Mermin inequalities for perfect correlations in many-qutrit systems

Lawrence, Jay

doi:10.1103/physreva.95.042123

Cited by 13 publications

(22 citation statements)

References 26 publications

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“…Such a contradiction has novel interesting features beyond the qubit case. Here we follow the theoretical construction given by Lawrence [11,32] and explicitly point to the conceptual differences as compared to the qubit case. Most interestingly to use hermitian local observables does not lead to a GHZ contradiction.…”

Section: Multi-setting Three-particle Ghz Experiments In Three-dimensionsmentioning

confidence: 99%

Experimental Greenberger–Horne–Zeilinger entanglement beyond qubits

et al. 2018

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The Greenberger-Horne-Zeilinger (GHZ) argument provides an all-or-nothing contradiction between quantum mechanics and local-realistic theories. In its original formulation, GHZ investigated three and four particles entangled in two dimensions only. Very recently, higher dimensional contradictions especially in three dimensions and three particles have been discovered but it has remained unclear how to produce such states. In this article we experimentally show how to generate a three-dimensional GHZ state from two-photon orbital-angular-momentum entanglement. The first suggestion for a setup which generates three-dimensional GHZ entanglement from these entangled pairs came from using the computer algorithm MELVIN. The procedure employs novel concepts significantly beyond the qubit case. Our experiment opens up the possibility of a truly high-dimensional test of the GHZ-contradiction which, interestingly, employs non-Hermitian operators.

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Section: Multi-setting Three-particle Ghz Experiments In Three-dimensionsmentioning

confidence: 99%

Experimental Greenberger–Horne–Zeilinger entanglement beyond qubits

et al. 2018

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“…Experiments like the ones described above will allow for the investigation of the strongest form of contradictions to local realism -namely deterministic violations of local realism as introduced by Greenberger, Horne and Zeilinger (GHZ) [108]. Generalizing GHZviolations to higher dimensions have been surprisingly difficult and has only been achieved very recently [114][115][116][117]. Those constructions departure significantly from their two-dimensional counterparts, and it seems as if they would help revealing the real nature of deterministic violations of local realism.…”

Section: G Experimental Creation Of a Greenberger-horne-zeilinger Stmentioning

confidence: 99%

Twisted photons: new quantum perspectives in high dimensions

et al. 2017

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Twisted photons can be used as alphabets to encode information beyond one bit per single photon. This ability offers great potential for quantum information tasks, as well as for the investigation of fundamental questions. In this review article, we give a brief overview of the theoretical differences between qubits and higher dimensional systems, qudits, in different quantum information scenarios. We then describe recent experimental developments in this field over the past three years. Finally, we summarize some important experimental and theoretical questions that might be beneficial to understand better in the near future.

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“…Inspired by the usefulness of recursive Bell operators for multi-qubit steering, we explore the possibility of tackling quantum steering in a qutrit case. Recently, multi-qutrit Mermin inequalities were proposed by Lawrence [ 48 ]. The Bell operators therein are

where

In addition, the Pauli matrix for the qutrit j are

and

(

; 0 otherwise).…”

Section: Steering Criteria For Qutrit Systemsmentioning

confidence: 99%

“…In addition, since the connection between joint measurability and unsteerability is also unclear for qutrits, one cannot determine whether

outperforms

to serve as steering criteria. Finally, as p goes infinity, the steering inequalities become

where

and

represents the GHZ state for

qutrits given by Lawrence [ 48 ]. Therefore, the violation of ( 26 ) indicates that nonlocality distributed among more than (

) qutrits can be achieved using the EPR-steering.…”

Section: Steering Criteria For Qutrit Systemsmentioning

confidence: 99%

Exploring Multipartite Steering Effect Using Bell Operators

Hsu

Kawamoto

2019

Entropy

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While Bell operators are exploited in detecting Bell nonlocality and entanglement classification, we demonstrate their usefulness in exploring Einstein–Podolsky–Rosen (EPR) steering, which represents the quantum correlation intermediate between entanglement and Bell nonlocality. We propose a task function that detects steerability of multi-qubit states in bipartite scenarios. A novel necessary and sufficient steering criterion is based on the superposition of the recursive Bell operators which are often employed for detecting Bell nonlocality. Utilizing the task function we can (i) reveal the one-to-one mapping relation between joint measurability and unsteerability, (ii) geometrically depict and compare the entanglement classification and the steering criteria and propose a geometrical measure, and (iii) compare the EPR steering with Bell nonlocality using an alternative task function. We extend the result to detect EPR steering for multi-qutrit cases and some numerical results are illustrated as examples. Finally, the steering criteria in a star-shaped quantum network is studied to see how the result is applied to a genuine multipartite steering case.

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Mermin inequalities for perfect correlations in many-qutrit systems

Cited by 13 publications

References 26 publications

Experimental Greenberger–Horne–Zeilinger entanglement beyond qubits

Experimental Greenberger–Horne–Zeilinger entanglement beyond qubits

Twisted photons: new quantum perspectives in high dimensions

Exploring Multipartite Steering Effect Using Bell Operators

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