Evolution Of Discord Research Articles

From disagreement to rupture: the Soviet-Albanian conflict of 1960-1961

The Soviet-Albanian conflict epitomized centrifugal tendencies within the global socialist system. This article draws on a diverse array of sources, including previously unpublished materials, such as documents from the State Archive of the Russian Federation and the Archive of Foreign Policy of the Russian Federation, as well as memoirs of key leaders (N. Khrushchev, E. Hoxha, R. Alia), and various official records. Notably, the TASS bureau in Tirana provided invaluable insights, collaborating with diplomats and journalists from other socialist nations to produce analytical reports, some of which were directed to the upper echelons of the CPSU. The article explores the evolution of discord between Moscow and Tirana, its culmination in open conflict, and the subsequent severance of party and state relations. Key findings include: 1) The conflict's primary catalysts were the divergent socialist models adopted by the USSR and Albania, coupled with the disparity in interests between the superpower and the bloc's smallest member; 2) The PLA's reluctance to conform to Soviet-style reforms was construed in Moscow as a challenge to the CPSU's hegemony within the global communist movement, while the PLA leadership viewed them as encroachments on its authority; 3) Disagreements pervaded all spheres, with ideology assuming heightened significance compared to conflicts with Yugoslavia; 4) External influences on the conflict's trajectory were marginal, with developments driven by internal dynamics, including Tirana's increasing alienation from the CPSU and the catalytic effect of deteriorating Soviet-Chinese relations; Western powers monitored events closely but refrained from direct intervention; 5) While objective factors underpinned the Soviet-Albanian discord, subjective elements were of secondary importance, yet pivotal in precipitating the conflict's acrimonious turn.

Discord in the voter model for complex networks.

Online social networks have become primary means of communication. As they often exhibit undesirable effects such as hostility, polarization, or echo chambers, it is crucial to develop analytical tools that help us better understand them. In this paper we are interested in the evolution of discord in social networks. Formally, we introduce a method to calculate the probability of discord between any two agents in the multistate voter model with and without zealots. Our work applies to any directed, weighted graph with any finite number of possible opinions, allows for various update rates across agents, and does not imply any approximation. Under certain topological conditions, the opinions are independent and the joint distribution can be decoupled. Otherwise, the evolution of discord probabilities is described by a linear system of ordinary differential equations. We prove the existence of a unique equilibrium solution, which can be computed via an iterative algorithm. The classical definition of active links density is generalized to take into account long-range, weighted interactions. We illustrate our findings on real-life and synthetic networks. In particular, we investigate the impact of clustering on discord and uncover a rich landscape of varied behaviors in polarized networks. This sheds lights on the evolution of discord between, and within, antagonistic communities.

Dynamics of quantum coherence and correlations in a transverse Ising spin chain environment

In this paper, we study the dynamical processes of quantum coherence and correlations for two central qubits system coupled with a transverse Ising spin chain. Suppose the initial state of quantum system is the Werner state and the initial state of environment is the ground state of spin chain, and the corresponding time evolution operator, decoherence factor and reduced density matrix are given. We deduce the analytical expressions of evolution of quantum coherence, entanglement and quantum discord. We find that when the spin chain undergoes quantum phase transition (QPT), the entanglement vanished at time [Formula: see text], and the coherence and discord vanished when the decoherence factor decayed to zero. Besides, we also find that the environmental scale N, coupling strength g and parameter P of Werner state do not change the evolution rules of quantum correlation, but accelerate their decay rate with these parameters’ increase.

Dephasing effects on quantum correlations and teleportation in presence of state dependent bath

Quantum information protocols are often designed in the ideal situation with no decoherence. However, in real setup, these protocols are subject to the decoherence and thus reducing fidelity of the measurement outcome. In this work, we analyze the effect of state-dependent bath on the quantum correlations and the fidelity of a single qubit teleportation. We model our system-bath interaction as qubits interacting with a common bath of bosons, and the state dependence of the bath is generated through a projective measurement on the joint state in thermal equilibrium. The analytic expressions for the time evolution of entanglement, discord and average fidelity of quantum teleportation are calculated. It is shown that due to the presence of initial system-bath correlations, the system maintains quantum correlations for long times. Furthermore, due to the presence of finite long-time entanglement of the quantum channel, the average fidelity is shown to be higher than its classical value.

Discord and decoherence

In quantum information theory, quantum discord has been proposed as a tool to characterise the presence of “quantum correlations” between the subparts of a given system. Whether a system behaves quantum-mechanically or classically is believed to be impacted by the phenomenon of decoherence, which originates from the unavoidable interaction between this system and an environment. Generically, decoherence is associated with a decrease of the state purity, i.e. a transition from a pure to a mixed state. In this paper, we investigate how quantum discord is modified by this quantum-to-classical transition. This study is carried out on systems described by quadratic Hamiltonians and Gaussian states, with generalised squeezing parameters. A generic parametrisation is also introduced to describe the way the system is partitioned into two subsystems. We find that the evolution of quantum discord in presence of an environment is a competition between the growth of the squeezing amplitude and the decrease of the state purity. In phase space, this corresponds to whether the semi-minor axis of the Wigner ellipse increases or decreases, which has a clear geometrical interpretation. Finally, these considerations are applied to primordial cosmological perturbations, thus allowing us to investigate how large-scale structures in our universe, which are believed to arise from quantum fluctuations, can exhibit classical properties.

Dynamics of the Quantum Discord with Weak Measurement for a Two-atom System in Thermal Reservoirs

Weak measurement is a kind of state partial collapse measurement developed on the basis of von Neumann measurement and positive operator value measurement, which allows us to explore the quantum world which has the least influence on the research system. Based on the weak measurement theory, the dynamics of quantum discord for two isolated atoms in their own thermal reservoirs is presented. We examine the time evolution of both standard quantum discord and quantum discord with weak measurement for the two-atom system, and analyzes the differences between the standard quantum discord and quantum discord with weak measurement in the evolution process with time, as well as the general role of the strength parameter in determing the discord and affecting its dynamic evolution. We show that quantum discords depend on how weak or strong one perturbs the quantum system. We also show that the difference of the standard quantum discord and the quantum discord with weak measurements increases as the strength parameter decreases. This means that the weak measurements can capture more quantum discord of a bipartite system. Our results show that the weak measurement performed on one of the subsystems can lead to the quantum discord that is a more natural measure of quantum correlations than the standard quantum discord captured by the projective measurements.

Quantum discord of two-qutrit system under quantum-jump-based feedback control**Project supported by the National Natural Science Foundation of China (Grant No. 11374096).

This paper studies quantum discord of two qutrits coupled to their own environments independently and coupled to the same environment simultaneously under quantum-jump-based feedback control. Our results show that spontaneous emission, quantum feedback parameters, classical driving, initial state, and detection efficiency all affect the evolution of quantum discord in a two-qutrit system. We find that under the condition of designing proper quantum-jump-based feedback parameters, quantum discord can be protected and prepared. In the case where two qutrits are independently coupled to their own environments, classical driving, spontaneous emission, and low detection efficiency have negative effect on the protection of quantum discord. For different initial states, it is found that the evolution of quantum discord under the control of appropriate parameters is similar. In the case where two qutrits are simultaneously coupled to the same environment, the classical driving plays a positive role in the generation of quantum discord, but spontaneous emission and low detection efficiency have negative impact on the generation of quantum discord. Most importantly, we find that the steady discord depends on feedback parameters, classical driving, and detection efficiency, but not on the initial state.

Preservation of entanglement and quantum correlations next to periodic plasmonic nanostructures

We study quantum correlations dynamics of two identical V-type quantum systems initially prepared in an extended Werner-like state, where each one independently interacts with a plasmonic nanostructure. Each V-type system can be decomposed as a two-level system with an additional third external level acting as an “umbrella level.” As the plasmonic nanostructure, we use a two-dimensional array of metal-coated dielectric nanoparticles. For the calculations, we combine quantum dynamics calculations using the density matrix equations and classical electromagnetic calculations. In order to describe the entanglement, we use the measure of entanglement of formation, while we use quantum discord to describe the total quantum correlations of our composite system. We find that the presence of the plasmonic nanostructure leads to high suppression of spontaneous emission rates along with a high degree of quantum interference. These phenomena affect the evolution of both entanglement and quantum discord, while they significantly prolong their dynamics.

Controlling steady-state entanglement and quantum discord through squeezing angle

Abstract We analyze the dynamics of entanglement and quantum discord in a two-qubit system coupled to squeezed reservoirs. We present analytical expressions that can be used to efficiently calculate the evolution of quantum discord and entanglement between the two qubits. Our results show that quantum discord is a more general and robust measure of quantum correlations than entanglement. Furthermore, there is a relationship between the time before sudden death of entanglement and the reservoir squeezing angle. Additionally, the increase of squeezing angle accelerates the decay of quantum discord. These results provide new avenues for controlling quantum correlations and designing quantum states that can be used for various quantum computing applications.

Dynamics of quantum discord of two coupled spin-1/2’s subjected to time-dependent magnetic fields

Abstract We describe the dynamics of quantum discord of two interacting spin-1/2’s subjected to controllable time-dependent magnetic fields. The exact time evolution of discord is given for various input mixed states consisting of classical mixtures of two Bell states. The quantum discord manifests a complex oscillatory behaviour in time and is compared with that of quantum entanglement, measured by concurrence. The interplay of the action of the time-dependent magnetic fields and the spin-coupling mechanism in the occurrence and evolution of quantum correlations is examined in detail.

Quantum correlations in quantum emitters strongly coupled with metallic nanoparticles

We study the dynamics of two initially entangled qubits prepared in an extended Werner-like state, where each one interacts locally with a spherical metallic nanoparticle. We combine quantum dynamics beyond the rotating-wave approximation with classical electromagnetic calculations in order to compute the time evolution of quantum discord and entanglement using entanglement of formation. We present results for qubits either quantum dots or J-aggregates and compare the evolution of quantum discord and entanglement of formation. We find interesting phenomena such as entanglement sudden death, periodic entanglement revival, entanglement oscillations and entanglement trapping by varying the initial state or the distance of each qubit to the corresponding nanoparticle.

Evolución de correlaciones cuánticas de dos qubits en una cavidad con disipación bifotónica

En este trabajo se estudia la evolución de correlaciones cuánticas en un modelo Tavis-Cummings que consta de dos qubits y un único modo cuantizado del campo electromagnético. Se consideran procesos de emisión/absorción de un sólo fotón y de dos fotones correlacionados, para cada uno de los qubits. El modelo se estudia teniendo en cuenta disipaciones unifotónicas y bifotónicas, a través de una cavidad que interactúa con un reservorio térmico. La solución numérica de una ecuación maestra Lindblad nos permite realizar una descripción de la evolución de las correlaciones cuánticas, entrelazamiento cuántico y discordia cuántica, en función del tiempo para un estado atómico tipo superposición. Se muestra que los diferentes resultados de las correlaciones cuánticas, presentan comportamientos cualitativamente diferentes en su evolución.

Markovian and Non-Markovian Dynamics of Non-classical Correlations and Wigner Function for GHZ-Type Coherent States

We process comparatively the time evolution of quantum discord, quantum entanglement and Wigner function for GHZ-type coherent states independently interacting with dephasing reservoirs and we address the influence of both Markovian and non-Markovian environments on their evolution. As a matter of fact, we show that in open multipartite systems negativity of Wigner function is sensitive not only to quantum entanglement but also to quantum discord. Indeed, we deem that the Wigner function can be used to capture and quantify general quantum correlations in open multipartite systems.

The Dynamics of Quantum Correlations in Multi-qubit Spin Chains Under the Effect of Dzyaloshinskii-Moriya Interaction

Several spin chains with 4 and 6 qubits are considered under the effect of Hamiltonian XY model and Dzyaloshinskii-Moriya (DM) interaction. In this paper, the time evolution of entanglement and quantum discord (quantum correlations) are studied. It is shown that quantum discord is more stable than entanglement. Also the effect of DM interaction depends on initial state and it may improve quantum correlations in spin chains with more than 3 qubits.

Quantum correlations dynamics of three-qubit states coupled to an XY spin chain: Role of coupling strengths☆☆Project supported by National Basic Research Program of China (Grant No. 2013CBA01702) and National Natural Science Foundation of China (Grant Nos. 61377016, 61575055, 10974039, 61307072, 61308017, and 61405056).

We investigate the prominent impacts of coupling strengths on the evolution of entanglement and quantum discord for a three-qubit system coupled to an XY spin-chain environment. In the case of a pure W state, more robust, even larger nonzero quantum correlations can be obtained by tailoring the coupling strengths between the qubits and the environment. For a mixed state consisting of the GHZ and W states, the dynamics of entanglement and quantum discord can characterize the critical point of quantum phase transition. Remarkably, a large nonzero quantum discord is generally retained, while the nonzero entanglement can only be obtained as the system-environment coupling satisfies certain conditions. We also find that the impact of each qubit’s coupling strength on the quantum correlation dynamics strongly depends on the variation schemes of the system-environment couplings.

Local probe of single phonon dynamics in warm ion crystals

The detailed characterization of non-trivial coherence properties of composite quantum systems of increasing size is an indispensable prerequisite for scalable quantum computation, as well as for understanding non-equilibrium many-body physics. Here, we show how autocorrelation functions in an interacting system of phonons as well as the quantum discord between distinct degrees of freedoms can be extracted from a small controllable part of the system. As a benchmark, we show this in chains of up to 42 trapped ions, by tracing a single phonon excitation through interferometric measurements of only a single ion in the chain. We observe the spreading and partial refocusing of the excitation in the chain, even on a background of thermal excitations. We further show how this local observable reflects the dynamical evolution of quantum discord between the electronic state and the vibrational degrees of freedom of the probe ion.

Generation of quantum discord in two-mode Gaussian systems in a thermal reservoir

In the framework of the theory of open quantum systems based on completely positive dynamical semigroups, we study the Gaussian quantum discord for a subsystem composed of two coupled bosonic modes immersed in a thermal environment. For Gaussian input states, the time evolution of discord is given in terms of the covariance matrix. For initial uni-modal squeezed states the generation of Gaussian discord takes place, for all non-zero values of the strength of interaction between the bosonic modes. After reaching some maximum value in the case of initial uni-modal squeezed states, and also for initial squeezed vacuum states with non-zero Gaussian discord, this measure of quantum correlations non-monotonically decreases in time and tends asymptotically for large times to some definite non-zero value. The asymptotic discord depends on the strength of interaction between the bosonic modes, temperature and dissipation coefficient.

Quantum discord and entanglement in grover search algorithm

Abstract Imperfections and noise in realistic quantum computers may seriously affect the accuracy of quantum algorithms. In this article we explore the impact of static imperfections on quantum entanglement as well as non-entangled quantum correlations in Grover’s search algorithm. Using the metrics of concurrence and geometric quantum discord, we show that both the evolution of entanglement and quantum discord in Grover algorithm can be restrained with the increasing strength of static imperfections. For very weak imperfections, the quantum entanglement and discord exhibit periodic behavior, while the periodicity will most certainly be destroyed with stronger imperfections. Moreover, entanglement sudden death may occur when the strength of static imperfections is greater than a certain threshold.

Phase effect on dynamics of quantum discord modulated by interaction between qubits**Project supported by the National Natural Science Foundation of China (Grant Nos. 11275064 and 11075050), the Specialized Research Fund for the Doctoral Program of Higher Education, China (Grant No. 20124306110003), the Scientific Research Foundation of the Education Department of Hunan Province, China (Grant No. 13C039), and the Construct Program

We study the effects of the interaction strength and the initial phase on the dynamics of quantum discord in a two-qubit system under both spontaneous emission and dephasing noisy channels. It is shown that the time evolution of quantum discord displays quicker oscillations with increasing inter-qubit interaction strength but the effect of the initial phase closely depends on the interaction between the qubits. Only for non-zero inter-qubit interaction cases, the evolution of quantum discord is affected by the initial phase and its oscillating amplitude increases with increasing initial phase. A comparison between evolutions of quantum discord and entanglement is also made.

Signatures of chaos in the dynamics of quantum discord.

We identify signatures of chaos in the dynamics of discord in a multiqubit system collectively modelled as a quantum kicked top. The evolution of discord between any two qubits is quasiperiodic in regular regions, while in chaotic regions the quasiperiodicity is lost. As the initial wave function is varied from the regular regions to the chaotic sea, a contour plot of the time-averaged discord remarkably reproduces the structures of the classical stroboscopic map. We also find surprisingly opposite behavior of two-qubit discord versus entanglement of the two qubits as measured by the concurrence. Our results provide evidence of signatures of chaos in dynamically generated discord.