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Quantum Entanglement Dynamics and Concurrence Preservation in a Noisy Two-Qubit System with External Control Field

Karim Ghorbani

Karim Ghorbani

Physics Department, Faculty of Science, Arak UniversityArak, Iran
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Ghorbani, Karim
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Reza Rezaee

Reza Rezaee

Physics Department, Faculty of Science, Arak UniversityArak, Iran
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Rezaee, Reza
  
Jul 01, 2025
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Article Category: Tutorial
Published Online: Jul 01, 2025
Page range: 290 - 298
Received: Mar 19, 2025
Accepted: May 06, 2025
DOI: https://doi.org/10.2478/qic-2025-0015
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© 2025 Karim Ghorbani et al., published by Sciendo
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Figure 1.

Time evolution of the concurrence for maximally entangled initial state |Φ+〉 when the included decoherence is spontaneous emission (left panel) and when the included decoherence is dephasing (right panel). The effect of control Hamiltonian is shown.
Time evolution of the concurrence for maximally entangled initial state |Φ+〉 when the included decoherence is spontaneous emission (left panel) and when the included decoherence is dephasing (right panel). The effect of control Hamiltonian is shown.

Figure 2.

Time evolution of the concurrence for the initial state |ψ〉 when the included decoherence is spontaneous emission (left panel) and when the included decoherence is dephasing (right panel). The effect of the control Hamiltonian is shown and compared when there is no control Hamiltonian.
Time evolution of the concurrence for the initial state |ψ〉 when the included decoherence is spontaneous emission (left panel) and when the included decoherence is dephasing (right panel). The effect of the control Hamiltonian is shown and compared when there is no control Hamiltonian.

Figure 3.

Time evolution of the concurrence for the initially prepared mixed state is defined as equal mixture of |Φ+〉 and |ii〉, where |ii〉 = |11〉, |00〉. In the top panel the included decoherence is spontaneous emission and in the bottom panel the included decoherence is dephasing. The effect of control Hamiltonian is shown for comparison.
Time evolution of the concurrence for the initially prepared mixed state is defined as equal mixture of |Φ+〉 and |ii〉, where |ii〉 = |11〉, |00〉. In the top panel the included decoherence is spontaneous emission and in the bottom panel the included decoherence is dephasing. The effect of control Hamiltonian is shown for comparison.

The optimized control parameters for decoherence type being spontaneous emission_

γ ≠ 0 A1 A2 A3 ω1 ω2 ω3
|Φ+〉 〈Φ+| + |11〉 〈11| 0.585 1.470 0.150 3.597 5.599 0
|Φ+〉 〈Φ+| + |00〉 〈00| 0.922 1.243 –0.279 10.295 –1.90 6.258

The optimized control parameters for decoherence type being dephasing_

γϕ ≠ 0 A1 A2 A3 ω1 ω2 ω3
|Φ+〉 〈Φ+| + |11〉 〈11| 0.223 0.276 0.348 3.191 8.545 4.945
|Φ+〉 〈Φ+| + |00〉 〈00| –2.628 –11.256 –2.188 51.388 75.113 17.965

The optimized control parameters for decoherence type being spontaneous emission or dephasing_ The initial state is a superposition of product and entangled states_

A1 A2 A3 ω1 ω2 ω3
γ ≠ 0 (spontaneous emission) 0.362 0.714 –0.130 13.416 5.675 5.456
γϕ ≠ 0 (dephasing) –1.244 0.270 1.079 19.642 16.755 0.508
Language:
English
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Journal Subjects:
Physics, Quantum Physics
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