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Frontiers of Physics

The uncertainty and quantum correlation of measurement in double quantum-dot systems

Long-Yu Cheng, Fei Ming, Fa Zhao, Ye Liu, Dong Wang

Published Aug 4, 2022• 10 citations
Publisher

Abstract

In this work, we study the entropic uncertainty and quantum discord in two double-quantum-dot (DQD) system coupled via a transmission line resonator (TLR). Explicitly, the dynamics of the systemic quantum correlation and measured uncertainty are analysed with respect to a general X-type state as the initial state. Interestingly, it is found that the different parameters, including the eigenvalue α of the coherent state, detuning amount δ , frequency ω and the coupling constant g , have subtle effects on the dynamics of the entropic uncertainty, such as the oscillation period of the uncertainty. It is clear to reveal that the quantum discord and the lower bound of the entropic uncertainty are anti-correlated when the initial state of the system is the Werner-type state, while quantum discord and the lower bound of the entropic uncertainty are not anti-correlated when the initial state of the system is the Bell-diagonal state. Thereby, we claim that the current investigation would provide an insight into the entropic uncertainty and quantum correlation in DQDs system, and are basically of importance to quantum precision measurement in practical quantum information processing.

DOI
10.1007/s11467-022-1178-x

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We explore the dynamical behaviors of the measurement uncertainty and quantum correlation for a vertical quantum-dot system in the presence of magnetic field, including electron-electron interaction and Coulomb-blocked systems. Stemming from the quantum-memory-assisted entropic uncertainty relation, the uncertainty of interest is associated with temperature and parameters related to the magnetic field. Interestingly, the temperature has two kinds of influences on the variation of measurement uncertainty with respect to the magnetic-field-related parameters. We also discuss the relation between the lower bound of Berta et al. and the quantum discord. It is found that there is a natural competition between the quantum discord and the entropy min Π i B S Π i B ( ρ A | B ) . Finally, we bring in two improved bounds to offer a more precise limit to the entropic uncertainty.
We study the dynamics of quantum coherence and quantum correlations in two semiconductor double-dot molecules separated by a distance and indirectly coupled via a transmission line resonator. Dominant dissipation processes are considered. The numerical results show the sudden death of entanglement and the robustness of quantum discord to sudden death. Furthermore, the results indicate the dephasing processes in our model can lead in the revival and decay of coherence and discord with the absence of entanglement for certain initial states. By observing the dynamics of coherence versus discord for different initial states, we find that the similarities and differences of coherence and discord are not only related to the dependance of discord on optimizing the measurement set, but more importantly to the coherences in individual qubits which are captured by the adopted coherence measure.
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.
Abstract We analyze the quantum correlations, the quantum-memory-assisted entropic uncertainty (QMA-EUR), and its lower bound in a quadruple quantum dot device for two charge qubits. Herein, we select incompatible Pauli operators σ ^ x and σ ^ z as a pair of observables of interest for the measurement of particle A, and the uncertainty can be predicted from the entanglement of particle A with quantum memory B . We explore the dynamics of quantum discord and QMA-EUR, taking into account the effects of electron temperature, energy offsets, tunneling coupling, and the strength of coupling (i.e., the Coulomb interaction between electrons). Interestingly, our results indicate that there are certain adjustable parameters that can be tuned to suppress the entropy uncertainty bound and enhance quantum correlations.
Abstract The uncertainty principle is one of the most comprehensive and fundamental concepts in quantum theory and it states that it is not possible to simultaneously measure two incompatible observables with high accuracy. In particular, we show that the entropic uncertainty relation that uses quantum memory is one of the most useful entropic uncertainty relations. In this work, we consider a quantum dot system as a solid-state system which is in the thermal regime, and we then probe the quantum correlations and the quantum-memory-assisted entropic uncertainty bound in this type of system. Interestingly, our results show that there are some system parameters that can be adjusted to suppress the entropic uncertainty bound and improve quantum correlations.
Abstract In this work, we investigate the dynamics of quantum-memory-assisted entropic uncertainty relation (EUR) and quantum correlation quantified by entropic discord and geometric discord within the Markovian reservoir and non-Markovian reservoir. Particularly, when the initial state is a pure sate or mixed state the EUR gradually increases during the evolution at first, but subsequently tends to stable in the long-time limit. On other hand, for the separable state the EUR almost keeps constant. In contrast, quantum discord decay asymptotically to zero for all types of initial states. As an application, we prove that both two quantum discords witnessed by the EUR are determined by the version of discord chosen, which regardless of the reservoir.