March 1, 2022
      
                  
        
  Author(s)
  Noah  Lupu-Gladstein,   Y. Batuhan  Yilmaz,   David  Arvidsson-Shukur,   Aharon  Brodutch,   Arthur  Pang,   Aephraim  Steinberg,   Nicole  Halpern
 
       
            
    
    
        Operator noncommutation, a hallmark of quantum theory, limits measurement precision, according to uncertainty principles. Wielded correctly, though, noncommutation can boost precision. A recent foundational result relates a metrological advantage with