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Physica Scripta

Exploration of entropic uncertainty bound in a symmetric multi-qubit system under noisy channels

Mohammad Reza Pourkarimi, Saeed Haddadi, Soroush Haseli

Published Oct 27, 2020• 24 citations
Publisher

Abstract

Abstract Considering one of the particles as a quantum memory in a bipartite system can remarkably improve the measurement accuracy for two incompatible observables. Herein, we study quantum-memory-assisted entropic uncertainty bound for an arbitrary two-qubit X-state, and then we get a clear formula as the entropic uncertainty bound. In the following, we examine analytically and numerically the dynamics of entropic uncertainty bound in a symmetric multi-qubit system under four types of noisy channels, i.e. phase-flip, amplitude damping, phase-damping, and depolarizing channels. Our results show that the entropic uncertainty bound dynamics is related to the number of particles and especially the noise channel used. Noteworthy, our remarks reveal that under the amplitude damping channel, the entropic uncertainty bound can be suppressed during the time. It turns out that under an amplitude damping channel, these results can be important in practical goals where the minimum uncertainty is required such as quantum computation.

DOI
10.1088/1402-4896/abc505

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Abstract Considering one of the particles as a quantum memory in a bipartite system can remarkably improve the measurement accuracy for two incompatible observables. Herein, we study quantum-memory-assisted entropic uncertainty bound for an arbitrary two-qubit X-state, and then we get a clear formula as the entropic uncertainty bound. In the following, we examine analytically and numerically the dynamics of entropic uncertainty bound in a symmetric multi-qubit system under four types of noisy channels, i.e. phase-flip, amplitude damping, phase-damping, and depolarizing channels. Our results show that the entropic uncertainty bound dynamics is related to the number of particles and especially the noise channel used. Noteworthy, our remarks reveal that under the amplitude damping channel, the entropic uncertainty bound can be suppressed during the time. It turns out that under an amplitude damping channel, these results can be important in practical goals where the minimum uncertainty is required such as quantum computation.
Recently, Xu et al. [Phys. Rev. A 2012, 86, 012113] have explored the behaviour of the entropic uncertainty relation under the influence of local unital and nonunital noisy channels for a class of Bell-diagonal states. We here improve 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 (nonunital channel), phase-damping and depolarizing channels (unital channels) have been taken into account. Analytical or numerical results is presented. The effect of channels with memory on dynamics of the entropic uncertainty (or its lower bound) has been discussed in detail. Compare with previous results, our results show that, the entropic uncertainty (or its lower bound) 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 in the presence of memory. Especially, in the limit of μ→1, the entropic uncertainty (or its lower bound) could be well protected and immune to decoherence of channels.
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 μμμ increasing, however they will be only reduced under phase-damping and depolarizing channels with memory. Especially, in the limit of μ→1μ\rightarrow1μ→1, 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.
Abstract The uncertainty principle is an inherent characteristic of quantum mechanics. This principle can be formulated in various forms. Fundamentally, this principle can be expressed in terms of the standard deviation of the measured observables. In quantum information theory, the preferred mathematical quantity to express the entropic uncertainty relation is Shannon’s entropy. In this work, we consider the generalized entropic uncertainty relation in which there is an additional particle as a quantum memory. Alice measures on her particle A and Bob, with memory particle B , predicts Alice’s measurement outcomes. It has a wide range of applications, for example, entanglement witnessing and quantum key distribution. We study the effects of the environment on the entropic uncertainty lower bound in the presence of weak measurement and measurement reversal. The dynamical model that is intended in this work is as follows: first the weak measurement is performed, second, the decoherence affects the system and finally the measurement reversal is performed on the quantum system. Here, we consider the generalized amplitude damping channel and depolarizing channel as environmental noises. We will show that in the presence of weak measurement and measurement reversal, despite the presence of environmental factors, the entropic uncertainty lower bound drops to an optimal minimum value. In fact, weak measurement and measurement reversal enhance the quantum correlation between the subsystems A and B , and thus the uncertainty of Bob regarding Alice’s measurement outcomes reduces. Based on the entropic uncertainty relation, one can also show that the weak measurement and measurement reversal can preserve the quantum secret key rate lower bound from decoherence.
Abstract Quantum objects are susceptible to noise from their surrounding environments, interaction with which inevitably gives rise to quantum decoherence or dissipation effects. In this work, we examine how different types of local noise under an open system affect entropic uncertainty relations for two incompatible measurements. Explicitly, we observe the dynamics of the entropic uncertainty in the presence of quantum memory under two canonical categories of noisy environments: unital (phase flip) and nonunital (amplitude damping). Our study shows that the measurement uncertainty exhibits a non-monotonic dynamical behavior—that is, the amount of the uncertainty will first inflate, and subsequently decrease, with the growth of decoherence strengths in the two channels. In contrast, the uncertainty decreases monotonically with the growth of the purity of the initial state shared in prior. In order to reduce the measurement uncertainty in noisy environments, we put forward a remarkably effective strategy to steer the magnitude of uncertainty by means of a local non-unitary operation (i.e. weak measurement) on the qubit of interest. It turns out that this non-unitary operation can greatly reduce the entropic uncertainty, upon tuning the operation strength. Our investigations might thereby offer an insight into the dynamics and steering of entropic uncertainty in open systems.
The measurement outcomes of two incompatible observables on a particle can be precisely predicted when it is maximally entangled with a quantum memory. In this work, we explore the behavior of the quantum-memory-assisted entropic uncertainty relation under the influence of local unital and nonunital noisy channels. For a class of Bell-diagonal states, we demonstrate that while the unital noises only increase the amount of uncertainty, the amplitude-damping nonunital noises may reduce the amount of uncertainty in the long-time limit. The mechanism behind this phenomenon is also explored by using two dissimilar methods.
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.