Experimental test of entropic noise-disturbance uncertainty relations for three-outcome qubit measurements

In our latest work ¹, we experimentally tested a tight information-theoretic measurement uncertainty relation, in terms of a proposed three-outcome POVM using neutron spin-1/2 qubits. Previously we reported a tight noise-disturbance uncertainty relation for projective qubit measurements ². Meanwhile, new theoretical analysis ³ predicts that projective measurements suboptimal, with respect to the noise-disturbance trade-offs, compared to generalized (or unsharp) measurements (see here for theoretical details). We developed a new experimental technique to realize general measurements, more precisely a three-outcome positive-operator valued measure (POVM), allowing to test the suboptimal nature of projective measurements regarding noise- disturbance uncertainty realtions. In the present manuscript we provide experimental evidence that when performing such general measurements, on a qubit system (in our case a neutron spin), tighter bounds of the noise-disturbance trade-offs are observed compared to projective measurements. This advantage of POVMs over projective measurements on noise-disturbance uncertainty relations has not previously been observed experimentally (see here for details of the experiment and more results).

1. S. Sponar, A. Danner, V. Pecile, N. Einsidler, B. Demirel, and Y. Hasegawa Phys. Rev. Research 3, 023175 (2021). ↩

2. G. Sulyok, S. Sponar, B. Demirel, F. Buscemi, M. J. W. Hall, M. Ozawa, and Y. Hasegawa Phys. Rev. A 115, 030401 (2016). ↩

3. A. A. Abbott and C. Branciard, Phys. Rev. A 94, 062110 (2016). ↩