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Absolute fully entangled fraction from spectrum

  • Regular Article – Quantum Information
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Abstract

Fully entangled fraction (FEF) is a significant figure of merit for density matrices. In bipartite \( d \otimes d \) quantum systems, the threshold value FEF \( > 1/d \), carries significant implications for quantum information processing tasks. Like separability, the value of FEF is also related to the choice of global basis of the underlying Hilbert space. A state having its FEF \( \le 1/d \), might give a value \( > 1/d \) in another global basis. A change in the global basis corresponds to a global unitary action on the quantum state. In the present work, we find that there are quantum states whose FEF remains less than 1/d, under the action of any global unitary, i.e., any choice of global basis. We invoke the hyperplane separation theorem to demarcate the set from states whose FEF can be increased beyond 1/d through global unitary action. Consequent to this, we probe the marginals of a pure three party system in qubits. We observe that under some restrictions on the parameters, even if two parties collaborate (through unitary action on their combined system) they will not be able to breach the FEF threshold. The study is further extended to include some classes of mixed three qubit and three qutrit systems. Furthermore, the implications of our work pertaining to k-copy nonlocality and teleportation are also investigated.

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Data Availability Statement

This manuscript has no associated data or the data will not be deposited. [Authors’ comment: Data sharing is not applicable to this article as no datasets were generated or analysed during the current study.]

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Acknowledgements

Tapaswini Patro would like to acknowledge the support from DST-Inspire fellowship No. DST/INSPIRE Fellowship/2019/IF190357. M.A.S. acknowledges the National Key R &D Program of China, Grant No. 2018YFA0306703.

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Authors and Affiliations

  1. Department of Mathematics, Birla Institute of Technology and Science-Pilani, Hyderabad Campus, Hyderabad, Telangana, India

    Tapaswini Patro & Nirman Ganguly

  2. Department of Mathematics, Government Girls’ General Degree College, Ekbalpore, Kolkata, India

    Kaushiki Mukherjee

  3. Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China, Chengdu, 610051, China

    Mohd Asad Siddiqui

  4. Center for Quantum Science and Technology and Center for Security, Theory and Algorithmic Research, International Institute of Information Technology-Hyderabad, Gachibowli, Telangana, India

    Indranil Chakrabarty

Authors
  1. Tapaswini Patro
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  2. Kaushiki Mukherjee
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  3. Mohd Asad Siddiqui
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  4. Indranil Chakrabarty
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  5. Nirman Ganguly
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All authors contributed equally to the paper.

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Correspondence to Tapaswini Patro.

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Patro, T., Mukherjee, K., Siddiqui, M.A. et al. Absolute fully entangled fraction from spectrum. Eur. Phys. J. D 76, 127 (2022). https://doi.org/10.1140/epjd/s10053-022-00458-8

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