Resolvable Block Designs in Construction of Approximate Real MUBs that are Sparse

Ajeet Kumar; Subhamoy Maitra

Paper 2021/901

Resolvable Block Designs in Construction of Approximate Real MUBs that are Sparse

Ajeet Kumar and Subhamoy Maitra

Abstract

Several constructions of Mutually Unbiased Bases (MUBs) borrow tools from combinatorial objects. In this paper we focus how one can construct Approximate Real MUBs (ARMUBs) with improved parameters using results from the domain of Resolvable Block Designs (RBDs). We first explain the generic idea of our strategy in relating the RBDs with MUBs/ARMUBs, which are sparse (the basis vectors have small number of non-zero co-ordinates). Then specific parameters are presented, for which we can obtain new classes and improve the existing results. To be specific, we present an infinite family of many ARMUBs for dimension , where and it is a prime power, such that for any two vectors belonging to different bases, . We also demonstrate certain cases, such as , where is a prime power and . These findings subsume and improve our earlier results in [Cryptogr. Commun. 13, 321-329, January 2021]. This present construction idea provides several infinite families of such objects, not known in the literature, which can find efficient applications in quantum information processing for the sparsity, apart from suggesting that parallel classes of RBDs are intimately linked with MUBs/ARMUBs.

Metadata

Available format(s): PDF
Category: Foundations
Publication info: Preprint. MINOR revision.
Keywords: (Approximate Real) Mutually Unbiased Bases Combinatorial Design Cryptology Hadamard Matrices Quantum Information Theory Resolvable Block Design.
Contact author(s): subho @ isical ac in
History: 2021-07-05: received
Short URL: https://ia.cr/2021/901
License: CC BY

BibTeX

@misc{cryptoeprint:2021/901,
      author = {Ajeet Kumar and Subhamoy Maitra},
      title = {Resolvable Block Designs in Construction of Approximate Real {MUBs} that are Sparse},
      howpublished = {Cryptology {ePrint} Archive, Paper 2021/901},
      year = {2021},
      url = {https://eprint.iacr.org/2021/901}
}