The uncertainty principle limits the ability for observer to precisely measure two incompatible observables, and plays a crucial role in quantum precision measurement in the quantum information science. When quantum systems interact with their surroundings, they inevitably result in decoherence, which increases the uncertainty of the system. In the process of quantum information processing, the effective regulation of uncertainty becomes a key problem that needs to be solved. In this work, we investigate the quantum-memory-assisted entropic uncertainty relation of a two-qubit system under correlated channels with dephasing colored noise. We demonstrate that it is possible to control the entropic uncertainty, U, and its lower bound, Ub, by combining correlations between successive uses of channels and the non-Markovianity of the dynamical evolution. Firstly, the evolutionary characteristics of the trace distance are employed to distinguish between Markovianity and non-Markovianity of the channel. Subsequently, the system is selected to be either a maximally entangled state or separated state initially. By adjusting the strength η of the correlations, we find that with the increase of η, the entropic uncertainty and its lower bound decrease. Especially, if the channel is fully correlated (η = 1), the entropic uncertainty and its lower bound remain constant under the channel, indicating that decoherence is completely suppressed. A comparison of Markovian channel with non-Markovian channel reveals that the entropic uncertainty and its lower bound exhibit oscillatory behaviour under non-Markovian channels. The combination of correlations and non-Markovianity of the channel demonstrates that the entropic uncertainty and its lower bound can be reduced under fully correlated channels where the non-Markovianity has no effect. This is because fully correlated channels suppress decoherence to a greatest extent. Under partially correlated channels, the combination of correlations and non-Markovianity can more effectively reduce the entropic uncertainty and its lower bound. Under such channels, correlations of the channel reduce the entropic uncertainty and its lower bound during the whole evolution, while the non-Markovianity contributes to their oscillations and reduce them in some specific time. Furthermore, the results show that the entropic uncertainty and its lower bound reach steady values that depend only on the strength of the correlations after long-time evolution. In other words, the stronger the correlations, the lower the entropy uncertainty and its lower bound of steady states will be. Finally, we analyse the physical nature of the decrease of the entropic uncertainty and its lower bound, and it is found that the decrease of the entropic uncertainty and its lower bound originate from the increase of the quantum correlations in the system.The uncertainty principle limits the ability for observer to precisely measure two incompatible observables, and plays a crucial role in quantum precision measurement in the quantum information science. When quantum systems interact with their surroundings, they inevitably result in decoherence, which increases the uncertainty of the system. In the process of quantum information processing, the effective regulation of uncertainty becomes a key problem that needs to be solved. In this work, we investigate the quantum-memory-assisted entropic uncertainty relation of a two-qubit system under correlated channels with dephasing colored noise. We demonstrate that it is possible to control the entropic uncertainty, U, and its lower bound, Ub, by combining correlations between successive uses of channels and the non-Markovianity of the dynamical evolution. Firstly, the evolutionary characteristics of the trace distance are employed to distinguish between Markovianity and non-Markovianity of the channel. Subsequently, the system is selected to be either a maximally entangled state or separated state initially. By adjusting the strength η of the correlations, we find that with the increase of η, the entropic uncertainty and its lower bound decrease. Especially, if the channel is fully correlated (η = 1), the entropic uncertainty and its lower bound remain constant under the channel, indicating that decoherence is completely suppressed. A comparison of Markovian channel with non-Markovian channel reveals that the entropic uncertainty and its lower bound exhibit oscillatory behaviour under non-Markovian channels. The combination of correlations and non-Markovianity of the channel demonstrates that the entropic uncertainty and its lower bound can be reduced under fully correlated channels where the non-Markovianity has no effect. This is because fully correlated channels suppress decoherence to a greatest extent. Under partially correlated channels, the combination of correlations and non-Markovianity can more effectively reduce the entropic uncertainty and its lower bound. Under such channels, correlations of the channel reduce the entropic uncertainty and its lower bound during the whole evolution, while the non-Markovianity contributes to their oscillations and reduce them in some specific time. Furthermore, the results show that the entropic uncertainty and its lower bound reach steady values that depend only on the strength of the correlations after long-time evolution. In other words, the stronger the correlations, the lower the entropy uncertainty and its lower bound of steady states will be. Finally, we analyse the physical nature of the decrease of the entropic uncertainty and its lower bound, and it is found that the decrease of the entropic uncertainty and its lower bound originate from the increase of the quantum correlations in the system.

Acta Physica SinicaJan 1, 20240 citations

The quantum uncertainty relations of quantum channels

Shi-Yun Kong, Ming‐Jing Zhao, Zhi‐Xi Wang +1 more

arXiv:2408.09082Quantum Information ProcessingAug 16, 20241 citation

The uncertainty of quantum channels in terms of variance

Yuan Sun, Nan Li

Quantum Information ProcessingJan 1, 202126 citations

Entropic uncertainty relation under quantum channels with memory

You-neng Guo, Mao-Fa Fang, Zeng, Ke

Recently, Xu et al. [Phys. Rev. A 86, 012113(2012)] explored the behavior of the entropic uncertainty relation under the influence of local unital and nonunital noisy channels for a class of Bell-diagonal states. We here reform their results and investigate the entropic uncertainty relation under the influence of unital and nonunital noisy channels with memory. Different types of noisy channels with memory, such as amplitude damping channel(nonunitary), phase-damping and depolarizing channels(unitary) have been taken into account. Some analytical or numerical results are presented. The effect of channels with memory on dynamics of the entropic uncertainties (or their lower bounds) has been discussed in detail. Compare with previous results, our results show that, the entropic uncertainties (or their lower bounds) subjecting to amplitude damping channel with memory will be reduced at first and then be lifted with the memory coefficient of channel $μ$ increasing, however they will be only reduced under phase-damping and depolarizing channels with memory. Especially, in the limit of $μ\rightarrow1$ , the entropic uncertainties (or their lower bounds) could be well protected and immune to decoherence of channle. Moreover, the mechanism behind these phenomena are also explored by using the purity of state.Recently, Xu et al. [Phys. Rev. A 86, 012113(2012)] explored the behavior of the entropic uncertainty relation under the influence of local unital and nonunital noisy channels for a class of Bell-diagonal states. We here reform their results and investigate the entropic uncertainty relation under the influence of unital and nonunital noisy channels with memory. Different types of noisy channels with memory, such as amplitude damping channel(nonunitary), phase-damping and depolarizing channels(unitary) have been taken into account. Some analytical or numerical results are presented. The effect of channels with memory on dynamics of the entropic uncertainties (or their lower bounds) has been discussed in detail. Compare with previous results, our results show that, the entropic uncertainties (or their lower bounds) subjecting to amplitude damping channel with memory will be reduced at first and then be lifted with the memory coefficient of channel $μ$ increasing, however they will be only reduced under phase-damping and depolarizing channels with memory. Especially, in the limit of $μ\rightarrow1$, the entropic uncertainties (or their lower bounds) could be well protected and immune to decoherence of channle. Moreover, the mechanism behind these phenomena are also explored by using the purity of state.

arXiv:1710.06344Oct 17, 20171 citation

Entropic uncertainty relation for qubits

G. M. Bosyk, M. Portesi, Steeve Zozor

Aug 5, 20130 citations

μ

increasing, however they will be only reduced under phase-damping and depolarizing channels with memory. Especially, in the limit of

μ\rightarrow1

, the entropic uncertainties (or their lower bounds) could be well protected and immune to decoherence of channle. Moreover, the mechanism behind these phenomena are also explored by using the purity of state.