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Mutually Unbiased Bases (MUBs) have important applications in several domains, particularly in Quantum Cryptography where the bases are used in designing the protocols related to Quantum Key Distribution (QKD). In this paper we consider parameterization of MUBs so that one can explore several classes of them for various applications. For dimension \(d=s^2\) , we present the construction of affine-parametric classes with \(MOLS(s)+2\) many MUBs, where MOLS(s) is the number of Mutually Orthogonal Latin Squares of dimension s. If s is a power of prime, then \(MOLS(s) = s-1\) , and the number of MUBs will be \(s+1\) . Considering the first one to be the identity matrix, in our construction, each of the rest \(MOLS(s)+1\) MUBs will have at least \(s(s-1)\) free parameters, that cannot be absorbed by a global unitary operation. In comparison to Goyeneche et al.’s paper (2015), our result produces larger number of MUBs as well as free parameters in most of the cases. This can help in exploring various choices of MUBs in the protocols for higher dimensional QKDs and other applications of MUBs related to quantum information.

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A Parametric Class of Mutually Unbiased Bases Using Resolvable Block Designs

  • 会议论文

  • 发表日期：

    2025年

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  • Ajeet Kumar,
  • Rakesh Kumar,
  • Subhamoy Maitra

摘要

Mutually Unbiased Bases (MUBs) have important applications in several domains, particularly in Quantum Cryptography where the bases are used in designing the protocols related to Quantum Key Distribution (QKD). In this paper we consider parameterization of MUBs so that one can explore several classes of them for various applications. For dimension \(d=s^2\) , we present the construction of affine-parametric classes with \(MOLS(s)+2\) many MUBs, where MOLS(s) is the number of Mutually Orthogonal Latin Squares of dimension s. If s is a power of prime, then \(MOLS(s) = s-1\) , and the number of MUBs will be \(s+1\) . Considering the first one to be the identity matrix, in our construction, each of the rest \(MOLS(s)+1\) MUBs will have at least \(s(s-1)\) free parameters, that cannot be absorbed by a global unitary operation. In comparison to Goyeneche et al.’s paper (2015), our result produces larger number of MUBs as well as free parameters in most of the cases. This can help in exploring various choices of MUBs in the protocols for higher dimensional QKDs and other applications of MUBs related to quantum information.