Experimental Test of Information-Theoretic Measurement Uncertainty Relation for general Qubit Observables

In our latest neutron optical experiment ¹ we test the joint-measurement noise trade-off for variouse Pauli observables by implementing four-outcome positive-operator valued measure POVMs. Our results confirm that POVM measurements outperform projective ones and allow for an experimentally saturation of a tight qubit uncertainty relation. Below an illustration of the applied four output POVM expressed as , where , and the are unit vectors on the Bloch sphere parametrized by the spherical coordinates with . For the POVM reduces to a single projective spin measurement along the direction , which is depicted below. On the other hand for a value of between and it corresponds to a mixture of projective measurements along the directions and with probabilities and . See here for details of our experiment. Our new results are now published in New Journal of Physics ¹ .

The final results are that we have   being non-convex, more precisely  . Here, the projective measurement is clearly suboptimal. The optimal values are obtained via POVMs with different  values measured along directions starting from  () and (). The shaded noise-noise regions are split in two areas: The orange area indicates values that cain only be obtained by POVMs. The purple area can be reached by projective measurements. Blue data points are measured in the -plane starting from () and increasing in steps of along  . Finally the purple points are obtained by projective measurements  out of the -plane by increasing the azimuthal angle .

1. Bülent Demirel, Stephan Sponar, Alastair A. Abbott, Cyril Branciard, and Yuji Hasegawa, New J. Phys 21,013038 (2019). ↩