Entropic uncertainty relation for pointer-based simultaneous measurements of conjugate observables

Abstract

We present a family of entropic uncertainty relations for pointer-based simultaneous measurements of conjugate observables. The lower bounds of these relations explicitly incorporate the influence of the measurement apparatus. We achieve this by using a mathematical theorem which states that the information entropy of convoluted probability distributions is bound from below. As a consequence of these results we can straightforwardly show that appropriately squeezed states are minimal entropy states for simultaneous measurements.

References in corpus (1)

• Formulation of the uncertainty relations in terms of the Renyi entropies

Cited by in corpus (2)

• Pointer-based simultaneous measurements of conjugate observables in a thermal environment
• Entropic uncertainty bound for open pointer-based simultaneous measurements of conjugate observables