Abstract The uncertainty principle is one of the most remarkable features of quantum mechanics, originally expressed in terms of the standard deviation of two incompatible observables. Alternatively, it can be modified and written in the form of entropy to eliminate the defect in the form of standard deviation, and can also be generalized by including a memory particle that is entangled with the particle to be measured. Herein we consider a realistic scenario where the particle A to be measured is in an open environment and B as quantum memory is under an environment typically characterized by non-Markovian regimes. Specifically, it shows that the quantum memory and the non-Markovian effect can essentially inhibit the increase of uncertainty, however, the quantum memory-assisted uncertainty will finally inflate inevitably, due to that the quantum correlation of the system will be damaged gradually by the noise from the surrounding environments. To be explicit, we study the dynamic evolution of the entropic uncertainty and correlation in open system where both particles experience the noise channels. Meanwhile, we put forward some effective operation strategies to reduce the magnitude of the measurement uncertainty under the open systems. Furthermore, we explore the applications of the uncertainty relation investigated on entanglement witness and quantum channel capacity. Thus, our investigations might offer an insight into quantum measurement estimation in open systems.
Abstract The uncertainty principle is one of the most remarkable features of quantum mechanics, originally expressed in terms of the standard deviation of two incompatible observables. Alternatively, it can be modified and written in the form of entropy to eliminate the defect in the form of standard deviation, and can also be generalized by including a memory particle that is entangled with the particle to be measured. Herein we consider a realistic scenario where the particle A to be measured is in an open environment and B as quantum memory is under an environment typically characterized by non-Markovian regimes. Specifically, it shows that the quantum memory and the non-Markovian effect can essentially inhibit the increase of uncertainty, however, the quantum memory-assisted uncertainty will finally inflate inevitably, due to that the quantum correlation of the system will be damaged gradually by the noise from the surrounding environments. To be explicit, we study the dynamic evolution of the entropic uncertainty and correlation in open system where both particles experience the noise channels. Meanwhile, we put forward some effective operation strategies to reduce the magnitude of the measurement uncertainty under the open systems. Furthermore, we explore the applications of the uncertainty relation investigated on entanglement witness and quantum channel capacity. Thus, our investigations might offer an insight into quantum measurement estimation in open systems.
Uncertainty principle plays a crucial role in quantum mechanics, because it captures the essence of the inevitable randomness associated with the outcomes of two incompatible quantum measurements. Information entropy can perfectly describe this type of randomness in information theory, because entropy can measure the degree of chaos in a given quantum system. However, the quantum-assisted uncertainty of entropy eventually inflate inevitably as the quantum correlations of the system are progressively corrupted by noise from the surrounding environment. In this paper, we investigate the dynamical features of the von Neumann entropic uncertainty in the presence of quantum memory, exploring the time evolution of entropic uncertainty suffer noise from the surrounding. Noteworthily, how the environmental noises affect the uncertainty of entropy is revealed, and specifically we verify how two types of noise environments, AD channel and BPF channel, influence the uncertainty. Meanwhile, we put forward some effective operation strategies to reduce the magnitude of the measurement uncertainty under the open systems. Furthermore, we explore the applications of the uncertainty relation investigated on entanglement witness and quantum channel capacity. Therefore , in open quantum correlation systems, our investigations could provide an insight into quantum measurement estimation
One of the defining traits of quantum mechanics is the uncertainty principle which was originally expressed in terms of the standard deviation of two observables. Alternatively, it can be formulated using entropic measures, and can also be generalized by including a memory particle that is entangled with the particle to be measured. Here we consider a realistic scenario where the memory particle is an open system interacting with an external environment. Through the relation of conditional entropy to mutual information, we provide a link between memory effects and the rate of change of conditional entropy controlling the lower bound of the entropic uncertainty relation. Our treatment reveals that the memory effects stemming from the non-Markovian nature of quantum dynamical maps directly control the lower bound of the entropic uncertainty relation in a general way, independently of the specific type of interaction between the memory particle and its environment.
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.
Abstract In this work, we investigate the dynamics of quantum-memory-assisted entropic uncertainty relations under open systems, and how to steer the uncertainty under different types of decoherence. Specifically, we develop the dynamical behaviors of the uncertainty of interest under two typical categories of noise; bit flipping and depolarizing channels. It has been shown that the measurement uncertainty firstly increases and then decreases with the growth of the decoherence strength in bit flipping channels. In contrast, the uncertainty monotonically increases with the increase of the decoherence strength in depolarizing channels. Notably, and to a large degree, it is shown that the uncertainty depends on both the systematic quantum correlation and the minimal conditional entropy of the observed subsystem. Moreover, we present a possible physical interpretation for these distinctive behaviors of the uncertainty within such scenarios. Furthermore, we propose a simple and effective strategy to reduce the entropic uncertainty by means of a partially collapsed operation—quantum weak measurement. Therefore, our investigations might offer an insight into the dynamics of the measurment uncertainty under decoherence, and be of importance to quantum precision measurement in open systems.
Uncertainty relations are a characteristic trait of quantum mechanics. Even though the traditional uncertainty relations are expressed in terms of the standard deviation of two observables, there exists another class of such relations based on entropic measures. Here we investigate the memory-assisted entropic uncertainty relation in an open quantum system scenario. We study the dynamics of the entropic uncertainty and its lower bound, related to two incompatible observables, when the system is affected by noise, which can be described by a correlated Pauli channel. In particular, we demonstrate how the entropic uncertainty for these two incompatible observables can be reduced as the correlations in the quantum channel grow stronger.