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![The blue region, orange region and green region stand for the sets of S\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb{S}}$$\end{document}/EBC, ℂ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb{C}}$$\end{document}/DBC and I\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb{I}}$$\end{document}/CBC respectively, where S\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb{S}}$$\end{document} and ℂ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb{C}}$$\end{document} stand for separable states and classical correlated states.](publication/324083609/figure/fig1/AS:959237035413518@1605711339500/The-blue-region-orange-region-and-green-region-stand-for-the-sets-of.jpg)
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The interaction of quantum system and its environment brings out abundant quantum phenomenons. The sudden death of quantum resources, including entanglement, quantum discord and coherence, have been studied from the perspective of quantum breaking channels (QBC). QBC of quantum resources reveal the common features of quantum resources. The definiti...
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Citations
... [23][24][25][26] Investigations into QDs' sudden birth and death have also been performed. 27 Furthermore, in non-Markovian conditions, the characteristics of Rènyi discord for two different dimer systems interacting with two correlated Fermi-spin environments have been examined. 28 It is well known that the use of quantum coherence may help estimate the unknown parameters imposed by classical physical limitations more accurately. ...
We consider a double Jaynes–Cummings model for a system of two atoms that interact with a radiation field defined in a thermal spin state. We examine the impact of the parameters of the quantum model on the temporal evolution of quantum discord, quantum Fisher information, and fidelity. We explain how the quantifiers can be affected by the thermal noise and spin number with and without the effect of time-dependent coupling. We show that, despite the damaging effects of thermal noise, there is still some amount of discord and Fisher information present during the temporal evolution in accordance with the values of the spin number.
... Based on the rigorous framework for quantifying quantum coherence [7], researchers have carried out extensive research on coherence and proposed a variety of coherence measures [8][9][10]. The relationship between quantum coherence and other quantum resources, such as quantum entanglement [11][12][13] and quantum discord [14][15][16][17][18][19], is also an important open question. ...
... We start by considering the relationship between the genuine tripartite coherence and quantum discord. The measurement-dependent global quantum discord [14,15,32] is ...
In this paper, we define the genuine multipartite coherence and genuine multipartite average coherence, discuss their properties and investigative the relationship between them and other quantum resources. Firstly, we prove that the genuine multipartite coherence can be represented by interaction information, and it can determine whether genuine multipartite discord exists. Secondly, comparing the global coherence and genuine multipartite coherence in noisy channels with different correlation strengths, the global coherence and genuine multipartite coherence are more stable with the increasing correlation strengths, and genuine multipartite coherence is more stable than global coherence. Finally, we find that the difference between genuine multipartite coherence and genuine multipartite average coherence can be expressed by quantum discord, and the genuine multipartite coherence is always greater than or equal to the genuine multipartite entanglement. For the tripartite pure states, we provide some trade-off relations between the total correlation, classical correlation, and quantum correlations.
... As a result, the system may lose its quantum properties partially or completely (known as sudden death), rendering it unusable for quantum information tasks. Up to now, the effects of decoherence channels on entanglement [38][39][40] , Bell nonlocality 41,42 , coherence 43,44 and discord 45,46 have been widely studied both theoretically and experimentally. From a practical point of view, it is necessary to study the dynamical behavior of quantum steering in the real world. ...
Multipartite quantum steering, a unique resource for asymmetric quantum network information tasks, is very fragile to the inevitable decoherence, which makes it useless for practical purposes. It is thus of importance to understand how it decays in the presence of noise channels. We study the dynamic behaviors of genuine tripartite steering, reduced bipartite steering, and collective steering of a generalized three-qubit W state when only one qubit interacts independently with the amplitude damping channel (ADC), phase damping channel (PDC) or depolarizing channel (DC). Our results provide the region of decoherence strength and state parameters that each type of steering can survive. The results show that these steering correlations decay the slowest in PDC and some non-maximally entangled states more robust than the maximally entangled ones. Unlike entanglement and Bell nonlocality, the sudden death of reduced bipartite steering and collective steering are directional. In addition, we fifind that not only one party can be steered by a group system, but also two parties can be steered by a single system. There is a trade-off between the monogamy relation involving one steered party and two steered parties. Our work provides comprehensive information about the effect of decoherence on multipartite quantum steering, which will help to realize quantum information processing tasks in the presence of noise environments.
... The superposition of the noise phase over the system phase has completely suppressed the fluctuating behaviour of the classical environments, which resulted in pure monotonic decay, with no entanglement oscillations. Thus, the transitions of the free states into resource states during the functional implementations of the quantum protocols will be restricted [78]. This indicates the Markovian character of the current environments for the quantum correlation, coherence, and information dynamics. ...
We address entanglement, coherence, and information protection in a system of four non-interacting qubits coupled with different classical environments, namely: common, bipartite, tripartite, and independent environments described by Ornstein-Uhlenbeck (ORU) noise. We show that quantum information preserved by the four qubit state is more dependent on the coherence than the entanglement using time-dependent entanglement witness, purity, and Shannon entropy. We find these two quantum phenomena directly interrelated and highly vulnerable in environments with ORU noise, resulting in the pure exponential decay of a considerable amount. The current Markovian dynamical map, as well as suppression of the fluctuating character of the environments, are observed to be entirely attributable to the Gaussian nature of the noise. The increasing number of environments are witnessed to speed up the amount of decay. Unlike other noises, the current noise parameter's flexible range is readily exploitable, ensuring long enough preserved memory properties. The four-qubit GHZ state, besides having a large information storage potential, stands partially entangled and coherent in common environments for an indefinite duration. In addition, we derive computational values for each system-environment interaction, which will help quantum practitioners to optimize the related classical environments.
... describes relaxation of a couple of two-level emitters interacting with a stochastic field [39]. For some quantum states, it has been shown frozen entanglement [40] and sudden death/birth of discord [39] under the effects of this sort of noise. ...
... describes relaxation of a couple of two-level emitters interacting with a stochastic field [39]. For some quantum states, it has been shown frozen entanglement [40] and sudden death/birth of discord [39] under the effects of this sort of noise. The Kraus operators associated to this noise are [41]: ...
... This can be understood due to the quadratic dependency of the density matrix elements introduced by the SDC noise on parameter p (see Eq. (A3) and compare with the linear dependency in Eq. (A1), in Appendix A). Despite the sudden death of discord reported in [39] for some states under SDC noise, we do not find any scenario in which that kind of behaviour takes place for the considered On the other hand, sudden death of steering and entanglement also is revealed by noisy effects due to SDC as shown in panels (a) and (b) of Fig. 5. Similarly, for fixed k the phenomenon occurs for both quantum properties but at different facets; for entanglement, it happens at the same value of p and arbitrary θ, while the phenomenon's profile appears as a function of both parameters for steering (see Fig. 12 in Appendix B). ...
Quantum entanglement, discord, and EPR-steering are properties which are considered as valuable resources for fuelling quantum information-theoretic protocols. EPR-steering is a property that is more general than Bell-nonlocality and yet more restrictive than entanglement. Quantum discord on the other hand, captures non-classical behaviour beyond that of entanglement, and its study has remained of active research interest during the past two decades. Exploring the behaviour of these quantum properties in different physical scenarios, like those simulated by open quantum systems, is therefore of crucial importance for understanding their viability for quantum technologies. In this work, we analyse the behaviour of EPR-steering, entanglement, and quantum discord, for two-qubit states under various quantum processes. First, we consider the three noisy channel scenarios of; phase damping, generalised amplitude damping and stochastic dephasing channel. Second, we explore the behaviour of these quantum properties in an entanglement swapping scenario. We quantify EPR-steering by means of an inequality with three-input two-output measurement settings, and address quantum discord as the interferometric power of quantum states. Our findings are the following. First, we show that some of the relatively straightforward noisy channels here considered, can induce non-trivial dynamics such as sudden death as well as death and revival of EPR-steering and entanglement. Second, we find that although noisy channels in general reduce the amount of correlations present in the system, the swapping protocol on the other hand displays scenarios where these quantum correlations can be enhanced. These results therefore illustrate that quantum processes do not exclusively affect the quantum properties of physical systems in a negative manner, but that they can also have positive effects on such properties.
... The superposition of the noise phase over the system phase has completely suppressed the fluctuating behaviour of the classical environments, which resulted in pure monotonic decay, with no entanglement oscillations. This would also block transitions of the free states into resource states during the functional implementations of the quantum protocols [72]. This indicates the Markovian character of the current environments for the quantum correlation, coherence, and information dynamics. ...
We address entanglement, coherence, and information protection in a system of four non-interacting qubits coupled with different classical environments, namely: common, bipartite, tripartite, and independent environments described by Ornstein-Uhlenbeck (ORU) noise. We show that quantum information preserved by the four qubit state is more dependent on the coherence than the entanglement using time-dependent entanglement witness, purity, and Shannon entropy. We find these two quantum phenomena directly interrelated and highly vulnerable in environments with ORU noise, resulting in the pure exponential decay of a considerable amount. The current Markovian dynamical map, as well as suppression of the fluctuating character of the environments are observed to be entirely attributable to the Gaussian nature of the noise. Furthermore, the increasing number of environments are witnessed to accelerate the amount of decay. Unlike other noises, the current noise parameter's flexible range is readily exploitable, ensuring long enough preserved memory properties. The four-qubit GHZ state, besides having a large information storage potential, stands partially entangled and coherent in common environments for an indefinite duration. Thus, it appeared to be a more promising resource for functional quantum computing than bipartite and tripartite quantum systems. In addition, we derive computational values for each system-environment interaction, which will help quantum practitioners to optimize the related kind of classical environments.
... Finally, we underline that in Ref. [77], Xia et al. have found an analogue process to our case (c) above on concurrence, but for quantum discord. They have investigated the dynamics of an open system, where the quantum channel was a stochastic dephasing channel along the z-direction. ...
... They have investigated the dynamics of an open system, where the quantum channel was a stochastic dephasing channel along the z-direction. In Figure 7 of Ref. [77], they have shown that sudden death and sudden birth of quantum discord occur for a two-qubit Bell-diagonal state. which presents a curve with the minimum value zero for quantum discord. ...
... One knows that if the quantum discord is equal to zero, then the concurrence is also zero, since a zero-discord state is separable. Therefore, in Ref. [77], they have presented sudden death and birth of both quantum discord and concurrence. ...
We study and compare the time evolutions of concurrence and quantum discord in a driven system of two interacting qubits prepared in a generic Werner state. The corresponding quantum dynamics is exactly treated and manifests the appearance and disappearance of entanglement. Our analytical treatment transparently unveils the physical reasons for the occurrence of such a phenomenon, relating it to the dynamical invariance of the X structure of the initial state. The quantum correlations which asymptotically emerge in the system are investigated in detail in terms of the time evolution of the fidelity of the initial Werner state.
... This usually occurs as an exponential decay in time, with it sometimes even undergoing sudden death [16,17]. It also sometimes happen how-ever, that more interesting dynamics take place in the form of death and revival or sudden birth of quantum correlations [18][19][20]. These different types of dynamics of correlations have been verified experimentally [21,22]. ...
We report on the existence of the phenomenon of sudden birth of maximal hidden quantum correlations in open quantum systems. Specifically, we consider the CHSH-inequality for Bell-nonlocality, the $\rm F_3$-inequality for EPR-steering, and usefulness for teleportation as quantum correlations in a bipartite qubit system under collective decoherence due to an environment. We show that, even though the system may undergo a sudden birth of entanglement, neither of the aforementioned correlations are present and yet, these can still be revealed by means of local filtering operations, thus evidencing the presence of hidden quantum correlations. Furthermore, there are extreme versions of this phenomenon for which the revealed correlations achieve their maximal amount allowed by quantum theory. The phenomenon of maximal hidden correlations relies on the qubits collective damping, and may take place even in long-distance separated qubits. These results prove that apparently-useless physical systems as quantum registers could still exhibit maximal correlations, which are hidden from us, but that can still be accessed by means of local filtering operations.
Multipartite quantum steering, a unique resource for asymmetric quantum network information tasks, is very fragile to the inevitable decoherence, which makes it useless for practical purposes. It is thus of importance to understand how it decays in the presence of noise channels. We study the dynamic behaviors of genuine tripartite steering, reduced bipartite steering, and collective steering of a generalized three-qubit W state when only one qubit interacts independently with the amplitude damping channel (ADC), phase damping channel (PDC) or depolarizing channel (DC). Our results provide the region of decoherence strength and state parameters that each type of steering can survive. The results show that these steering correlations decay the slowest in PDC and some non-maximally entangled states more robust than the maximally entangled ones. Unlike entanglement and Bell nonlocality, the thresholds of decoherence strength that reduced bipartite steering and collective steering can survive depend on the steering direction. In addition, we find that not only one party can be steered by a group system, but also two parties can be steered by a single system. There is a trade-off between the monogamy relation involving one steered party and two steered parties. Our work provides comprehensive information about the effect of decoherence on multipartite quantum steering, which will help to realize quantum information processing tasks in the presence of noise environments.
Quantum entanglement, quantum discord, and EPR-steering are properties which are considered as valuable resources for fuelling quantum information-theoretic protocols. EPR-steering is a correlation weaker than nonlocality (in the Bell's sense) and yet stronger than entanglement. Quantum discord on the other hand, captures non-classical behaviour beyond that of entanglement, and its study has remained of active research interest during the past two decades. Exploring the behaviour of these quantum correlations in different physical scenarios, like those simulated by open quantum systems, is therefore of crucial importance for understanding their viability for quantum technologies. In this work, we analyse the behaviour of EPR-steering, entanglement, and quantum discord, for partially entangled two-qubit states with coloured noise, introduced by Ameida et al. [1], under various quantum processes. First, we consider the three noisy channel scenarios of; phase damping, generalised amplitude damping and stochastic dephasing channel. Second, we explore their behaviour in an entanglement swapping scenario. We quantify EPR-steering by means of an inequality with three-input two-output measurement settings, and address quantum discord as the interferometric power of quantum states. We discuss the sudden death of steering and entanglement induced by the noisy processes. Additionally, in the case of generalised amplitude damping, a death and revival behaviour can be interpreted in terms of one of the noise's parameters. Second, we contrast the fact that noisy channels in general reduce the amount of correlations present in the system, with the swapping protocol, which displays scenarios where these quantum correlations can be enhanced with respect to the correlations at the initial stage of the protocol. In particular, we present a trade-off between the post-swap amount of correlations and their probability of occurrence.
