Entropic uncertainty relations for Markovian and non-Markovian processes under a structured bosonic reservoir

Abstract

The uncertainty relation is a fundamental limit in quantum mechanics and is of great importance to quantum information processing as it relates to quantum precision measurement. Due to interactions with the surrounding environment, a quantum system will unavoidably suffer from decoherence. Here, we investigate the dynamic behaviors of the entropic uncertainty relation of an atom-cavity interacting system under a bosonic reservoir during the crossover between Markovian and non-Markovian regimes. Specifically, we explore the dynamic behavior of the entropic uncertainty relation for a pair of incompatible observables under the reservoir-induced atomic decay effect both with and without quantum memory. We find that the uncertainty dramatically depends on both the atom-cavity and the cavity-reservoir interactions, as well as the correlation time, τ, of the structured reservoir. Furthermore, we verify that the uncertainty is anti-correlated with the purity of the state of the observed qubit-system. We also propose a remarkably simple and efficient way to reduce the uncertainty by utilizing quantum weak measurement reversal. Therefore our work offers a new insight into the uncertainty dynamics for multi-component measurements within an open system, and is thus important for quantum precision measurements.

Dynamical Measurement's Uncertainty in the Curved Space‐Time

“…[29,30] Additionally, some authors have made many efforts to improve the lower bounds in, [31][32][33][34][35][36] and the uncertainty inequality has been expanded to multipartite systems [37,38] and the stronger entropic uncertainty relations for multiple measurements have been reported. [40][41][42][43][44][45][46][47] Besides, there are also some investigations on the dynamics of QMA-EUR under the noninertial system [48] and the solid-state system. Based on this consideration, it is in demand to understand how the decoherence or dissipation influences the dynamics of the measurement uncertainty.…”

Quantum‐Memory‐Assisted Entropic Uncertainty Relations

“…Wang et al . studied the dynamics of the entropic uncertainty without a quantum memory in the structured reservoir when a qubit undergoes a crossover of non‐Markovian and Markovian regimes.…”

The Entropic Uncertainty Relation for Two Qubits in the Cavity‐Based Architecture

“…In general, the higher ξ corresponds to higher mixedness or lesser purity of . The underlying physics for the dynamical evolution of uncertainty was analyzed in recent works, where the increase of mixedness ξ is considered to result in the enhancement of uncertainty, and vice versa. However, an unusual relation is found in ref.…”

“…Therefore, it is of great importance to address the roles of various decoherence effects in EUR. Recently, more attention has been devoted to explore the dynamical behaviors of QMA‐EUR for the open quantum systems . For instance, Xu et al .…”

“…So far, to our best knowledge, few works have been presented for the dynamical evolution of QMA‐EUR in the hierarchical environment, although it is an important and open topic deserving investigation. Motivated by current studies, we in this paper investigate the dynamics of QMA‐EUR for two noninteracting qubits, each of which is locally embedded in one of two coupled lossy cavities.…”