Quantum-memory-assisted entropic uncertainty principle under noise

TL;DR

This paper investigates how different types of noise affect the quantum-memory-assisted entropic uncertainty principle, revealing that unital noise increases uncertainty while nonunital noise can reduce it over time.

Contribution

It provides a detailed analysis of the impact of local noisy channels on the uncertainty relation, highlighting the contrasting effects of unital and nonunital noise.

Findings

Unital noise increases measurement uncertainty.

Nonunital amplitude-damping noise can decrease uncertainty over time.

Counterintuitive reduction of uncertainty explained by quantum correlations and information dynamics.

Abstract

The measurement outcomes of two incompatible observables on a particle can be precisely predicted when it is maximally entangled with a quantum memory, as quantified recently [Nature Phys. 6, 659 (2010)]. We explore the behavior of the uncertainty relation under the influence of local unital and nonunital noisy channels. While the unital noises only increase the amount of uncertainty, the amplitude-damping nonunital noises may amazingly reduce the amount of uncertainty in the long-time limit. This counterintuitive phenomenon could be justified by different competitive mechanisms between quantum correlations and the minimal missing information after local measurement.