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Classification and measurement of multipartite entanglement by reconstruction of correlation tensors on an NMR quantum processor

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Abstract

We introduce a protocol to classify three-qubit pure states into different entanglement classes and implement it on an NMR quantum processor. The protocol is designed in such a way that the experiments performed to classify the states can also measure the amount of entanglement present in the state. The classification requires the experimental reconstruction of the correlation matrices using 13 operators. The rank of the correlation matrices provides the criteria to classify the state in one of the five classes, namely separable, biseparable (of three types), and genuinely entangled (of two types, GHZ and W). To quantify the entanglement, a concurrence function is defined which measures the global entanglement present in the state, using the same 13 operators. Global entanglement is zero for separable states and nonzero otherwise. We demonstrate the efficacy of the protocol by implementing it on states chosen from each of the six inequivalent (under stochastic local operations and classical communication) classes for three qubits. We also implement the protocol on states picked at random from the state space of three-qubit pure states.

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Data Availability Statement

This manuscript has no associated data or the data will not be deposited. [Authors’ comment: The datasets generated analyzed during the current study are available from the corresponding author on reasonable request.]

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Acknowledgements

All experiments were performed on a 600 MHz FT-NMR spectrometer at the NMR Research Facility IISER Mohali. Arvind acknowledges financial support from DST/ICPS/QuST/Theme-1/2019/General Project Number Q-68. K.D. acknowledges financial support from DST/ICPS/QuST/Theme-2/2019/General Project Number Q-74.

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Authors and Affiliations

  1. Department of Physical Sciences, Indian Institute of Science Education and Research Mohali, Sector 81, SAS Nagar, PO 140306, Manauli, Punjab, India

    Vaishali Gulati,  Arvind & Kavita Dorai

  2. Vice Chancellor, Punjabi University, Patiala, Punjab, 147002, India

    Arvind

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  1. Vaishali Gulati
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  2. Arvind
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VG performed the experiments. VG, KD and Arvind discussed the physics, experimental and computational results and jointly wrote the manuscript. KD and Arvind supervised the project.

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Correspondence to Kavita Dorai.

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Gulati, V., Arvind & Dorai, K. Classification and measurement of multipartite entanglement by reconstruction of correlation tensors on an NMR quantum processor. Eur. Phys. J. D 76, 194 (2022). https://doi.org/10.1140/epjd/s10053-022-00527-y

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