Details

Autor(en) / Beteiligte

• Mitra, Arindam

Titel

Quantifying Unsharpness of Observables in an Outcome-Independent way

Ist Teil von

• International journal of theoretical physics, 2022-09, Vol.61 (9), Article 236

Ort / Verlag

New York: Springer US

Erscheinungsjahr

2022

Link zum Volltext

Quelle

SpringerLink

Beschreibungen/Notizen

• Recently, in the paper (Liu and Luo, Phys. Rev. A 104 , 052227, 2021) a very beautiful measure of the unsharpness (fuzziness) of the observables constructed via uncertainty is discussed. This measure does not depend on the values of the outcomes and can measure the intrinsic unsharpness of the observables. In this work, we also quantify the unsharpness of observables in an outcome-independent way. But our approach is operationally motivated and different than the approach of the paper (Liu and Luo, Phys. Rev. A 104 , 052227, 2021). In this work, at first, we construct two Lüders instrument-based unsharpness measures and provide the tight upper bounds of those measures. Then we prove the monotonicity of our proposed measures under a class of fuzzifying processes (processes that make the observables more fuzzy). This is consistent with the resource-theoretic framework. Then we relate our approach to the approach of the paper (Liu and Luo, Phys. Rev. A 104 , 052227, 2021). Next, we try to construct two instrument-independent unsharpness measures. In particular, we define two instrument-independent unsharpness measures and provide the tight upper bounds of those measures and then we derive the condition for the monotonicity of those measures under a class of fuzzifying processes and prove the monotonicity for dichotomic qubit observables. Then we show that for an unknown measurement, the values of all of these measures can be determined experimentally. Finally, we present the idea of the resource theory of the sharpness of the observables and discuss an example where the sharpness of the observables can be considered as a resource.