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Computing on quantum shared secrets for general quantum access structures

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Abstract

Quantum secret sharing is a method for sharing a secret quantum state among a number of individuals such that certain authorized subsets of participants can recover the secret shared state by collaboration and other subsets cannot. In this paper, we first propose a method for sharing a quantum secret in a basic (2, 3) threshold scheme, only by using qubits and the 7-qubit CSS code. Based on this (2, 3) scheme, we propose a new (n, n) scheme, and we also construct a quantum secret sharing scheme for any quantum access structure by induction. Secondly, based on the techniques of performing quantum computation on 7-qubit CSS codes, we introduce a method that authorized subsets can perform universal quantum computation on this shared state, without the need for recovering it. This generalizes recent attempts for doing quantum computation on (n, n) threshold schemes.

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Notes

  1. More precisely, if the discarded share contains no important data, which means it is not included in any minimal authorized set, the resulting access structure is still maximal. This means that the purification produces a redundant share, that is what we desire.

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Acknowledgements

We thank the referees, specially one of them, whose very careful reading of the manuscript and very valuable comments led to a much better presentation of this article. This work was done with a support from the research council of the Sharif University of Technology, and with the financial support from Sharif University of Technology under Grant No. G951418, and with partial support from Iran National Science Foundation under the Grant INSF-96011347.

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Authors and Affiliations

  1. Department of Computer Engineering, Sharif University of Technology, P.O. Box 11155-9161, Tehran, Iran

    Roozbeh Bassirian & Sadra Boreiri

  2. Department of Physics, Sharif University of Technology, P.O. Box 11155-9161, Tehran, Iran

    Sadra Boreiri & Vahid Karimipour

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  1. Roozbeh Bassirian
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  2. Sadra Boreiri
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  3. Vahid Karimipour
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Correspondence to Roozbeh Bassirian.

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Bassirian, R., Boreiri, S. & Karimipour, V. Computing on quantum shared secrets for general quantum access structures. Quantum Inf Process 18, 109 (2019). https://doi.org/10.1007/s11128-019-2224-7

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