Dynamics Of Quantum Entanglement Research Articles

Advanced Analytical and Numerical Studies on Coupled Schrödinger Equations with Fractional Order Damping

This paper embarks on a thorough analytical and numerical exploration of coupled Schrödinger equations under the influence of fractional order damping mechanisms. By integrating fractional damping, which introduces memory effects and non-local dissipative interactions, into the coupled Schrödinger framework, we aim to dissect and understand the nuanced dynamics that govern these complex quantum systems. The research delves into the mathematical underpinnings, stability characteristics, and the dynamical behaviors that emerge from the intricate balance between quantum coupling and fractional damping effects. Through a blend of analytical rigor and sophisticated numerical simulations, this study unveils new insights into the complex interplay among quantum entanglement, dissipation, and non-linear dynamics, offering potential implications for quantum computing, optical systems, and beyond.

Dynamics of Quantum Correlation in a Two‐qutrit Heisenberg XXZ Model with Heitler‐London and Dzyaloshinskii‐Moriya Couplings

AbstractThis study investigates the dynamics of quantum coherence and entanglement in the spin‐1 Heisenberg XXZ model. Particularly, the effects of the Heitler‐London (HL) coupling and the Dzyaloshinskii‐Moriya (DM) interaction are examined. By utilizing tools from quantum information theory, the concept of quantum correlated coherence and negativity are explored. The results show intrinsic decoherence leads to a decay of both correlated coherence and negativity. Interestingly, it is found that a small value of the Dzyaloshinskii‐Moriya interaction can significantly enhance coherence and entanglement. Various factors influence the system dynamics, including the initial state, anisotropy parameter, and the coupling distance between spins. It is shown that, by fixing the anisotropy parameter, the isotropic Heisenberg models XX and XXX can be easily recovered. Ultimately, the findings highlight that the system maintains a coherent temporal evolution despite decoherence.

Quantum Dynamics of Cavity–Bose–Einstein Condensates in a Gravitational Field

We theoretically studied the quantum dynamics of a cavity–Bose–Einstein condensate (BEC) system in a gravitational field, which is composed of a Fabry–Pérot cavity and a BEC. We also show how to deterministically generate the transient macroscopic quantum superposition states (MQSSs) of the cavity by the use of optomechanical coupling between the cavity field and the BEC. The quantum dynamics of the cavity–BEC system specifically include phase space trajectory dynamics, system excitation number dynamics, quantum entanglement dynamics, and quantum coherence dynamics. We found that the system performs increasingly complex trajectories for larger values of the Newtonian gravity parameter. Moreover, the number of phonon excitations of the system can be increased by coupling the cavity–BEC system to Newtonian gravity, which is analogous to an external direct current drive. The scattering of atoms inside the BEC affects the periodicity of the quantum dynamics of the system. We demonstrate a curious complementarity relation between the quantum entanglement and quantum coherence of cavity–BEC systems and found that the complementarity property can be sustained to some extent, despite being in the presence of the cavity decay. This phenomenon also goes some way to show that quantum entanglement and quantum coherence can be referred to together as quantum resources.

Simultaneous control of quantum phase synchronization and entanglement dynamics in a gain-loss optomechanical cavity system

Simultaneous control of quantum phase synchronization and entanglement dynamics in a gain-loss optomechanical cavity system

Quantum memory and entanglement dynamics induced by interactions of two moving atoms with a coherent cavity

This study explores the dynamics of atomic entanglement of formation and entropic uncertainty relation (EUR) of two moving atoms interacting with an even coherent cavity during a two-photon interaction. We investigate the impact of the initial even coherent amplitude, the atom–photon coupling strengths, and the atomic motion coupling on the dynamics of quantum memory (QM) entropic uncertainty and entanglement. The dynamics of the entropic uncertainty and entanglement of formation are significantly altered by the atom-photon-atom interaction parameters. By increasing the initial mean photon number, the QM entropic uncertainty and the atomic entanglement can be improved. Bob’s capacity to limit his uncertainty regarding Alice’s measurement results depends on the initial even coherent state, the atom–photon couplings, and the atomic motion parameter. The atomic location couplings produce QM entropic uncertainty and entanglement with regular oscillatory behavior. The system parameters control the sudden death-birth entanglement phenomenon, which is improved by increasing the atomic location coupling.

Quantum entanglement dynamics of spacetime and matter

It was known long ago that quantum theory and general relativity are in sharp conflict in their foundations. Their fundamental inconsistencies render a consistent theory of quantum gravity the most challenging problem in physics. Here we propose an information-complete quantum field theory (ICQFT), which describes elementary fermions, their gauge fields, and gravity (together, called the trinary fields) as an elementary trinity without any conceptual inconsistency of existing theories. The ICQFT unifies matter and spacetime (gravity) as information via spacetime-matter entanglement, which encodes complete physical predictions of the theory and leads to a compelling solution to the problem of time. We consider two particular forms of spacetime-matter entangled states and their physical consequences. One of them results in a universal relation between entanglement entropy and geometry (area and volume), allowing us to determine the cosmological constant term in the classical Einstein equation. Based on a quantum-information definition of dark energy, our Universe is not strictly holographic. We predict the interior quantum state of a Schwarzschild black hole to be maximally information-complete. As a concrete quantum formulation of gravity coupled with matter, the ICQFT is quantum entanglement dynamics for spacetime and matter and eliminates the conceptual obstacles of existing quantum gravity theory.

Theoretical investigation of dynamics and concurrence of entangled {{mathcal {P}}}{{mathcal {T}}} and anti-{{mathcal {P}}}{{mathcal {T}}} symmetric polarized photons

Non-Hermitian systems with parity-time mathcal {(PT)} symmetry and anti-parity-time mathcal {(APT)} symmetry have exceptional points (EPs) resulting from eigenvector co-coalescence with exceptional properties. In the quantum and classical domains, higher-order EPs for {{mathcal {P}}}{{mathcal {T}}} symmetry and mathcal {APT}-symmetry systems have been proposed and realized. Both two-qubits mathcal {APT}-mathcal {APT} and {{mathcal {P}}}{{mathcal {T}}}-{{mathcal {P}}}{{mathcal {T}}} symmetric systems have seen an increase in recent years, especially in the dynamics of quantum entanglement. However, to our knowledge, neither theoretical nor experimental investigations have been conducted for the dynamics of two-qubits entanglement in the {{mathcal {P}}}{{mathcal {T}}}-mathcal {APT} symmetric system. We investigate the {{mathcal {P}}}{{mathcal {T}}}-mathcal {APT} dynamics for the first time. Moreover, we examine the impact of different initial Bell-state conditions on entanglement dynamics in {{mathcal {P}}}{{mathcal {T}}}-{{mathcal {P}}}{{mathcal {T}}}, mathcal {APT}-mathcal {APT} and {{mathcal {P}}}{{mathcal {T}}}-mathcal {APT} symmetric systems. Additionally, we conduct a comparative study of entanglement dynamics in the {{mathcal {P}}}{{mathcal {T}}}-{{mathcal {P}}}{{mathcal {T}}} symmetrical system, mathcal {APT}-mathcal {APT} symmetrical system, and {{mathcal {P}}}{{mathcal {T}}}-mathcal {APT} symmetrical systems in order to learn more about non-Hermitian quantum systems and their environments. Entangled qubits evolve in a {{mathcal {P}}}{{mathcal {T}}}-mathcal {APT} symmetric unbroken regime, the entanglement oscillates with two different oscillation frequencies, and the entanglement is well preserved for a long period of time for the case when non-Hermitian parts of both qubits are taken quite away from the exceptional points.

Random Quantum Circuits

Quantum circuits—built from local unitary gates and local measurements—are a new playground for quantum many-body physics and a tractable setting to explore universal collective phenomena far from equilibrium. These models have shed light on longstanding questions about thermalization and chaos, and on the underlying universal dynamics of quantum information and entanglement. In addition, such models generate new sets of questions and give rise to phenomena with no traditional analog, such as dynamical phase transitions in quantum systems that are monitored by an external observer. Quantum circuit dynamics is also topical in view of experimental progress in building digital quantum simulators that allow control of precisely these ingredients. Randomness in the circuit elements allows a high level of theoretical control, with a key theme being mappings between real-time quantum dynamics and effective classical lattice models or dynamical processes. Many of the universal phenomena that can be identified in this tractable setting apply to much wider classes of more structured many-body dynamics.

Quantum Correlation Dynamics of Three Qubits in Non-Markovian Environments

We investigate the quantum correlation dynamics of three independent qubits each locally interacting with a zero temperature non-Markovian reservoir by using the Geometric measure of quantum discord (GQD). The dependence of quantum correlation dynamicson amount of non-Markovian, the degree of initial quantum correlation and purity of the initial states are studied in detail. It is found that the quantum correlation of such three qubits system revives after instantaneous disappearance period when a proper amount of non-Markovian is present. A comparison to the pairwise quantum discord and entanglement dynamics in three qubits system is also made.

Dynamics of quantum correlations in two 2-level atoms coupled to thermal reservoirs

In this paper, we examine the dynamics of quantum correlations in two noninteractive two-level atoms coupled to two separate identical thermal reservoirs. The two atoms are initially produced in a Gisin state, which is a blend of a maximally entangled two-qubit state and a separable mixed state. Quantum entanglement is measured by logarithmic negativity, while the nonclassical correlations are characterized by trace distance discord and local quantum uncertainty. Using the mean photon number of reservoirs and spontaneous emission rates of atoms as inputs, we explore how these quantum resources behave. Consequently, we demonstrate that the dynamics of quantum entanglement and quantum correlations depend upon the parameters driving the system. Significantly, we further demonstrate that specific parameters may be tweaked to preserve the quantum resources in the system. The results give a full grasp of the quantum features of such a two-level atomic system, showing capabilities to construct quantum technology.

Protecting quantum entanglement in thermal reservoir by detuning

In this work, the quantum entanglement dynamics of a two-atom system in the thermal reservoir is investigated. An analytical solution of the single atom in the thermal reservoir and the expression of the quantum entanglement of the two-atom system in the thermal reservoir are obtained by the Markovian master equation method. The results showed that the nonzero temperature leads to sudden death of entanglement under the weak coupling limit. The higher the temperature, the faster the decay of entanglement. In particular, the detuning and the smaller spectrum width in the weak atom-reservoir coupling regime can effectively protect the quantum entanglement of the two-atom system in the thermal reservoir under the weak atom-reservoir coupling regime. The corresponding physical explanation is given by the entropy production rare.

Comparative study of the dynamics of quantum entanglement, purity and degree of purity in two hybrid quantum systems: non-Markovian and Markovian regime

Comparative study of the dynamics of quantum entanglement, purity and degree of purity in two hybrid quantum systems: non-Markovian and Markovian regime

Dynamics of entanglement in coherent states, entangled SchrÖdinger cat state and distribution function

We exploit the dynamics of entangled system between a harmonic oscillator and a single mode electromagnetic field as two harmonic oscillators, to examine quantum entanglement in coherent states. Through the Schrödinger cat state, we compute analytically its distribution function. Then, we check graphically the evolution of entanglement and the distribution function for two particular cases: the first is defined by two harmonic oscillators in quantum motion in a Paul trap; here whatever the quantum state , the system is at most entangled. The second case is visualised by two harmonic oscillators with a perturbative force, in that case, by varying the displacement numbers of the coherent states, the quantum entanglement and the distribution function present a similar evolution and they reach very large values. Comparing the two models: in the first, the dynamics of quantum entanglement exhibits a multi-frequency lines behaviour while in the second model, it shows an exponential behaviour.

Entanglement dynamics in anti- PT -symmetric systems

In the past years, many efforts have been made to study various noteworthy phenomena in both parity-time ($\mathcal{PT}$) and anti-parity-time ($\mathcal{APT}$) symmetric systems. However, entanglement dynamics in $\mathcal{APT}$-symmetric systems has not previously been investigated in both theory and experiments. Here, we investigate the entanglement evolution of two qubits in an $\mathcal{APT}$-symmetric system. In the $\mathcal{APT}$-symmetric unbroken regime, our theoretical simulations demonstrate the periodic oscillations of entanglement when each qubit evolves identically, while the nonperiodic oscillations of entanglement when each qubit evolves differently. In particular, when each qubit evolves near the exceptional point in the $\mathcal{APT}$-symmetric unbroken regime, there exist entanglement sudden vanishing and revival. Moreover, our simulations demonstrate rapid decay and delayed death of entanglement provided one qubit evolves in the $\mathcal{APT}$-symmetric broken regime. In this work, we also perform an experiment with a linear optical setup. The experimental results agree well with our theoretical simulation results. Our findings reveal novel phenomena of entanglement evolution in the $\mathcal{APT}$-symmetric system and opens a new direction for future studies on the dynamics of quantum entanglement in multiqubit $\mathcal{APT}$-symmetric systems or other non-Hermitian quantum systems.

Sensitivity of entanglement measures in bipartite pure quantum states

Entanglement measures quantify the amount of quantum entanglement that is contained in quantum states. Typically, different entanglement measures do not have to be partially ordered. The presence of a definite partial order between two entanglement measures for all quantum states, however, allows for meaningful conceptualization of sensitivity to entanglement, which will be greater for the entanglement measure that produces the larger numerical values. Here, we have investigated the partial order between the normalized versions of four entanglement measures based on Schmidt decomposition of bipartite pure quantum states, namely, concurrence, tangle, entanglement robustness and Schmidt number. We have shown that among those four measures, the concurrence and the Schmidt number have the highest and the lowest sensitivity to quantum entanglement, respectively. Further, we have demonstrated how these measures could be used to track the dynamics of quantum entanglement in a simple quantum toy model composed of two qutrits. Lastly, we have employed state-dependent entanglement statistics to compute measurable correlations between the outcomes of quantum observables in agreement with the uncertainty principle. The presented results could be helpful in quantum applications that require monitoring of the available quantum resources for sharp identification of temporal points of maximal entanglement or system separability.

Time evolution of quantum correlations in presence of state dependent bath

The emerging quantum technologies heavily rely on the understanding of dynamics in open quantum systems. In the Born approximation, the initial system-bath correlations are often neglected which can be violated in the strong coupling regimes and quantum state preparation. In order to understand the influence of initial system-bath correlations, we study the extent to which these initial correlations and the distance of separation between the qubits influence the dynamics of quantum entanglement and coherence. It is shown that at low temperatures, the initial correlations have no role to play while at high temperatures, these correlations strongly influence the dynamics. Furthermore, we have shown that the distance of separation between the qubits in presence of a collective bath helps to maintain entanglement and coherence at long times.

Acute entanglement and Photon/Phonons statistics in a balanced/unbalanced [formula omitted]-symmetry systems

We study the significance of Photon/Phonons bunching and antibunching on the dynamics of the quantum entanglement in the presence of coupled PT-symmetry systems with balanced/unbalanced gain and loss. We suggest a hybrid electromechanical system to realize a strong and tunable coupling between a Coplanar-Waveguide (CPW) microwave cavity and a nanomechanical resonator (NAMR) via a superconducting Transmon qubit. The hybrid electromechanical system consists of a non-hermitian Hamiltonian with balanced/unbalanced gain and loss. The interplay between the quantum entanglement and the PT-symmetry systems is also thoroughly investigated. We frame a connection between Number operators, Photon/Phonons antibunching, and entanglement. It has been observed that the relative Photon/Phonons numbers play a key role in the quantum entanglement dynamics. Furthermore, we study that quantum entanglement can be characterized by defining a Photon/Phonons antibunching. The Photon/Phonons antibunching is strongly dependent on the initial squeezed state and the rate of balanced/unbalanced gain and loss of the system.

Spatiotemporal heterogeneity of entanglement in many-body localized systems

We propose a spatio-temporal characterization of the entanglement dynamics in many-body localized (MBL) systems, which exhibits a striking resemblance with dynamical heterogeneity in classical glasses. Specifically, we find that the relaxation times of local entanglement, as measured by the concurrence, are spatially correlated yielding a dynamical length scale for quantum entanglement. As a consequence of this spatio-temporal analysis, we observe that the considered MBL system is made up of dynamically correlated clusters with a size set by this entanglement length scale. The system decomposes into compartments of different activity such as active regions with fast quantum entanglement dynamics and inactive regions where the dynamics is slow. We further find that the relaxation times of the on-site concurrence become broader distributed and more spatially correlated, as disorder increases or the energy of the initial state decreases. Through this spatio-temporal characterization of entanglement, our work unravels a previously unrecognized connection between the behavior of classical glasses and the genuine quantum dynamics of MBL systems.

Measurement-Induced Transition in Long-Range Interacting Quantum Circuits.

The competition between scrambling unitary evolution and projective measurements leads to a phase transition in the dynamics of quantum entanglement. Here, we demonstrate that the nature of this transition is fundamentally altered by the presence of long-range, power-law interactions. For sufficiently weak power laws, the measurement-induced transition is described by conformal field theory, analogous to short-range-interacting hybrid circuits. However, beyond a critical power law, we demonstrate that long-range interactions give rise to a continuum of nonconformal universality classes, with continuously varying critical exponents. We numerically determine the phase diagram for a one-dimensional, long-range-interacting hybrid circuit model as a function of the power-law exponent and the measurement rate. Finally, by using an analytic mapping to a long-range quantum Ising model, we provide a theoretical understanding for the critical power law.

Dynamics of quantum entanglement in a zigzag graphene nanoribbon

We study the dynamics of entanglement between two edge spins in a zigzag graphene nanoribbon (ZGNR) which is thermalized with a reservoir at temperature T. The results show that the entanglement evolution displays oscillating behaviors in the presence of an external magnetic field. Such oscillating behaviors of entanglement strongly depend on the field frequency and relative location between two inter-edge coupled spins. At some critical field frequencies, the entanglement exhibits a periodic structure. When the temperature is low, the oscillating patterns of entanglement are quite regular and symmetrical. When the temperature is high, the patterns of entanglement evolution occur irregular distortions due to the thermal fluctuations. However, the entanglement between two inter-edge coupled spins in ZGNR still exists a nontrivial value even at room temperature.