Three-qubit Heisenberg Research Articles

Tripartite entropic uncertainty relation under phase decoherence

We formulate the tripartite entropic uncertainty relation and predict its lower bound in a three-qubit Heisenberg XXZ spin chain when measuring an arbitrary pair of incompatible observables on one qubit while the other two are served as quantum memories. Our study reveals that the entanglement between the nearest neighbors plays an important role in reducing the uncertainty in measurement outcomes. In addition we have shown that the Dolatkhah’s lower bound (Phys Rev A 102(5):052227, 2020) is tighter than that of Ming (Phys Rev A 102(01):012206, 2020) and their dynamics under phase decoherence depends on the choice of the observable pair. In the absence of phase decoherence, Ming’s lower bound is time-invariant regardless the chosen observable pair, while Dolatkhah’s lower bound is perfectly identical with the tripartite uncertainty with a specific choice of pair.

Three-qubit Heisenberg XY Chain with Nearest-neighbour Interaction in the Ultrastrong Coupling Regime of Superconducting Circuits

We explore the simulation of three-qubit Heisenberg XY chain with nearest-neighbour interaction in a system of superconducting charge qubits ultrastrongly coupled to a LC resonator. By resorting to parametric modulation of external magnetic fields, the derived effective Hamiltonian is just the required Heisenberg XY chain with nearest-neighbour interaction. This effective Hamiltonian can be utilized to create two/three-qubit entangled states at the time scale of nanoseconds with high fidelity. Since the entangled states have been widely used in different quantum protocols as valuable resource states, the enhanced fast generation of those states reduces errors at the level of resource states.

Dense Coding in a Three-Qubit Heisenberg XXZ Spin Chain with Three-Site Interactions

This paper investigates the quantum dense coding of a three-qubit XXZ Heisenberg spin chain at thermal equilibrium, with three-site interactions in the presence of an external magnetic field. We analyze the effects of various system parameters on the dense coding in multiple cases with different types of three-site interactions. The results show that the most ideal case for dense coding is the model including both types of three-site interactions, with the imposed condition of XZX + YZY type of three-site interaction is larger than the XZY − YZX type of three-site interaction. The inclusion of the z direction coupling parameter JZ, and external magnetic parameter B are found to be effective for optimizing the dense coding capacity, while the temperature T is turned out to be destructive. Moreover, the ferromagnet (FM) is shown to be more ideal for quantum dense coding than the antiferromagnet (AFM). For FM, by comparing the two types of three-site interactions (XZY − YZX and XZX + YZY), the appropriate model for valid dense coding is suggested and their dominant regions are clarified.

Quantum Otto heat engine with three-qubit [formula omitted] model as working substance

A quantum Otto heat engine is established with a three-qubit Heisenberg XXZ model with Dzyaloshinskii–Moriya (DM) interaction under a homogeneous magnetic field as the working substance. The quantum Otto engine is composed of two quantum isochoric processes and two quantum adiabatic processes. Here we have restricted Bc∕Bh=Jc∕Jh=r in the two adiabatic processes, where r is the adiabatic compression ratio. The work output and efficiency are calculated for our cycle. The possible adiabatic compression ratios and the ratios of work output between our working substance and a single spin under the same external conditions in the Otto cycle are analyzed with different DM interaction parameters and anisotropic parameters. The effects of pairwise entanglements on the heat engine efficiency are discussed.

Qubit-loss-free fusion of W states

Fusion technique plays a key role in the preparation of large-scale $W$ states, but the currently existing fusion schemes are suffering from the qubit loss problem, i.e., the number of the output entangled qubits is smaller than the sum of numbers of the input entangled qubits, which will inevitably decrease the fusion efficiency and increase the number of fusion steps as well as the requirement of quantum memories. In this paper, we design a fusion mechanism to fuse two small-size $W$ states into a large-scale $W$ state without qubit loss, and thus we call it qubit-loss-free (QLF) fusion mechanism. This QLF fusion mechanism is based on a two-outcome positive-operator valued measurement on two qubits extracting from two small-size $W$ states, and works for both pure and mixed $W$ states. The QLF nature of this fusion mechanism clearly increases the final size of the obtained $W$ state, and greatly reduces the number of fusion steps as well as the requirement of quantum memories required to achieve a $W$ state of a target size, so it is more efficient and feasible than the currently existing fusion schemes. There is no complete failure output in our QLF fusion scheme, and all the garbage states are recyclable. Two example schemes are proposed to realize this QLF fusion mechanism in a cavity quantum electrodynamics system and three-qubit Heisenberg XYZ model, respectively, which demonstrates the possibility of the physical realization of this QLF fusion mechanism.

Quantum discord and quantum phase transition in the XXZ spin chain with three-site interaction

Pairwise quantum discord (QD) and entanglement of the three-qubit XXZ Heisenberg spin chain with two types of three-site interactions and an external magnetic field are investigated. Our study found that both entanglement and quantum discord could detect the quantum critical phenomena of this model. We were able to obtain a nonzero value of quantum discord even at high temperature with the increase of XZX[Formula: see text]YZY or XZY[Formula: see text]YZX three-site interaction, however, the cooperative effect of XZX[Formula: see text]YZY and XZY[Formula: see text]YZX interactions is more ideal. Furthermore, in contrast to XZY[Formula: see text]YZX and XZX[Formula: see text]YZY interactions, the cooperative effect of XZX[Formula: see text]YZY and XZY[Formula: see text]YZX three-site interactions is more efficient to enhance the maximum value of quantum discord. Likewise, the cooperative effect of XZX[Formula: see text]YZY and XZY[Formula: see text]YZX interactions is the most optimal to increase the range of magnetic field or anisotropy parameter where quantum discord maintains the maximum value.

Effects of Dzyaloshinskii-Moriya interacton and decoherence on entanglement dynamics in Heisenberg spin chain system with different initial states

With considering the intrinsic decoherence, the dynamic behaviors of quantum entanglement in a three-qubit XXZ Heisenberg system with Dzyaloshinskii-Moriya (DM) interaction and anisotropy for different initial states are investigated. The research result shows that the anisotropy parameter does not affect the system entanglement, however, the intrinsic decoherence has obvious inhibitory effect on entanglement. When the initial state of system is an entangled state, we can obtain the stable value of entanglement by adjusting DM interaction parameters appropriately. As the system initial state is a separation state, entanglement oscillates, and the amplitude of oscillation decays with time periodically, and there will appear the death phenomenon after each oscillation, and with time going on, its concurrence will be zero. When the initial state is entangled, by choosing the proper DM parameter, the three pairs of entanglements oscillate with time and eventually approach to a steady value. The increase of accelerates the decay of concurrence. When the initial state is separated, entanglement oscillates, and the amplitude of oscillation decays with time periodically, and there will appear the death phenomenon after each oscillation, with time going on, its concurrence will be zero. Therefore, the proper initial state and DM interaction parameters can control the concurrence effectively under the intrinsic decoherence, thereby obtaining the preferable entanglement resource.

Quantum Metrology: Surpassing the shot-noise limit with Dzyaloshinskii-Moriya interaction.

Entanglement is at the heart of quantum technologies such as quantum information and quantum metrology. Providing larger quantum Fisher information (QFI), entangled systems can be better resources than separable systems in quantum metrology. However the effects on the entanglement dynamics such as decoherence usually decrease the QFI considerably. On the other hand, Dzyaloshinskii-Moriya (DM) interaction has been shown to excite entanglement. Since an increase in entanglement does not imply an increase in QFI, and also there are cases where QFI decreases as entanglement increases, it is interesting to study the influence of DM interaction on quantum metrology. In this work, we study the QFI of thermal entanglement of two-qubit and three-qubit Heisenberg models with respect to SU(2) rotations. We show that even at high temperatures, DM interaction excites QFI of both ferromagnetic and antiferromagnetic models. We also show that QFI of the ferromagnetic model of two qubits can surpass the shot-noise limit of the separable states, while QFI of the antiferromagnetic model in consideration can only approach to the shot-noise limit. Our results open new insights in quantum metrology with Heisenberg models.

Quantum teleportation in a three-qubit Heisenberg chain with Dzyaloshinsky–Moriya interaction

The quantum teleportation via thermally entangled states of three-qubit Heisenberg spin chains with Dzyaloshinsky–Moriya (DM) interactions under a homogeneous magnetic field has been investigated. It is found that average fidelity and critical temperature depend on not only temperature, magnetic field, but also coupling coefficients, and DM interactions. What is more, we also find that average fidelity has little to do with entanglement.

Entanglement and quantum teleportation in a three-qubit Heisenberg chain with three-site interactions

The thermal entanglement of a three-qubit XXZ Heisenberg model with three-site interactions in an external magnetic field, and the quantum teleportation via this model in thermal equilibrium state are investigated. It is found that entanglement and average fidelity depend on temperature, magnetic field, and anisotropy parameter $$J_Z$$JZ. Only ferromagnetic system is suitable for quantum teleportation. $$\hbox {XZX}+\hbox {YZY}$$XZX+YZY interaction is in favor of entanglement, average fidelity, and critical temperatures, while $$\text{ XZY }- \hbox {YZX}$$XZY-YZX interaction against all of them. Moreover, we also find entanglement does not fully reflect average fidelity in virtue of study the relation between entanglement and average fidelity.

Influence of intrinsic decoherence on entanglement teleportation via a Heisenberg XYZ model with different Dzyaloshinskii–Moriya interactions

We investigate the characteristics of entanglement teleportation of a two-qubit and three-qubit Heisenberg XYZ model under different Dzyaloshinskii---Moriya (DM) interactions with intrinsic decoherence taken into account. The two-qubit results reveal that the dynamics of entanglement is a symmetric function about the coupling coefficient $$J$$J for the $$z$$z-component DM system, whereas it is not for the $$x$$x-component DM system. The ferromagnetic case is superior to the antiferromagnetic case to restrain decoherence when using the $$x$$x-component DM system. The dependencies of entanglement, the output entanglement, and the average fidelity on initial state angle $$\alpha $$? all demonstrate periodicity. Moreover, the $$x$$x-component DM system can get a high fidelity both in two-qubit and in three-qubit teleportation protocol.

Quantum teleportation in an XXZ spin chain system with three-site interaction

In this paper, we study carefully the quantum teleportation by means of a channel of a three-qubit Heisenberg XXZ ring, and calculate the fidelity of quantum teleportation. Comparing the four XXZ models: one without three-site interaction, one with XZX +YZY type three-site interaction, one with XZY-YZX type three-site interaction, one with both the two kinds of the three-site interaction, we find some ideal models by which the teleportation only needs a weakest magnetic field and a highest temperature to work successfully. The result could provide a theoretical basis for later experiments.

Tripartite correlations in a Heisenberg [formula omitted] spin ring in thermal equilibrium

Tripartite correlations are investigated at length by various witnesses such as tripartite negativity, genuine tripartite entanglement, total tripartite correlations and genuine tripartite correlations. Their behaviors following various tunable system parameters as well as their connections with quantum phase transitions (QPTs) in a three-qubit Heisenberg XXZ spin ring with three-spin interaction in thermal equilibrium are discussed. The results show that these tripartite correlation witnesses can faithfully detect the critical points associated with QPTs at zero temperature limit in this model. In addition, total tripartite correlations and genuine tripartite correlations can even signal critical points with respect to anisotropy Δ at finite low temperatures.

Quantum discord in the three-spin XXZ chain with Dzyaloshinskii-Moriya interaction

The quantum discord (QD) of a three-qubit Heisenberg XXZ system with the Dzyaloshinskii-Moriya (DM) interaction parameter is investigated, and the three-qubit QD under Ornstein-Uhlenbeck noise is calculated. We find that both DM interaction parameter Dz and anisotropic parameter Jz can increase QD and entanglement but Dz is a more efficient parameter in the antiferromagnetic case. We observe a complex range of QD with the change of Dz and a sudden change of QD with the variation of Jz in the ferromagnetic case. We show that the decrease durations of both QD and entanglement can be prolonged by increasing DM interaction and reducing noise bandwidth  in the evolutionary process. quantum discord, XXZ-spin chain, DM interaction, Ornstein-Uhlenbeck noise

Pairwise quantum correlations of a three-qubit XY chain with phase decoherence

Quantum correlations, including entanglement and discord with its geometric measure in a three-qubit Heisenberg XY chain, with phase decoherence, are investigated when a nonuniform magnetic field is applied. When the qubits are initially in an unentangled state, the nearest neighbor pairwise correlations are destroyed by phase decoherence, but stationary correlations appear for next-to-neighbor qubits. With an inhomogeneous magnetic field, the stationary correlations appear for nearest neighbor qubits and they disappear for next-to-nearest neighbor qubits. But when the qubits are initially in an entangled state, an inhomogeneous magnetic field can enhance the stationary correlations of next-to-neighbor qubits, but it cannot do so for nearest neighbor qubits. The decoherence effect on stationary correlations is much stronger for next-to-nearest neighbor qubits than it is for nearest neighbor qubits. Finally, a uniform magnetic field can affect the correlations when the qubits are initially in an entangled state, but it cannot affect them when the qubits are initially in an unentangled state.

Quantum Correlation in Three-Qubit Heisenberg Model with Dzyaloshinskii—Moriya Interaction

We investigate the pairwise thermal quantum discord in a three-qubit XXZ model with Dzyaloshinskii—Moriya (DM) interaction. We find that the effects of DM interaction on antiferromagnetic system is distinct from that of ferromagnetic system. The magnetic field supplemented with DM term contribute to enhance the range of quantum discord. It is revealed that the situations where quantum discord fails to indicate a sudden change of groundstate at finite temperature though indicating such a sudden change of groundstate at zero temperature. Dynamics of pairwise thermal quantum discord is considered as well. Thermal quantum discord vanishes in asymptotic limit regardless of its initial values, however, thermal entanglement suddenly disappears in finite time.

Quantum Phase Transition and Thermal Entanglement in the Isotropic XXX Model

We investigate the quantum phase transition (QPT) and the pairwise thermal entanglement in the three-qubit Heisenberg XXX chain with Dzyaloshinskii—Moriya (DM) interaction under a magnetic field. The ground states of the system exist crossing points, which shows that the system exhibits a QPT. At a given temperature, the entanglement undergoes two sudden changes (platform-like behavior) as the DM interaction or external magnetic field increases. This special property can be used as the entanglement switch, which is also influenced by the temperature. We can modulate the DM interaction or external magnetic field to control the entanglement switch.

Thermal Entangled Quantum Heat Engine Working with a Three-Qubit Heisenberg XX Model

Based on a three-qubit isotropic Heisenberg XX model with a constant external magnetic field, we construct an entangled quantum heat engine (QHE). The expressions for several thermodynamic quantities such as the heat transferred, the work and the efficiency are derived. Moreover, the influence of the entanglement on the thermodynamic quantities is investigated analytically and numerically. Several interesting features of the variation of the heat transferred, the work and the efficiency with the concurrences of the thermal entanglement of two different thermal equilibrium states in zero and nonzero magnetic fields are obtained. At last, we discussed the maximum efficiency of the QHE.

Pairwise entanglement in the Heisenberg XX model with three-site interactions

We investigate the effects of three-site interactions on the pairwise entanglement in a three-qubit Heisenberg XX model. We find the three-site interactions only in favor of the thermal entanglement and benefit the teleportation between the next-to-nearest neighbor qubits. In addition, we also study the stationary entangled state in the model with intrinsic decoherence taken into account. The influence of different types of three-site interactions on the stationary entangled state is then examined.

Pairwise thermal entanglement in a three-qubit Heisenberg XX model with a nonuniform magnetic field and Dzyaloshinski—Moriya interaction

Pairwise thermal entanglement in a three-qubit Heisenberg XX model is investigated when a nonuniform magnetic field and the Dzyaloshinski—Moriya interaction are included. We find that the nonuniform magnetic field and Dzyaloshinski—Moriya interaction are the more efficient control parameters for the increase of entanglement and critical temperature. For both the nearest neighbour sites and the next nearest neighbour sites, the magnetic field can induce entanglement to a certain extent and the Dzyaloshinski—Moriya interaction can enhance the entanglement to a stable value. The steady value of the nearest neighbour site entanglement C12 is larger than the next nearest neighbour site entanglement C13. An interesting phenomenon is that the entanglement curve of C12 appears a peak value when the Dzyaloshinski—Moriya interaction is considered in a nonuniform magnetic field.