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Laser Physics

The entropic uncertainty preservation in non-Markovian environment via classical driving fields

H. Hajihoseinlou, Bahram Ahansaz

Published Jun 6, 2024• 2 citations
Publisher

Abstract

Abstract Uncertainty relations in terms of entropies were initially proposed to deal with conceptual shortcomings in the original formulation of the uncertainty principle and, hence, play an important role in quantum foundations. In quantum information theory, the preferred mathematical quantity to express the entropic uncertainty relation is the Shannon’s entropy. In this work, we investigate the effect of a classical driving field on entropic uncertainty lower bound (EULB). In this regard, we consider a particle as the quantum memory correlated with a measured particle, where during the interaction with the environment, the quantum memory is driven by the external classical field. Our result reveals that in the presence of the classical driving fields, the EULB is reduced and consequently, the measurement accuracy is increased.

DOI
10.1088/1555-6611/ad4eb8

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Abstract Uncertainty relations in terms of entropies were initially proposed to deal with conceptual shortcomings in the original formulation of the uncertainty principle and, hence, play an important role in quantum foundations. In quantum information theory, the preferred mathematical quantity to express the entropic uncertainty relation is the Shannon’s entropy. In this work, we investigate the effect of a classical driving field on entropic uncertainty lower bound (EULB). In this regard, we consider a particle as the quantum memory correlated with a measured particle, where during the interaction with the environment, the quantum memory is driven by the external classical field. Our result reveals that in the presence of the classical driving fields, the EULB is reduced and consequently, the measurement accuracy is increased.
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 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.
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 BBB which has correlation with the measured particle AAA. 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 BBB, 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 BBB and measured particle AAA. In the sense that, Bob who holds the quantum memory BBB can predict Alice's measurement results on particle AAA more accurately, when the amount of correlation between AAA and BBB 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.
Abstract The uncertainty principle limits the ability to simultaneously predict measurement outcomes for two non‐commuting observables of a quantum particle. However, the uncertainty can be violated by considering a particle as a quantum memory correlated with the primary particle. By modeling an Unruh–Dewitt detector coupled to a massless scalar field, it is explored how the Unruh effect affects the entropic uncertainty and the tighter lower bound for a pair of entangled detectors is probed when one of them is accelerated. It is found that Unruh thermal noise really gives rise to an increase of entropic uncertainty for the given conditions since the correlation between quantum memory and the measured system is decreased. It is shown that the bound of the entropic uncertainty relations, in the presence of memory, can be formulated by introducing the Holevo quantity and mutual information. It is also noticed that Adabi's lower bound is tighter than that of Berta, and just the optimal bound under the Unruh effect. Moreover, it is shown that Berta's lower bound is unrelated to the choice of complementary observables, while the optimal Adabi's lower bound is dependent on the measurement choice. It is worth mentioning that the investigations may offer a better understanding of the entropic uncertainty in a relativistic motion.
The uncertainty principle sets a bound on our ability to predict the measurement outcomes of two incompatible observables which are measured on a quantum particle simultaneously. In quantum information theory, the uncertainty principle can be formulated in terms of the Shannon entropy. Entropic uncertainty bound can be improved by adding a particle which correlates with the measured particle. The added particle acts as a quantum memory. In this work, a method is provided for obtaining the entropic uncertainty relations in the presence of a quantum memory by using quantum coherence. In the method, firstly, one can use the quantum relative entropy of quantum coherence to obtain the uncertainty relations. Secondly, these relations are applied to obtain the entropic uncertainty relations in the presence of a quantum memory. In comparison with other methods this approach is much simpler. Also, for a given state, the upper bounds on the sum of the relative entropies of unilateral coherences are provided, and it is shown which one is tighter. In addition, using the upper bound obtained for unilateral coherence, the nontrivial upper bound on the sum of the entropies for different observables is derived in the presence of a quantum memory.
Abstract One of the fundamental arguments in quantum information theory is the uncertainty principle. According to this principle, two incompatible observables cannot be measured with high precision at the same time. In this work, we will use the entropic uncertainty relation in the presence of quantum memory. Considering a dissipative environment, the effects of the detuning between the transition frequency of a quantum memory and the center frequency of a cavity on entropic uncertainty bound and the quantum correlation between quantum memory and measured particle will be studied. It is shown that by increasing the detuning, quantum correlation is maintained. As a result, due to the inverse relationship between the uncertainty bound and quantum correlations, the measurement results are guessed more accurately.