Probing a Hybrid Channel for the Dynamics of Non-Local Features
<p>The physical model of the hybrid channel with thermal, magnetic, and classical dephasing parts controlled by static noise employed for the dynamics of the two-qubit Heisenberg spin state characterized by various parameters, such as spin–spin, DM, and KSEA interaction.</p> "> Figure 2
<p>Dynamics of negativity (<b>a</b>), entropic uncertainty (<b>b</b>), <math display="inline"><semantics> <msub> <mo>ℓ</mo> <mn>1</mn> </msub> </semantics></math>-norm coherence (<b>c</b>), and linear entropy (<b>d</b>) as functions of static noise disorder parameter <math display="inline"><semantics> <msub> <mo>Δ</mo> <mi>Q</mi> </msub> </semantics></math> against time in a two-spin system influenced by an external TMCC. For all the plots, we set <math display="inline"><semantics> <mrow> <mi>λ</mi> <mo>=</mo> <mn>0.1</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi>K</mi> <mi>z</mi> </msub> <mo>=</mo> <mn>5</mn> </mrow> </semantics></math>, and <math display="inline"><semantics> <mrow> <mi>J</mi> <mo>/</mo> <mi>T</mi> <mo>/</mo> <msub> <mi>D</mi> <mi>z</mi> </msub> <mo>/</mo> <msub> <mi>J</mi> <mi>z</mi> </msub> <mo>/</mo> <msub> <mo>Δ</mo> <mi>z</mi> </msub> <mo>/</mo> <mi>B</mi> <mo>/</mo> <mi>J</mi> <mo>/</mo> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>.</p> "> Figure 3
<p>Dynamics of negativity (<b>a</b>), entropic uncertainty (<b>b</b>), <math display="inline"><semantics> <msub> <mo>ℓ</mo> <mn>1</mn> </msub> </semantics></math>-norm coherence (<b>c</b>), and linear entropy (<b>d</b>) as functions of classical field’s coupling strength <math display="inline"><semantics> <mi>λ</mi> </semantics></math> against time in a two-spin state influenced by an external TMCC. For all the plots, we set <math display="inline"><semantics> <mrow> <msub> <mo>Δ</mo> <mi>Q</mi> </msub> <mo>=</mo> <mn>2</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi>K</mi> <mi>z</mi> </msub> <mo>=</mo> <mn>5</mn> </mrow> </semantics></math>, and <math display="inline"><semantics> <mrow> <mi>J</mi> <mo>/</mo> <mi>T</mi> <mo>/</mo> <msub> <mi>D</mi> <mi>z</mi> </msub> <mo>/</mo> <msub> <mi>J</mi> <mi>z</mi> </msub> <mo>/</mo> <msub> <mo>Δ</mo> <mi>z</mi> </msub> <mo>/</mo> <mi>B</mi> <mo>/</mo> <mi>J</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>.</p> "> Figure 4
<p>Dynamics of negativity (<b>a</b>), entropic uncertainty (<b>b</b>), <math display="inline"><semantics> <msub> <mo>ℓ</mo> <mn>1</mn> </msub> </semantics></math>-norm coherence (<b>c</b>), and linear entropy (<b>d</b>) as functions of temperature <span class="html-italic">T</span> against time in a two-spin system influenced by an external TMCC. For all the plots, we set <math display="inline"><semantics> <mrow> <msub> <mo>Δ</mo> <mi>Q</mi> </msub> <mo>=</mo> <mn>2</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>λ</mi> <mo>=</mo> <mn>0.1</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi>K</mi> <mi>z</mi> </msub> <mo>=</mo> <mn>5</mn> </mrow> </semantics></math>, and <math display="inline"><semantics> <mrow> <mi>J</mi> <mo>/</mo> <msub> <mi>D</mi> <mi>z</mi> </msub> <mo>/</mo> <msub> <mi>J</mi> <mi>z</mi> </msub> <mo>/</mo> <msub> <mo>Δ</mo> <mi>z</mi> </msub> <mo>/</mo> <mi>B</mi> <mo>/</mo> <mi>J</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>.</p> "> Figure 5
<p>Dynamics of negativity (<b>a</b>), entropic uncertainty (<b>b</b>), <math display="inline"><semantics> <msub> <mo>ℓ</mo> <mn>1</mn> </msub> </semantics></math>-norm coherence (<b>c</b>), and linear entropy (<b>d</b>) as functions of KSEA interaction along the <span class="html-italic">z</span>-axis <math display="inline"><semantics> <msub> <mi>K</mi> <mi>z</mi> </msub> </semantics></math> against time in a two-spin state influenced by an external TMCC. For all the plots, we set <math display="inline"><semantics> <mrow> <msub> <mo>Δ</mo> <mi>Q</mi> </msub> <mo>=</mo> <mn>2</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>λ</mi> <mo>=</mo> <mn>0.1</mn> </mrow> </semantics></math>, and <math display="inline"><semantics> <mrow> <mi>J</mi> <mo>/</mo> <msub> <mi>D</mi> <mi>z</mi> </msub> <mo>/</mo> <msub> <mi>J</mi> <mi>z</mi> </msub> <mo>/</mo> <msub> <mo>Δ</mo> <mi>z</mi> </msub> <mo>/</mo> <mi>B</mi> <mo>/</mo> <mi>J</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>.</p> "> Figure 6
<p>Dynamics of negativity (<b>a</b>), entropic uncertainty (<b>b</b>), <math display="inline"><semantics> <msub> <mo>ℓ</mo> <mn>1</mn> </msub> </semantics></math>-norm coherence (<b>c</b>), and linear entropy (<b>d</b>) as functions of magnetic field strength <span class="html-italic">B</span> against time in a two-spin state influenced by an external TMCC. For all the plots, we set <math display="inline"><semantics> <mrow> <msub> <mo>Δ</mo> <mi>Q</mi> </msub> <mo>=</mo> <mn>2</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>λ</mi> <mo>=</mo> <mn>0.1</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi>K</mi> <mi>z</mi> </msub> <mo>=</mo> <mn>5</mn> </mrow> </semantics></math>, and <math display="inline"><semantics> <mrow> <mi>J</mi> <mo>/</mo> <msub> <mi>D</mi> <mi>z</mi> </msub> <mo>/</mo> <msub> <mi>J</mi> <mi>z</mi> </msub> <mo>/</mo> <msub> <mo>Δ</mo> <mi>z</mi> </msub> <mo>/</mo> <mi>J</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>.</p> "> Figure 7
<p>Dynamics of negativity (<b>a</b>), entropic uncertainty (<b>b</b>), <math display="inline"><semantics> <msub> <mo>ℓ</mo> <mn>1</mn> </msub> </semantics></math>-norm coherence (<b>c</b>), and linear entropy (<b>d</b>) as functions of DM interaction strength along the <span class="html-italic">z</span>-axis <math display="inline"><semantics> <msub> <mi>D</mi> <mi>z</mi> </msub> </semantics></math> against time in a two-spin state influenced by an external TMCC. For all the plots, we set <math display="inline"><semantics> <mrow> <msub> <mo>Δ</mo> <mi>Q</mi> </msub> <mo>=</mo> <mn>2</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>λ</mi> <mo>=</mo> <mn>0.1</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi>K</mi> <mi>z</mi> </msub> <mo>=</mo> <mn>5</mn> </mrow> </semantics></math>, and <math display="inline"><semantics> <mrow> <mi>J</mi> <mo>/</mo> <msub> <mi>D</mi> <mi>z</mi> </msub> <mo>/</mo> <msub> <mo>Δ</mo> <mi>z</mi> </msub> <mo>/</mo> <mi>B</mi> <mo>/</mo> <mi>J</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>.</p> "> Figure 8
<p>Dynamics of negativity (<b>a</b>), entropic uncertainty (<b>b</b>), <math display="inline"><semantics> <msub> <mo>ℓ</mo> <mn>1</mn> </msub> </semantics></math>-norm coherence (<b>c</b>), and linear entropy (<b>d</b>) as functions of the symmetric exchange spin-spin interaction strength in the <span class="html-italic">z</span>-direction along <math display="inline"><semantics> <msub> <mo>Δ</mo> <mi>z</mi> </msub> </semantics></math> against time in a two-spin state influenced by an external TMCC. For all the plots, we set <math display="inline"><semantics> <mrow> <msub> <mo>Δ</mo> <mi>Q</mi> </msub> <mo>=</mo> <mn>2</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>λ</mi> <mo>=</mo> <mn>0.1</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi>K</mi> <mi>z</mi> </msub> <mo>=</mo> <mn>5</mn> </mrow> </semantics></math>, and <math display="inline"><semantics> <mrow> <mi>J</mi> <mo>/</mo> <msub> <mi>D</mi> <mi>z</mi> </msub> <mo>/</mo> <mi>B</mi> <mo>/</mo> <mi>J</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>.</p> "> Figure 9
<p>Dynamics of negativity (<b>a</b>), entropic uncertainty (<b>b</b>), <math display="inline"><semantics> <msub> <mo>ℓ</mo> <mn>1</mn> </msub> </semantics></math>-norm coherence (<b>c</b>), and linear entropy (<b>d</b>) as functions of the Heisenberg exchange interaction strength <span class="html-italic">J</span> against time in a two-spin state influenced by an external TMCC. For all the plots, we set <math display="inline"><semantics> <mrow> <msub> <mo>Δ</mo> <mi>Q</mi> </msub> <mo>=</mo> <mn>2</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>λ</mi> <mo>=</mo> <mn>0.1</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi>K</mi> <mi>z</mi> </msub> <mo>=</mo> <mn>5</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>T</mi> <mo>=</mo> <mn>0.5</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>J</mi> <mo>/</mo> <msub> <mi>D</mi> <mi>z</mi> </msub> <mo>/</mo> <mi>B</mi> <mo>/</mo> <mi>J</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>.</p> "> Figure 10
<p>(<b>a</b>) Dynamics of fidelity between states <math display="inline"><semantics> <mrow> <msub> <mi>ρ</mi> <mrow> <mi>s</mi> <mi>t</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>,</mo> <mi>T</mi> <mo>)</mo> </mrow> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>ρ</mi> <mo>(</mo> <mn>0</mn> <mo>,</mo> <mi>T</mi> <mo>)</mo> </mrow> </semantics></math> for the two-qubit case when exposed to the hybrid channel against various strengths of classical dephasing while setting <math display="inline"><semantics> <mrow> <mi>λ</mi> <mo>=</mo> <mn>0.1</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi>K</mi> <mi>z</mi> </msub> <mo>=</mo> <mn>5</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>T</mi> <mo>=</mo> <mn>0.5</mn> </mrow> </semantics></math>, and <math display="inline"><semantics> <mrow> <mi>J</mi> <mo>/</mo> <msub> <mi>D</mi> <mi>z</mi> </msub> <mo>/</mo> <mi>B</mi> <mo>/</mo> <mi>J</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>. (<b>b</b>) Same as (<b>a</b>), but for <math display="inline"><semantics> <mrow> <msub> <mi>ρ</mi> <mrow> <mi>s</mi> <mi>t</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>,</mo> <mi>T</mi> <mo>)</mo> </mrow> </mrow> </semantics></math> and <math display="inline"><semantics> <msub> <mi>ρ</mi> <mn>0</mn> </msub> </semantics></math>.</p> ">
Abstract
:1. Introduction
2. Physical Model
2.1. Thermal and Magnetic Interaction
2.2. The Exposure to a Classical Channel
The Influence of Classical Static Noise Disorder
2.3. Quantum Criteria Quantifiers
2.3.1. Bipartite Negativity
2.3.2. The Entropic Uncertainty Measure
2.3.3. -Norm of Coherence
2.3.4. Linear Entropy
3. Results
Fidelity of the State
4. Experimental Feasibility
5. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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Rahman, A.u.; Yang, M.; Zangi, S.M.; Qiao, C. Probing a Hybrid Channel for the Dynamics of Non-Local Features. Symmetry 2023, 15, 2189. https://doi.org/10.3390/sym15122189
Rahman Au, Yang M, Zangi SM, Qiao C. Probing a Hybrid Channel for the Dynamics of Non-Local Features. Symmetry. 2023; 15(12):2189. https://doi.org/10.3390/sym15122189
Chicago/Turabian StyleRahman, Atta ur, Macheng Yang, Sultan Mahmood Zangi, and Congfeng Qiao. 2023. "Probing a Hybrid Channel for the Dynamics of Non-Local Features" Symmetry 15, no. 12: 2189. https://doi.org/10.3390/sym15122189
APA StyleRahman, A. u., Yang, M., Zangi, S. M., & Qiao, C. (2023). Probing a Hybrid Channel for the Dynamics of Non-Local Features. Symmetry, 15(12), 2189. https://doi.org/10.3390/sym15122189