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Broadcasting of NPT entanglement in two qutrit systems

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Abstract

It is known that beyond \(2 \otimes 2\) and \(2 \otimes 3\) dimensional quantum systems, Peres–Hordecki criterion is no longer sufficient as an entanglement detection criterion as there are entangled states with both positive and negative partial transpose (PPT and NPT). Further, it is also true that all PPT entangled states are bound entangled states. However, in the class of NPT states, there exist bound entangled states as well as free entangled states. All free/useful/distillable entanglements are part of the class of NPT entangled states. In this article, we ask the question that given an NPT entangled state in \(3 \otimes 3\) dimensional system as a resource, how much entanglement can we broadcast so that resource still remains NPT. We have chosen \(3 \otimes 3\) system as a first step to understand broadcasting of NPT states in higher dimensional systems. In particular, we find out the range of broadcasting of NPT entanglement for two-parameter class of states (TPCS) and isotropic states (IS). Interestingly, as a derivative of this process we are also able to locate the existence of absolute PPT (ABPPT) states in \(3 \otimes 3\) dimensional system. Here we implement the strategy of broadcasting through approximate cloning operations.

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Acknowledgements

NG would like to acknowledge support from the Research Initiation Grant of BITS-Pilani, Hyderabad vide letter No. BITS/GAU/RIG/2019/H0680 dated 22 April 2019.

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Authors and Affiliations

  1. Centre for Computational Natural Sciences and Bioinformatics, International Institute of Information Technology-Hyderabad, Gachibowli, 500 032, India

    Rounak Mundra & Sabuj Chattopadhyay

  2. Centre for Security, Theory and Algorithmic Research, International Institute of Information Technology-Hyderabad, Gachibowli, 500 032, India

    Indranil Chakrabarty

  3. Department of Mathematics, Birla Institute of Technology and Science Pilani, Hyderabad Campus, Hyderabad, 500 078, India

    Nirman Ganguly

Authors
  1. Rounak Mundra
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  2. Sabuj Chattopadhyay
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  3. Indranil Chakrabarty
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  4. Nirman Ganguly
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Correspondence to Rounak Mundra.

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Mundra, R., Chattopadhyay, S., Chakrabarty, I. et al. Broadcasting of NPT entanglement in two qutrit systems. Pramana - J Phys 95, 60 (2021). https://doi.org/10.1007/s12043-021-02098-w

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  • DOI: https://doi.org/10.1007/s12043-021-02098-w

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