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Physical Review A

Interplay between nonequilibrium and non-Markovianity in controlling the entropic uncertainty bound

Abdul Basit, Hamad Ali, Gao Xianlong, Fuli Li, Gehad Sadiek, Hichem Eleuch

Published Jul 9, 2024• 7 citations
Publisher

Abstract

The entropic uncertainty relation imposes a limit on the accuracy of measurement outcomes of two conjugate observables, which can be reduced in the presence of quantum memory. We theoretically study the dynamical behaviors of the quantum-memory-assisted entropic uncertainty relation for a bipartite system under local nonequilibrium dephasing environments and a common nonequilibrium dephasing environment. Particularly, we study the influence of the competition between nonequilibrium and non-Markovianity in controlling the entropic uncertainty bound (EUB) in weak- and strong-coupling regimes. We find that the nonequilibrium nature renders a promising protocol to efficiently harness the EUB in both regimes without requiring any operations on the main system. Further, we reveal that the EUB can be significantly reduced in a common bath case compared to the case of local baths. Moreover, we elucidate the primary factor responsible for governing the dynamical behaviors of EUB by examining the interplay between quantum discord and the minimal missing information about the particle to be measured. In addition, we investigate the state preparation and measurement choice (SPMC) condition in both environmental setups with weak- and strong-coupling regimes. Remarkably, we show that the SPMC condition does not hold in the common environment scenario.

DOI
10.1103/physreva.110.012429

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The entropic uncertainty relation imposes a limit on the accuracy of measurement outcomes of two conjugate observables, which can be reduced in the presence of quantum memory. We theoretically study the dynamical behaviors of the quantum-memory-assisted entropic uncertainty relation for a bipartite system under local nonequilibrium dephasing environments and a common nonequilibrium dephasing environment. Particularly, we study the influence of the competition between nonequilibrium and non-Markovianity in controlling the entropic uncertainty bound (EUB) in weak- and strong-coupling regimes. We find that the nonequilibrium nature renders a promising protocol to efficiently harness the EUB in both regimes without requiring any operations on the main system. Further, we reveal that the EUB can be significantly reduced in a common bath case compared to the case of local baths. Moreover, we elucidate the primary factor responsible for governing the dynamical behaviors of EUB by examining the interplay between quantum discord and the minimal missing information about the particle to be measured. In addition, we investigate the state preparation and measurement choice (SPMC) condition in both environmental setups with weak- and strong-coupling regimes. Remarkably, we show that the SPMC condition does not hold in the common environment scenario.
Abstract The uncertainty principle sets a fundamental bound on the precision of measurement outcomes of two incompatible observables, which can be reduced in the presence of quantum memory. In this work, we investigate the dynamics of entropic uncertainty bound (EUB) for a bipartite system, where only the quantum memory is exposed to a nonequilibrium dephasing environment with an Ohmic-class spectrum, which is compared with the thermal equilibrium case. The nonequilibrium feature is defined by a nonstationary random function which can be controlled by engineering the relative initial phases of the bath modes. We show that this model renders a promising avenue for significantly suppressing the maximum steady-state value of the EUB for all the Ohmic spectral densities. Furthermore, we unveil the role of the reservoir’s Ohmic spectrum and the interplay between quantum discord and minimal conditional entropy of the measured particle in reducing the EUB. Additionally, we examine the state preparation and measurement choice condition in the engineered nonequilibrium environment case. The condition persists, and the nonequilibrium feature serves as a promising tool to impose a stronger limit on entropic uncertainty, enabling more accurate measurement outcomes under decoherence.
The entropic uncertainty principle imposes a limit on how precisely two incompatible observables can be measured, which can be reduced when quantum memory is involved. We theoretically investigate the dynamics of the quantum-memory-assisted entropic uncertainty relation when either quantum memory alone or both the measured particle and the quantum memory interact with a squeezed-vacuum bath through energy-preserving interactions. We show that in both scenarios, the squeezing phase of the reservoir decreases the entropic uncertainty (EU), whereas the squeezing strength increases the EU. In addition, we find that EU can be significantly reduced when both the measured particle and quantum memory are subjected to a common squeezed-vacuum bath. Furthermore, we explore the key factors controlling the behavior of EU by exploring the competition between quantum discord and minimal missing information. Moreover, we examine the tightness of the entropic uncertainty bound (EUB) in both system-environment setups and observe that the EUB is less tight when both the measured particle and quantum memory are coupled to a common squeezed-vacuum bath.
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.
Abstract We address the dynamics of the lower bound of geometric quantum discord and quantum-memory-assisted entropic uncertainty in a two-qutrit system when exposed to classical channels characterized by power-law (PL) and random telegraph (RT) noises. The system-channel coupling strategy is examined in two contexts: common qutrit-environment (CQE) and different qutrit-environment (DQE) configurations. We show that the geometric quantum discord functions remain anti-correlated with entropic uncertainty and decline as uncertainty appears in the system. The rate of entropic uncertainty appearance seems more prevalent than the decline rate of quantum discord function, suggesting that uncertainty causes the quantum correlations to fade in quantum systems. We find that non-local correlations estimated by the lower bound of geometric quantum discord are not destroyed even at the maximum entropic disorder and entropic uncertainty. In addition, the efficacy of entropic uncertainty and the lower bound is strongly influenced by the state’s purity factor, with the former being more robust at higher purity values and the latter at lower purity values. All the parameters impact entropic uncertainty, however, the mixedness of the state is noticed to greatly alter the generation of quantum memory. Besides, PL noise caused Markovian behavioral dynamics, and the RT noise allowed non-Markovian dynamics, while the latter remains more resourceful for the quantum correlations preservation and entropic uncertainty suppression. We also demonstrate how to model longer quantum correlations and provide optimal parameter settings for suppressing the dephasing and entropic uncertainty effects.
The uncertainty of measurement on a quantum system can be reduced in presence of quantum memory [M. Berta et. al. Nature Phys. {\bf 6}, 659 (2010)]. By measurement on quantum memory, some information (non-classical information) is inaccessible, hence, it limits the lower bound of entropic uncertainty relation. In the present work, we improve the lower bound of entropic uncertainty relation in presence of quantum memory by considering inaccessibility of non classical correlation at Bob side and also compare the lower bound given by M. Berta et. al. and our prescription for two different kind of shared bipartite state.
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.