Classification of multipartite entanglement containing infinitely many kinds of states

Chen, Lin; Chen, Yixin; Mei, Yu-Xue

doi:10.1103/physreva.74.052331

Cited by 41 publications

(50 citation statements)

References 29 publications

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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.…”

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confidence: 99%

Operational Determination of Multiqubit Entanglement Classes via Tuning of Local Operations

et al. 2009

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We present a physical setup with which it is possible to produce arbitrary symmetric long-lived multiqubit entangled states in the internal ground levels of photon emitters, including the paradigmatic GHZ and W states. In the case of three emitters, where each tripartite entangled state belongs to one of two well-defined entanglement classes, we prove a one-to-one correspondence between welldefined sets of experimental parameters, i.e., locally tunable polarizer orientations, and multiqubit entanglement classes inside the symmetric subspace.PACS numbers: 42.50. Ex, 03.65.Ud, 03.67.Bg, 42.50.Dv Entanglement is a distinctive property of quantum physics associated with the nonseparable character of multipartite quantum systems. For the case of two-qubit systems, entanglement is well understood and can be precisely quantified [1]. 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. We show that it is possible to associate well-defined sets of locally tuned polarizer orientations with multiqubit entanglement classes, allowing their monitoring in an operational manner. Hereby, multipath quantum interferences, associated with qubit permutation symmetry, play a key role in explaining the underlying physics.We consider a chain of N equally separated single photon emitters, say trapped neutral atoms, trapped ions, quantum dots, or any other equivalent physical system with access to similar behaviour. Each emitter defines a three-level Λ system, where |e denotes the excited state and the two long-lived sublevels, |+ and |− , define a qubit. We assume that the transitions between the excited state and the two lower sublevels have an equal wavenumber and dipole moment, and that they are circularly polarized, σ + and σ − , respectively. Figure 1 exemplifies the N -emitter case discussed throughout this paper. All emitters are initially excited and we will study the cases in which all spontaneously emitted photons are detected by N detectors located in the far-field re- gion, each of them being equipped with a polarization filter in front. The far-field detection ensures the erasure of which-way information of the arriving photons, and the polarizers allow the generation of quantum superpositions of the lower atomic states when considering arbitrary polarizations. As a consequence each photodetection event projects the emitters onto linear combinations of the long-lived states |+ and |− [8]. This results at the end in a coherent superposition between the qubit states |±, . . . , ± . The indeterminacy of which detector

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confidence: 99%

Operational Determination of Multiqubit Entanglement Classes via Tuning of Local Operations

et al. 2009

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“…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 parametric symmetry and numbers of the entangled class of 2 × M × N system

Liu

et al. 2011

Sci. China Phys. Mech. Astron.

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We present in the work two intriguing results in the entanglement classification of a pure and true tripartite entangled state of 2 × M × N under stochastic local operation and classical communication: (i) the internal symmetric properties of the nonlocal parameters in the continuous entangled class; (ii) the analytic expression for the total numbers of the true and pure entangled class 2 × M × N states. These properties help better understand the nature of the 2 × M × N entangled system. entanglement, quantum information, matrix theory

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“…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%

Experimental construction of aWsuperposition state and its equivalence to the Greenberger-Horne-Zeilinger state under local filtration

et al. 2015

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We experimentally construct a novel three-qubit entangled W-superposition (WW) state on an NMR quantum information processor. We give a measurement-based filtration protocol for the invertible local operation (ILO) that converts the WW state to the GHZ state, using a register of three ancilla qubits. Further we implement an experimental protocol to reconstruct full information about the three-party WW state using only two-party reduced density matrices. An intriguing fact unearthed recently is that the WW state which is equivalent to the GHZ state under ILO, is in fact reconstructible from its two-party reduced density matrices, unlike the GHZ state. We hence demonstrate that although the WW state is interconvertible with the GHZ state, it stores entanglement very differently.

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Classification of multipartite entanglement containing infinitely many kinds of states

Cited by 41 publications

References 29 publications

Operational Determination of Multiqubit Entanglement Classes via Tuning of Local Operations

Operational Determination of Multiqubit Entanglement Classes via Tuning of Local Operations

The parametric symmetry and numbers of the entangled class of 2 × M × N system

Experimental construction of aWsuperposition state and its equivalence to the Greenberger-Horne-Zeilinger state under local filtration

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