• DOI:10.1007/s11005-021-01434-w
• Corpus ID: 235592755

Schmidt rank constraints in quantum information theory

@inproceedings{Cariello2021SchmidtRC,
  title={Schmidt rank constraints in quantum information theory},
  author={Daniel Cariello},
  year={2021}
}

• D. Cariello
• Published 8 April 2020
• Computer Science, Mathematics

Abstract. Can vectors with low Schmidt rank form mutually unbiased bases? Can vectors with high Schmidt rank form positive under partial transpose states? In this work, we address these questions by presenting several new results related to Schmidt rank constraints and their compatibility with other properties. We provide an upper bound on the number of mutually unbiased bases of Cm ⊗ Cn (m ≤ n) formed by vectors with low Schmidt rank. In particular, the number of mutually unbiased product bases of Cm ⊗ Cn cannot exceed m + 1, which solves a conjecture proposed by McNulty et al. Then we show how to create a positive under partial transpose entangled state from any state supported on the antisymmetric space and how their Schmidt numbers are exactly related. Finally, we show that the Schmidt number of operator Schmidt rank 3 states of Mm ⊗Mn (m ≤ n) that are invariant under left partial transpose cannot exceed m− 2.