Unsharpness of generalized measurement and its effects in entropic uncertainty relations

Abstract

Under the scenario of generalized measurements, it can be questioned how much of quantum uncertainty can be attributed to measuring device, independent of the uncertainty in the measured system. On the course to answer the question, we suggest a new class of entropic uncertainty relation that differentiates quantum uncertainty from device imperfection due to the unsharpness of measurement. In order to quantify the unsharpness, we {suggest} and analyze the quantity that characterizes the uncertainty in the measuring device, based on Shannon entropy. Using the quantity, we obtain a new lower bound of entropic uncertainty with unsharpness and it has been shown that the relation can also be obtained under the scenario that sharp observables are affected by the white noise and amplitude damping.

12 pages, 5 figures

References in corpus (4)

• Heisenberg's Uncertainty Principle
• Joint measurability of generalized measurements implies classicality
• Notes on Joint Measurability of Quantum Observables
• Joint measurability, steering and entropic uncertainty

Cited by in corpus (5)

• A complete and operational resource theory of measurement sharpness
• Entropic uncertainty relations for successive generalized measurements
• Quantifying unsharpness of observables in an outcome-independent way
• Entropic Uncertainty Relations via Direct-Sum Majorization Relation for Generalized Measurements
• Measurement sharpness and disturbance tradeoff