Controlling entropic uncertainty bound through memory effects

Abstract

One of the defining traits of quantum mechanics is the uncertainty principle which was originally expressed in terms of the standard deviation of two observables. Alternatively, it can be formulated using entropic measures, and can also be generalized by including a memory particle that is entangled with the particle to be measured. Here we consider a realistic scenario where the memory particle is an open system interacting with an external environment. Through the relation of conditional entropy to mutual information, we provide a link between memory effects and the rate of change of conditional entropy controlling the lower bound of the entropic uncertainty relation. Our treatment reveals that the memory effects stemming from the non-Markovian nature of quantum dynamical maps directly control the lower bound of the entropic uncertainty relation in a general way, independently of the specific type of interaction between the memory particle and its environment.

5 pages, 3 figures

References in corpus (4)

• Quantum information can be negative
• Enhanced quantum entanglement in the non-Markovian dynamics of biomolecular excitons
• Non-Markovianity through flow of information between a system and an environment
• Quantum-memory-assisted entropic uncertainty principle under noise

Cited by in corpus (13)

• Entropic Uncertainty Relations and their Applications
• Quantum-memory-assisted entropic uncertainty relations
• Entropic uncertainty relations for Markovian and non-Markovian processes under a structured bosonic reservoir
• Dynamical decoupling efficiency versus quantum non-Markovianity
• Reducing the entropic uncertainty lower bound in the presence of quantum memory via local operation and classical communication
• Estimating the degree of non-Markovianity using machine learning
• Continuous-time quantum walk on spatially correlated noisy lattices
• Inequivalence of Correlation-based Measures of Non-Markovianity
• Bose-Hubbard lattice as a controllable environment for open quantum systems
• Memory in quantum processes with indefinite time direction and causal order
• The role of the total entropy production in dynamics of open quantum systems in detection of non-Markovianity
• The role of interparticle interaction and environmental coupling in a two-particle open quantum system
• Entropic uncertainty under indefinite causal order and input-output direction