Maximally non-projective measurements are not always symmetric informationally complete

• URL: http://arxiv.org/abs/2508.03652v1
• Date: Tue, 05 Aug 2025 17:01:03 GMT
• Title: Maximally non-projective measurements are not always symmetric informationally complete
• Authors: Gabriele Cobucci, Raphael Brinster, Shishir Khandelwal, Hermann Kampermann, Dagmar Bruß, Nikolai Wyderka, Armin Tavakoli,
• Abstract summary: Most well-known class of non-projective measurements is called symmetric informationally complete (SIC)<n>We show that beyond qubit systems, the SIC property is in general not associated with the most non-projective measurement.<n>This method allows us to determine quantitative simulability thresholds for generic POVMs and to put forward a conjecture on which qutrit and ququart measurements are most strongly non-projective.
• Score: 8.883278455726012
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Whereas standard quantum measurements are projective, the most general notion of a measurement is represented by positive operator-valued measures (POVMs). It is therefore natural to consider how accurately an experimenter with access only to projective measurements and classical processing can simulate POVMs. The most well-known class of non-projective measurements is called symmetric informationally complete (SIC). Such measurements are both ubiquitous in the broader scope of quantum information theory and known to be the most strongly non-projective measurements in qubit systems. Here, we show that beyond qubit systems, the SIC property is in general not associated with the most non-projective measurement. For this, we put forward a semidefinite programming criterion for detecting genuinely non-projective measurements. This method allows us to determine quantitative simulability thresholds for generic POVMs and to put forward a conjecture on which qutrit and ququart measurements that are most strongly non-projective.

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