitely many kinds of states

Abstract: We give a further investigation of the range criterion and Low-to-High Rank Generating Mode (LHRGM) introduced in [17], which can be used for the classification of 2 × M × N states under reversible local filtering operations. By using of these techniques, we entirely classify the family of 2 × 4 × 4 states, which actually contains infinitely many kinds of states. The classifications of true entanglement of 2 × (M + 3) × (2M + 3) and 2 × (M + 4) × (2M + 4) systems are briefly listed respectively.

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Cited by 41 publications
(50 citation statements)
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“…Apart from the trivial disentangled case, three qubits possess two genuine tripartite inequivalent entanglement classes [2,3]. Efforts have been done recently towards higher number of qubits [4,5,6], including an inductive method [7], though so far no comprehensive and scalable classification has been developed. In this letter, we introduce a physical setup consisting of N emitters, incoherently radiating single photons that may be absorbed remotely by detectors equipped with polarizers and producing long-lived multiqubit entangled states among the emitters.…”
mentioning
confidence: 99%
“…Apart from the trivial disentangled case, three qubits possess two genuine tripartite inequivalent entanglement classes [2,3]. Efforts have been done recently towards higher number of qubits [4,5,6], including an inductive method [7], though so far no comprehensive and scalable classification has been developed. In this letter, we introduce a physical setup consisting of N emitters, incoherently radiating single photons that may be absorbed remotely by detectors equipped with polarizers and producing long-lived multiqubit entangled states among the emitters.…”
mentioning
confidence: 99%
“…In ref. [11], Chen et al constructed the true entanglement classes of 2 × M × N which have finite entanglement classes, and then they found the entanglement class with one continuous parameter in the 2 × 4 × 4 system using their range criterion and Low-to-High Rank Generating Mode method [12]. There they also noticed that the continuous parameter in the entanglement class is not totally free.…”
Section: Introductionmentioning
confidence: 96%
“…The entanglement of the GHZ state is fragile under qubit loss, i.e when any one of the qubits is traced out, the other two qubits become completely disentangled [2,8]. Hence if one of the parties decides not to cooperate, the entanglement resources of the GHZ state cannot be used.…”
Section: Introductionmentioning
confidence: 99%