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.
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.
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.
Within the framework of thermo-field-dynamics, we define the reduced probability densities, and investigate the sum of information-theoretic entropies in quantum mechanics associated with the measurements of the position and momentum of a particle surrounded by the thermal environment. It is found that this quantity cannot be made arbitrarily small but has a universal lower bound dependent on the temperature. We develop the finite-temperature variational technique for the reduced system, and show that this relation, termed the thermal information-entropic uncertainty relation, is exactly saturated by the thermal coherent state. We also show that the Heisenberg uncertainty relation at finite temperature can be derived from this relation.
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.
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.
The uncertainty principle is one of the most important issues that clarify the distinction between classical and quantum theory. This principle sets a bound on our ability to predict the measurement outcome of two incompatible observables precisely. Uncertainty principle can be formulated via Shannon entropies of the probability distributions of measurement outcome of the two observables. It has shown that the entopic uncertainty bound can be improved by considering an additional particle as the quantum memory B which has correlation with the measured particle A. In this work we consider the memory assisted entropic uncertainty for the case in which the quantum memory and measured particle are topological qubits. In our scenario the topological quantum memory B, is considered as an open quantum system which interacts with its surrounding. The motivation for this model is associated with the fact that the basis of the memory-assisted entropic uncertainty relation is constructed on the correlation between quantum memory B and measured particle A. In the sense that, Bob who holds the quantum memory B can predict Alice's measurement results on particle A more accurately, when the amount of correlation between A and B is great. Here, we want to find the influence of environmental effects on uncertainty bound while the quantum memory interacts with its surrounding. In this work we will consider Ohmic-like Fermionic and Bosonic environment. We have also investigate the effect of the Fermionic and Bosonic environment on the lower bounds of the amount of the key that can be extracted per state by Alice and Bob for quantum key distribution protocols.