Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Vestnik of Samara University Natural Science Series

Dynamics of entanglement of separable three-qubit states in the Tavis — Cummings multiphoton model

A. R. Bagrov, E. K. Bashkirov

Published Dec 11, 2025• 0 citations
Publisher

Abstract

In this work we study in detail the generalized Tavis — Cummings model, in which three identical qubits are trapped in a lossless single-mode resonator and interact resonantly with the quantized thermal electromagnetic field of this resonator by means of multiphoton processes. An exact solution of the unsteady Schr¨odinger equation for separable qubit states and Fock states of the resonator field was demonstrated for the model under study. The resulting expressions were used to calculate the density matrix in the case of the thermal field of the resonator and to calculate the criterion for pairwise entanglement of qubits — Wootters concurrence. The results showed that the thermal field can induce pairwise entanglement between qubits for all initial separable states for certain system parameters. The calculations also showed that the photon multiple can be considered as an effective mechanism for controlling the entanglement of qubits, since its increase leads to a significant suppression of the effect of the sudden death of entanglement and to an increase in the maximum degree of entanglement for some separable qubit states.

DOI
10.18287/2541-7525-2025-31-2-7-21

Related papers

Dynamics of entanglement of qubits in the three-qubit Tavis — Cummings model with dipole-dipole interaction

Alexander R. Bagrov, Eugene K. Bashkirov

The article studies the dynamics of pairwise entanglement of three qubits, two of which are trapped in a resonator and interact with a single-mode ideal resonator through single-photon transitions, and the third qubit is outside the resonator. This takes into account the dipole-dipole coupling between the isolated qubit and the qubit in the resonator. We have found a solution to the quantum nonstationary Schrodinger equation for the total wave function of the system for the initial separable and biseparable states of qubits and the thermal initial state of the resonator field. Using these solutions, the criterion of entanglement of qubit pairs - negativity is calculated. The results of numerical simulation of the negativity criterion have shown that the including of a small dipole-dipole coupling between an isolated and one of the trapped qubits can lead to significant entanglement of qubit pairs for all initial states. There is a transition of entanglement from one pair of atoms to other pairs of atoms during the evolution of the system. It is also shown that for some separable and biseparable states, the dipole-dipole interaction can suppress the effect of sudden death of entanglement.

Vestnik of Samara University Natural Science Series•Oct 28, 2024•0 citations

DYNAMICS OF THE THREE-QUBITS TAVIS — CUMMINGS MODEL

Alexander R. Bagrov, Eugene K. Bashkirov

In this article, we have studied the entanglement dynamics of three identical qubits (natural or artificial two-level atoms) resonantly interacting with the one mode of the thermal field of a microwave lossless resonator via one-photon transitions. An exact solution of the quantum time Schrodinger equation is found for the total wave function of the system for the initial separable and entangled states of qubits and the Fock initial state of the resonator. On the basis of this solution, an exact solution of the quantum Liouville equation for the total time-dependent density matrix of the system in the case of a thermal field of the resonator is constructed. The exact solution for the full density matrix is used to calculate the criterion of entanglement of pairs of qubits negativity. The resultsof numerical simulation of the time dependence of the negativity of pairs of qubits showed that with an increase in the intensity of the thermal resonator field, the degree of entanglement of pairs of qubits decreases. It is also shown that In the model under consideration, for any initial states of qubits and intensities of the thermal field of the resonator, the effect of sudden death of entanglement takes place. This behavior of the entanglement parameter in the model under consideration differs from that in the two-qubit model. For two-qubit model, the effect of the sudden death of entanglement takes place only for the initial entangled states of qubits and intense thermal fields of the resonator.

Vestnik of Samara University Natural Science Series•Dec 29, 2022•4 citations

Qubit-qubit entanglement in the Tavis–Cummings model with two independent resonators

Alexander R. Bagrov, Eugene K. Bashkirov

In this paper, a three-qubit Tavis-Cummings model with two independent lossless single-mode resonators is considered. It is assumed that the initial states of the resonator fields are thermal fields and the qubits are in genuine entangled W- and GHZ-type states. For the model under study and the specified initial states of the resonator fields and qubits, we have exactly solved the quantum Liouville equation for the full density matrix. The full density matrix was used to calculate the entanglement parameters - negativity and fidelity. The computer simulation results showed that in the investigated model, the entanglement for all initial qubit states breaks down rapidly with increasing intensity of the thermal fields of the resonators compared to the previously investigated three-qubit models. Moreover, a sudden death of entanglement is observed even for vacuum resonator fields.

•Jan 1, 2025•0 citations

Dynamics of a two-qubit Tavis-Cummings model in the presence of an Ising-type interaction between qubits

Eugene K. Bashkirov

In this paper, we investigated the dynamics of entanglement of two qubits interacting non-resonantly with the thermal field of a one-mode lossless resonator, taking into account the Ising-type direct interaction between qubits. Based on the exact solution of the quantum Liouville equation, we found the density matrix of the system under consideration. With its help, the reduced qubit-qubit density matrix was calculated and the entanglement criteriоn of the two-qubit system, Pres-Horodeсki parameter, was found. It was shown that for the resonance model and separable initial states of qubits, the direct interaction of qubits leads to a significant increase in the maximum degree of their entanglement. It was also found that for the nonresonant interaction between qubits and field, the increase of the maximum degree of entanglement of qubits is much greater than that due to direct interaction. For the original entangled Bell-type state of the qubits, the direct interaction was found to lead to the vanishing of the effect of the sudden death of entanglement in the case of a resonant qubit-field interaction and, conversely, to an increase in this effect for a nonresonant interaction.

Computer Optics•Aug 1, 2024•1 citation

Sudden death of entanglement in a thermal three-qubit Tavis-Cummings model

Alexander R. Bagrov, Eugene K. Bashkirov

In this article, we consider the entanglement between three identical qubits resonantly interacting with a thermal field of an Q-infinite resonator. We derived the exact solution of the evolution equation for density matrix of the considered system. On it basis we calculate the negativity as a criteria of entanglement between pairs of qubits for biseparable and entangled W-type states of qubits. The results showed that for considered initial qubits states the effect of the entanglement sudden death occurs for all values of the average number of thermal photons.

International Conference on Information Technology and Nanotechnology (ITNT)•Apr 17, 2023•4 citations

Analysis of the behavior of entanglement parameters for the three-qubit Tavis-Cummings model with multiphoton processes

Alexander R. Bagrov, Башкиров Е. К

In this paper, we analyze in detail the dynamics of the negativity criterion, fidelity and concurrence fill for the Tavis-Cummings model in which three qubits are in a common single-mode ideal resonator and interact resonantly with the field mode via multiphoton processes. By solving the unsteady Schrödinger equation, we give analytic solutions for genuine entangled Werner- and Greenberger-Horn-Zeilinger states. It is shown that the multiplicity of photon transitions can significantly stabilize the genuine entangled states of both types. Key features in the dynamics pattern of the entanglement parameters are highlighted. We conclude that the negativity criterion is not suitable for describing the dynamics of entanglement of qubits in the case of three-qubit Greenberger-Horn-Zeilinger states. Main advantages of the concurrence fill over the negativity criterion are shown.

Computer Optics•Dec 1, 2025•0 citations
In this work we study in detail the generalized Tavis — Cummings model, in which three identical qubits are trapped in a lossless single-mode resonator and interact resonantly with the quantized thermal electromagnetic field of this resonator by means of multiphoton processes. An exact solution of the unsteady Schr¨odinger equation for separable qubit states and Fock states of the resonator field was demonstrated for the model under study. The resulting expressions were used to calculate the density matrix in the case of the thermal field of the resonator and to calculate the criterion for pairwise entanglement of qubits — Wootters concurrence. The results showed that the thermal field can induce pairwise entanglement between qubits for all initial separable states for certain system parameters. The calculations also showed that the photon multiple can be considered as an effective mechanism for controlling the entanglement of qubits, since its increase leads to a significant suppression of the effect of the sudden death of entanglement and to an increase in the maximum degree of entanglement for some separable qubit states.
The article studies the dynamics of pairwise entanglement of three qubits, two of which are trapped in a resonator and interact with a single-mode ideal resonator through single-photon transitions, and the third qubit is outside the resonator. This takes into account the dipole-dipole coupling between the isolated qubit and the qubit in the resonator. We have found a solution to the quantum nonstationary Schrodinger equation for the total wave function of the system for the initial separable and biseparable states of qubits and the thermal initial state of the resonator field. Using these solutions, the criterion of entanglement of qubit pairs - negativity is calculated. The results of numerical simulation of the negativity criterion have shown that the including of a small dipole-dipole coupling between an isolated and one of the trapped qubits can lead to significant entanglement of qubit pairs for all initial states. There is a transition of entanglement from one pair of atoms to other pairs of atoms during the evolution of the system. It is also shown that for some separable and biseparable states, the dipole-dipole interaction can suppress the effect of sudden death of entanglement.
In this article, we have studied the entanglement dynamics of three identical qubits (natural or artificial two-level atoms) resonantly interacting with the one mode of the thermal field of a microwave lossless resonator via one-photon transitions. An exact solution of the quantum time Schrodinger equation is found for the total wave function of the system for the initial separable and entangled states of qubits and the Fock initial state of the resonator. On the basis of this solution, an exact solution of the quantum Liouville equation for the total time-dependent density matrix of the system in the case of a thermal field of the resonator is constructed. The exact solution for the full density matrix is used to calculate the criterion of entanglement of pairs of qubits negativity. The resultsof numerical simulation of the time dependence of the negativity of pairs of qubits showed that with an increase in the intensity of the thermal resonator field, the degree of entanglement of pairs of qubits decreases. It is also shown that In the model under consideration, for any initial states of qubits and intensities of the thermal field of the resonator, the effect of sudden death of entanglement takes place. This behavior of the entanglement parameter in the model under consideration differs from that in the two-qubit model. For two-qubit model, the effect of the sudden death of entanglement takes place only for the initial entangled states of qubits and intense thermal fields of the resonator.
In this paper, a three-qubit Tavis-Cummings model with two independent lossless single-mode resonators is considered. It is assumed that the initial states of the resonator fields are thermal fields and the qubits are in genuine entangled W- and GHZ-type states. For the model under study and the specified initial states of the resonator fields and qubits, we have exactly solved the quantum Liouville equation for the full density matrix. The full density matrix was used to calculate the entanglement parameters - negativity and fidelity. The computer simulation results showed that in the investigated model, the entanglement for all initial qubit states breaks down rapidly with increasing intensity of the thermal fields of the resonators compared to the previously investigated three-qubit models. Moreover, a sudden death of entanglement is observed even for vacuum resonator fields.
In this paper, we investigated the dynamics of entanglement of two qubits interacting non-resonantly with the thermal field of a one-mode lossless resonator, taking into account the Ising-type direct interaction between qubits. Based on the exact solution of the quantum Liouville equation, we found the density matrix of the system under consideration. With its help, the reduced qubit-qubit density matrix was calculated and the entanglement criteriоn of the two-qubit system, Pres-Horodeсki parameter, was found. It was shown that for the resonance model and separable initial states of qubits, the direct interaction of qubits leads to a significant increase in the maximum degree of their entanglement. It was also found that for the nonresonant interaction between qubits and field, the increase of the maximum degree of entanglement of qubits is much greater than that due to direct interaction. For the original entangled Bell-type state of the qubits, the direct interaction was found to lead to the vanishing of the effect of the sudden death of entanglement in the case of a resonant qubit-field interaction and, conversely, to an increase in this effect for a nonresonant interaction.
In this article, we consider the entanglement between three identical qubits resonantly interacting with a thermal field of an Q-infinite resonator. We derived the exact solution of the evolution equation for density matrix of the considered system. On it basis we calculate the negativity as a criteria of entanglement between pairs of qubits for biseparable and entangled W-type states of qubits. The results showed that for considered initial qubits states the effect of the entanglement sudden death occurs for all values of the average number of thermal photons.
In this paper, we analyze in detail the dynamics of the negativity criterion, fidelity and concurrence fill for the Tavis-Cummings model in which three qubits are in a common single-mode ideal resonator and interact resonantly with the field mode via multiphoton processes. By solving the unsteady Schrödinger equation, we give analytic solutions for genuine entangled Werner- and Greenberger-Horn-Zeilinger states. It is shown that the multiplicity of photon transitions can significantly stabilize the genuine entangled states of both types. Key features in the dynamics pattern of the entanglement parameters are highlighted. We conclude that the negativity criterion is not suitable for describing the dynamics of entanglement of qubits in the case of three-qubit Greenberger-Horn-Zeilinger states. Main advantages of the concurrence fill over the negativity criterion are shown.