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MON: Monday Contributed Sessions

MON 7: Foundational / Mathematical Aspects – Quantum Measurement

MON 7.5: Talk

Monday, September 8, 2025, 15:15–15:30, ZHG008

Quantifying quantum coherence and the deviation from the total probability formula — •Antoine Soulas — IQOQI Vienna, Austria

Quantum coherence is the main resource exploited by quantum computers. Unsurprisingly, over the past few years, there has been a strong interest in the task of finding appropriate measures of coherence. We propose a novel approach which, contrary to the previous ones, relies on foundational/philosophical considerations. It allows to solve two drawbacks of the resource theoretic approach: the lack of physical meaning, and the restriction to one particular basis in which to quantify coherence. In our approach, coherence is understood as the ability for a quantum system's statistics to deviate from the total probability formula.

After motivatng the importance of the total probability formula in quantum foundations, we then propose a new set of axioms that a measure of coherence should satisfy, and show that it defines a class of measures different from the previous proposals. Finally, we prove a general result about the dependence of the l2-coherence norm on the basis of interest, namely that it is well approximated by the square root of the purity in most bases. Such a behaviour (the nearly constant level of coherence in most bases) is actually expected for any measure of coherence, because of the mathematical phenomenon known as "concentration of measure".

Keywords: Quantum coherence; Quantum information theory; Philosophy of physics; Mathematical physics