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Protocols of quantum key agreement solely using Bell states and Bell measurement

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Abstract

Two protocols of quantum key agreement (QKA) that solely use Bell state and Bell measurement are proposed. The first protocol of QKA proposed here is designed for two-party QKA, whereas the second protocol is designed for multi-party QKA. The proposed protocols are also generalized to implement QKA using a set of multi-partite entangled states (e.g., 4-qubit cluster state and \(\Omega \) state). Security of these protocols arises from the monogamy of entanglement. This is in contrast to the existing protocols of QKA where security arises from the use of non-orthogonal state (non-commutativity principle). Further, it is shown that all the quantum systems that are useful for implementation of quantum dialogue and most of the protocols of secure direct quantum communication can be modified to implement protocols of QKA.

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Notes

  1. Here subscripts A, B, C denote Alice, Bob, and Charlie, respectively.

  2. In the stabilizer formalism of quantum error correction Pauli group is frequently used (see Section 10.5.1 of [32]). It is usually defined as \(G_{1}=\left\{ \pm I,\pm iI,\pm \sigma _{x},\pm i\sigma _{x},\pm \sigma _{y},\pm i\sigma _{y},\pm \sigma _{z},\pm i\sigma _{z}\right\} ,\) where \(\sigma _{i}\) is a Pauli matrix. The inclusion of \(\pm 1\) and \(\pm i\) ensures that \(G_{1}\) is closed under standard matrix multiplication, but the effect of \(\sigma _{i},\,-\sigma _{i},\, i\sigma _{i}\), and \(-i\sigma _{i}\) on a quantum state is the same. So in [33], we redefined the multiplication operation for two elements of the group in such a way that global phase is ignored from the product of matrices. This is consistent with the quantum mechanics and it gives us a modified Pauli group \(G_{1}=\{I,\,\sigma _{x},\, i\sigma _{y},\,\sigma _{z}\}=\{I,\, X,\, iY,\, Z\}.\)

  3. In \(\mathrm{PP^{GV}}\)Alice does not need to disclose her key \(K_{A}\). Everything else is the same and as a consequence \(b=2n,\, q=4n\) and \(c=n\) with \(c\) being the number of bits in the message or key that is transmitted.

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Acknowledgments

AP thanks Department of Science and Technology (DST), India for support provided through the DST project No. SR/S2/LOP-0012/2010 and he also acknowledges the supports received from the projects CZ.1.05/2.1.00/03.0058 and CZ.1.07/2.3.00/20.0017 of the Ministry of Education, Youth and Sports of the Czech Republic.

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Authors and Affiliations

  1. Jaypee Institute of Information Technology, A-10, Sector-62, Noida, 201307, Uttar Pradesh, India

    Chitra Shukla & Anirban Pathak

  2. Department of Physics Visva Bharati, Santiniketan, 731235, West Bengal, India

    Nasir Alam

  3. RCPTM, Joint Laboratory of Optics of Palacky University, Institute of Physics of Academy of Science of the Czech Republic, Faculty of Science, Palacky University, 17. listopadu 12, 771 46 , Olomouc, Czech Republic

    Anirban Pathak

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Shukla, C., Alam, N. & Pathak, A. Protocols of quantum key agreement solely using Bell states and Bell measurement. Quantum Inf Process 13, 2391–2405 (2014). https://doi.org/10.1007/s11128-014-0784-0

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