Position-Momentum Uncertainty Relations in the Presence of Quantum Memory

Understand

A prominent formulation of the uncertainty principle identifies the fundamental quantum feature that no particle may be prepared with certain outcomes for both position and momentum measurements.

• Often the statistical uncertainties are thereby measured in terms of entropies providing a clear operational interpretation in information theory and cryptography.
• Recently, entropic uncertainty relations have been used to show that the uncertainty can be reduced in the presence of entanglement and to prove security of quantum cryptographic tasks.
• However, much of this recent progress has been focused on observables with only a finite number of outcomes not including Heisenberg's original setting of position and momentum observables.