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<p>GSIC POVMs and MUMs serve as generalizations of symmetric informationally complete (SIC) POVMs and mutually unbiased bases (MUBs), respectively. Both GSIC POVMs and MUMs are suitable for linear quantum state tomography. In this work, we investigate the relationship between GSIC POVMs and MUMs by employing mutually unbiased striations (MUSs), and we present simple and conceptually transparent constructions of MUMs from GSIC POVMs, and vice versa. In these constructions, the efficiency parameter of MUMs is shown to be a monotonically increasing function of that of GSIC POVMs, and vice versa. Interestingly, SIC POVMs and MUBs are not only unnecessary but also excluded in certain constructions, underscoring the distinctive relationship between GSIC POVMs and MUMs revealed in this study.</p>

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Structural Relations Between General Symmetric Informationally Complete Positive Operator-valued Measures and Mutually Unbiased Measurements

  • 期刊论文

  • 发表日期：

    2025年11月5日

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  • Masakazu Yoshida,
  • Tsubasa Saishita,
  • Yuri Serikawa

摘要

GSIC POVMs and MUMs serve as generalizations of symmetric informationally complete (SIC) POVMs and mutually unbiased bases (MUBs), respectively. Both GSIC POVMs and MUMs are suitable for linear quantum state tomography. In this work, we investigate the relationship between GSIC POVMs and MUMs by employing mutually unbiased striations (MUSs), and we present simple and conceptually transparent constructions of MUMs from GSIC POVMs, and vice versa. In these constructions, the efficiency parameter of MUMs is shown to be a monotonically increasing function of that of GSIC POVMs, and vice versa. Interestingly, SIC POVMs and MUBs are not only unnecessary but also excluded in certain constructions, underscoring the distinctive relationship between GSIC POVMs and MUMs revealed in this study.