In this paper we investigate the fractional quantum correlations via squashed entanglement and negativity, where an analytical solution of a fractional Schrödinger equation under an XXX model of a spin-spin Hamiltonian has been introduced. It has shown that, by starting with an initially large entangled state, both quantifiers decrease during the interaction. This decay increases as one increases the degree of the fractional order and the coupling constant between the two spins. However, the squashed entanglement and the negativity increase gradually if the initial state contains a small amount of quantum correlations. The sudden/gradual changes of these phenomena have been observed at small/large values of the fractional order, respectively. The constant behavior of these measures is observed at small values of fractional orders. Our results show that the fractional state can be used as a quantum channel with high efficiency to perform quantum teleportation. The long-lived constant behavior of the teleportation inequality indicates that the efficiency of this channel will be constant during the teleportation process.
In this paper we investigate the fractional quantum correlations via squashed entanglement and negativity, where an analytical solution of a fractional Schrödinger equation under an XXX model of a spin-spin Hamiltonian has been introduced. It has shown that, by starting with an initially large entangled state, both quantifiers decrease during the interaction. This decay increases as one increases the degree of the fractional order and the coupling constant between the two spins. However, the squashed entanglement and the negativity increase gradually if the initial state contains a small amount of quantum correlations. The sudden/gradual changes of these phenomena have been observed at small/large values of the fractional order, respectively. The constant behavior of these measures is observed at small values of fractional orders. Our results show that the fractional state can be used as a quantum channel with high efficiency to perform quantum teleportation. The long-lived constant behavior of the teleportation inequality indicates that the efficiency of this channel will be constant during the teleportation process.
A fractional quantum state has created between two-qubit system by a Heisenberg XYZ model in the presence of the Dzyaloshinskii–Moriya (DM) interaction. The impact of the initial state settings and the interaction parameters on the amount of the quantum correlation is discussed. We used the concurrence and local quantum uncertainty to quantify these correlations. It is shown that, both quantifiers increase suddenly/gradually depending on the order of the fractional state, and whether the system is ferromagnetic or anti-ferromagnetic. The fractional parameter may increase/ stabilized the memory of the generated fractional state. Small values of the DM interaction can maximize the initial quantum correlation of a partial entangled state. The possibility of using these fractional time-dependent states as quantum channels to perform quantum teleportation has examined. It is shown that, preparing the system in anti-ferromagnetic regime improves the fidelity of the teleported state. The strength of the DM interaction and the fractional’s order has a clear effect on the fidelity’s behavior, where they may be used as control parameters to increase the efficiency of the fractional quantum channel in the context of quantum communication.
The efficiency of the fractional state that is generated between a single atom and field by using anti-Jaynes–Cummings model (AJCM) is discussed. The fractional degree and the interaction parameters may be used as controllers to increase the efficiency of the fractional state in the context of quantum communication. It has been shown that, the quantum correlation, capacity, and the ability of the fractional state, increase suddenly/gradually at small/large fractional degree, respectively. At small fractional orders, the constant behavior for all these phenomena is displayed at a short interaction time. The fractional quantum state that is generated by the anti-Jaynes–Cummings model is more efficient than that generated by the well-known Jaynes–Cummings model (JCM), where it can be used to teleport an unknown two-qubit state with larger fidelity.
Abstract Our work explores the time evolution of entanglement, local quantum uncertainty, and correlated coherence within a system modeled by two coupled double quantum dots. The dynamics is described using a time-fractional Schrödinger equation, which is treated here as a phenomenological effective framework introducing temporal nonlocality and memory-like effects, rather than as a first-principles open-system reduction. We vary the fractional parameter τ , the tunneling amplitudes δ A and δ B , and the inter-dot Coulomb interaction strength V , in order to investigate how these key parameters govern the generation, stabilization, and decay of quantum resources within the system. The obtained results reveal that, for both initial states (separable and partially entangled), fractional dynamics with a small τ rapidly generates entanglement reaching maximal values LN ≈ 1 together with strong non-classical correlations quantified by the local quantum uncertainty. Conversely, when τ is closer to unity, entanglement builds up more slowly but the memory-like effects allow quantum resources to remain significant for a longer time, with the negativity remaining above ≈ 0.6 . We also find that higher Coulomb-interaction frequencies V accelerate the build-up of correlations and stabilize coherence, while a strong tunneling asymmetry degrades entanglement and coherence despite the initial benefits of increasing quantum resources. We find that the standard unitary Schrödinger evolution is recovered analytically at τ = 1 , where the Mittag–Leffler functions reduce to ordinary exponentials, while decreasing τ progressively introduces fractional-time nonlocal (memory-like) effects.
Our work explore the time evolution of entanglement, local quantum uncertainty, and correlated coherence, within a system modeled by two double quantum dots. The dynamics is represented using a time-fractional Schrödinger equation, which includes memory effects in a non-Markovian regime. We vary the fractional parameter τ, the tunneling amplitudes δA and δB, as well as the inter-dot interaction strength V, to investigate how these key parameters govern the generation, stabilization, and decay of quantum resources within the system. The obtained results reveal that, for both initial states, fractional dynamics with a low τ rapidly generates entanglement expecting maximal values LN≈1 and non-classical correlations quantified by local quantum uncertainty. Conversely, higher values of τ lead to slower entanglement but memory effects allow quantum resources to remain significant for a longer time, with the negativity remaining above (≈0.6). We also find that higher interaction frequencies V accelerate correlations and stabilize coherence, while a strong tunneling asymmetry degrades entanglement and coherence despite the initial benefits of increasing quantum resources.
Natural thermal entanglement between two qubits with XXX Heisenberg interaction is studied. For the antiferromagnet, increasing coupling strength or decreasing temperature under critical point increases the entanglement. Based on the thermal entanglement as quantum channel, entanglement and information of an input entangled state are transferred via partial teleportation. We find that the entanglement transferred will be lost during the process, and for the entanglement fidelity the partial teleportation is superior to classical communication as concurrence of entangled channel beyond 1/4. We show that both correlation information in input entangled state and individual information of the teleported particle are linearly dissipated. With more entanglement in quantum channel, more entanglement and correlation information can be transferred.
In this paper, the features of quantum teleportation of a maximally entangled input thermal state using a system, consisting of two qubits (spin-1/2) anisotropic XY Heisenberg model with Herring–Flicker coupling in the presence of a magnetic field, are discussed. So, we study the influence on the thermal entanglement of different physical parameters such as temperature [Formula: see text], magnetic field [Formula: see text], degree of anisotropy [Formula: see text] and distance [Formula: see text] between the two spins. The goal is to determine the conditions of use of the system as a good channel to promote quantum teleportation. The amount of output entanglement is quantified by the concurrence [Formula: see text], and the quality of teleportation is analyzed using the concept of fidelity [Formula: see text]. It is shown that [Formula: see text] presents a maximum at extremely low temperature for a large range of the parameter [Formula: see text]. Also, when we increase the temperature, we observe a dissipation of the appropriate range of [Formula: see text] and the decrease of the amplitude of [Formula: see text]. Besides, under an external magnetic field [Formula: see text], we show the appearance of quantum phase transitions with the entanglement vanishing when the condition [Formula: see text] is fulfilled, then the system can ensure the ideal communication transmission. Concerning the Ising model [Formula: see text] in the ground state, the output entanglement is nonzero only in the presence of the magnetic field [Formula: see text], and this model is useful for ensuring a distorted transmission. At finite temperature, the fidelity [Formula: see text] is less than the value 2/3, so that the system is useless as a quantum channel for providing quantum teleportation.