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Laser Physics

Effects of detuning on entropic uncertainty bound and quantum correlations in dissipative environments

Shahram Mehrmanesh, Maryam Hadipour, Soroush Haseli

Published Feb 15, 2024• 1 citation
Publisher

Abstract

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.

DOI
10.1088/1555-6611/ad2448

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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.
One of the fundamental arguments in quantum information theory is the uncertainty principle. In accordance with 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 entrpic uncertainty bound and 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 correlation, the measurement results is guessed more accurately.
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.
The uncertainty principle is one of the comprehensive and fundamental concept in quantum theory. This principle states that it is not possible to simultaneously measure two incompatible observatories with high accuracy. Uncertainty principle has been formulated in various form. The most famous type of uncertainty relation is expressed based on the standard deviation of observables. In quantum information theory the uncertainty principle can be formulated using Shannon and von Neumann entropy. Entropic uncertainty relation in the presence of quantum memory is one of the most useful entropic uncertainty relations. Due to their importance and scalability, solid state systems have received considerable attention nowadays. In this work we will consider a quantum dot system as a solid state system. We will study the quantum correlation and quantum memory assisted entropic uncertainty in this typ of system. We will show that the temperature in of quantum dot system can affect the quantum correlation and entropic uncertainty bound. It will be observed that the entropic uncertainty bound decreases with decreasing temperature and quantum correlations decreases with increasing the temperature.
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 a fundamental principle in quantum physics. It implies that the measurement outcomes of two incompatible observables cannot be predicted simultaneously. In quantum information theory, this principle can be expressed in terms of entropic measures. M. Berta et al. [Nat. Phys. 6, 659 (2010)] have indicated that uncertainty bound can be altered by considering a particle as a quantum memory correlating with the primary particle. In this article, we obtain a lower bound for entropic uncertainty in the presence of a quantum memory by adding an additional term depending on the Holevo quantity and mutual information. We conclude that our lower bound will be tightened with respect to that of Berta et al. when the accessible information about measurements outcomes is less than the mutual information about the joint state. Some examples have been investigated for which our lower bound is tighter than Berta et al.'s lower bound. Using our lower bound, a lower bound for the entanglement of formation of bipartite quantum states has been obtained, as well as an upper bound for the regularized distillable common randomness.
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.