Abstract In this paper, we have performed a detailed investigation of the dynamics of the entropic uncertainty relation for a qutrit with and without a memory system under an amplitude damping channel at finite temperature. We focus mainly on how the temperature affects the entropic uncertainty relation. The results show that the dynamics of the entropic uncertainty exhibits a non-monotonic phenomenon. As r increases ( r is usually a function of temperature), the amount of the entropic uncertainty will first increase and then subsequently decrease. Moreover, based on measurement reversal from a weak measurement, we have also investigated the reduction of the entropic uncertainty for a qutrit system under decoherence. It has been found that the measurement reversal technique can always reduce the entropic uncertainty effectively at finite temperature, while the prior weak measurement technique is valid only at a lower temperature but fails at a higher channel temperature. Finally, a phenomenological explanation of our results is also presented.
Abstract In this paper, we have performed a detailed investigation of the dynamics of the entropic uncertainty relation for a qutrit with and without a memory system under an amplitude damping channel at finite temperature. We focus mainly on how the temperature affects the entropic uncertainty relation. The results show that the dynamics of the entropic uncertainty exhibits a non-monotonic phenomenon. As r increases ( r is usually a function of temperature), the amount of the entropic uncertainty will first increase and then subsequently decrease. Moreover, based on measurement reversal from a weak measurement, we have also investigated the reduction of the entropic uncertainty for a qutrit system under decoherence. It has been found that the measurement reversal technique can always reduce the entropic uncertainty effectively at finite temperature, while the prior weak measurement technique is valid only at a lower temperature but fails at a higher channel temperature. Finally, a phenomenological explanation of our results is also presented.
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.
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.
High-dimensional quantum system plays an important role in quantum information tasks. However, the interaction between quantum system and environment would give rise to decoherence. In this paper, we examine the quantum-memory-assisted entropic uncertainty relation under amplitude damping (AD) decoherence. It is found that entropic uncertainty first inflates and then reduces to a nonzero value with the growing decoherence strength. In addition, it is revealed that the mixedness is not closely associated with entropic uncertainty which is different from the previous result. Furthermore, we construct a remarkably effective filtering operator to steer and reduce the entropic uncertainty. Our exploration might offer fresh insights into the dynamics and manipulation of the entropic uncertainty in high-dimensional quantum system.
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→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.
Because realistic quantum systems inevitably interact with their surroundings, understanding how environmental factors affect the entropic uncertainty relation remains a major challenge. In this work, we analyze how ambient temperature impacts the lower bound of the memory-assisted entropic uncertainty relation. We model the coupling between the system and its thermal environment using a generalized amplitude damping channel, featuring temperature-dependent parameters. Notably, we find that the uncertainty lower bound drops when the damping parameter (r) decreases, and rises when it increases. By contrast, shifting the parameter) p (yields much smaller variations. This stark difference highlights our main novel finding: in a finite-temperature environment, the lower bound of the entropic uncertainty relation is significantly more sensitive to the damping parameter (r) than to (p). Ultimately, these results offer a clearer look at how thermal reservoirs influence open quantum systems and affect practical quantum information processing.
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.