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.
Highlights
The uncertainty principle, originally proposed by Heisenberg[1], is a fascinating aspect of quantum mechanics
In the presence of memory effects the evolution of the atom system is determined by the strength of the cavity and the structured reservoir
In the absence of memory effects, we numerically verified that the amount of entropic uncertainty relation (EUR) is correlated with the coupling strengths of the atom-cavity and the cavity-reservoir
Summary
The uncertainty principle, originally proposed by Heisenberg[1], is a fascinating aspect of quantum mechanics. It sets a bound to the precision for simultaneous measurements regarding a pair of incompatible observables, e.g. position (x) and momentum (p). The uncertainty principle was generalized, by Kennard[2] and Robertson[3] as applying to an arbitrary pair of non-commuting observables (say ˆ and ˆ ) where the standard deviation is given as. The standard deviation in Robertson’s relation is not always an optimal measurement for the uncertainty as the right-hand side of the relation depends on the state ρ of the system, which will lead to a trivial bound if the operators ˆ and ˆ do not commute. Backflow for any pair of non-degenerate observables ˆ and ˆ in terms of Shannon entropy, i.e. the so-called entropic uncertainty relation (EUR). Kraus[5], as well as Maassen and Uffink[6] made a significant improvement by refining Deutsch’s result to
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