The Underlying Order Induced by Orthogonality and the Quantum Speed Limit
We perform a comprehensive analysis of the set of parameters <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>{</mo><msub><mi>r</mi><mi>i</mi></msub><m...
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-07-01
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| Series: | Quantum Reports |
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| Online Access: | https://www.mdpi.com/2624-960X/3/3/24 |
| _version_ | 1797517414994280448 |
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| author | Francisco J. Sevilla Andrea Valdés-Hernández Alan J. Barrios |
| author_facet | Francisco J. Sevilla Andrea Valdés-Hernández Alan J. Barrios |
| author_sort | Francisco J. Sevilla |
| collection | DOAJ |
| description | We perform a comprehensive analysis of the set of parameters <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>{</mo><msub><mi>r</mi><mi>i</mi></msub><mo>}</mo></mrow></semantics></math></inline-formula> that provide the energy distribution of pure qutrits that evolve towards a distinguishable state at a finite time <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>τ</mi></semantics></math></inline-formula>, when evolving under an arbitrary and time-independent Hamiltonian. The orthogonality condition is exactly solved, revealing a non-trivial interrelation between <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>τ</mi></semantics></math></inline-formula> and the energy spectrum and allowing the classification of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>{</mo><msub><mi>r</mi><mi>i</mi></msub><mo>}</mo></mrow></semantics></math></inline-formula> into families organized in a 2-simplex, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>δ</mi><mn>2</mn></msup></semantics></math></inline-formula>. Furthermore, the states determined by <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>{</mo><msub><mi>r</mi><mi>i</mi></msub><mo>}</mo></mrow></semantics></math></inline-formula> are likewise analyzed according to their quantum-speed limit. Namely, we construct a map that distinguishes those <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>r</mi><mi>i</mi></msub></semantics></math></inline-formula>s in <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>δ</mi><mn>2</mn></msup></semantics></math></inline-formula> correspondent to states whose orthogonality time is limited by the Mandelstam–Tamm bound from those restricted by the Margolus–Levitin one. Our results offer a complete characterization of the physical quantities that become relevant in both the preparation and study of the dynamics of three-level states evolving towards orthogonality. |
| first_indexed | 2024-03-10T07:16:18Z |
| format | Article |
| id | doaj.art-4bfe21e44c0f48ada8624c9a028e5da2 |
| institution | Directory Open Access Journal |
| issn | 2624-960X |
| language | English |
| last_indexed | 2024-03-10T07:16:18Z |
| publishDate | 2021-07-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Quantum Reports |
| spelling | doaj.art-4bfe21e44c0f48ada8624c9a028e5da22023-11-22T15:01:51ZengMDPI AGQuantum Reports2624-960X2021-07-013337638810.3390/quantum3030024The Underlying Order Induced by Orthogonality and the Quantum Speed LimitFrancisco J. Sevilla0Andrea Valdés-Hernández1Alan J. Barrios2Instituto de Física, Universidad Nacional Autónoma de México, Apdo. Postal 20-364, Ciudad de México 01000, MexicoInstituto de Física, Universidad Nacional Autónoma de México, Apdo. Postal 20-364, Ciudad de México 01000, MexicoInstituto de Física, Universidad Nacional Autónoma de México, Apdo. Postal 20-364, Ciudad de México 01000, MexicoWe perform a comprehensive analysis of the set of parameters <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>{</mo><msub><mi>r</mi><mi>i</mi></msub><mo>}</mo></mrow></semantics></math></inline-formula> that provide the energy distribution of pure qutrits that evolve towards a distinguishable state at a finite time <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>τ</mi></semantics></math></inline-formula>, when evolving under an arbitrary and time-independent Hamiltonian. The orthogonality condition is exactly solved, revealing a non-trivial interrelation between <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>τ</mi></semantics></math></inline-formula> and the energy spectrum and allowing the classification of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>{</mo><msub><mi>r</mi><mi>i</mi></msub><mo>}</mo></mrow></semantics></math></inline-formula> into families organized in a 2-simplex, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>δ</mi><mn>2</mn></msup></semantics></math></inline-formula>. Furthermore, the states determined by <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>{</mo><msub><mi>r</mi><mi>i</mi></msub><mo>}</mo></mrow></semantics></math></inline-formula> are likewise analyzed according to their quantum-speed limit. Namely, we construct a map that distinguishes those <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>r</mi><mi>i</mi></msub></semantics></math></inline-formula>s in <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>δ</mi><mn>2</mn></msup></semantics></math></inline-formula> correspondent to states whose orthogonality time is limited by the Mandelstam–Tamm bound from those restricted by the Margolus–Levitin one. Our results offer a complete characterization of the physical quantities that become relevant in both the preparation and study of the dynamics of three-level states evolving towards orthogonality.https://www.mdpi.com/2624-960X/3/3/24quantum speed limitorthogonality timethree-level systemsdynamics towards orthogonality |
| spellingShingle | Francisco J. Sevilla Andrea Valdés-Hernández Alan J. Barrios The Underlying Order Induced by Orthogonality and the Quantum Speed Limit Quantum Reports quantum speed limit orthogonality time three-level systems dynamics towards orthogonality |
| title | The Underlying Order Induced by Orthogonality and the Quantum Speed Limit |
| title_full | The Underlying Order Induced by Orthogonality and the Quantum Speed Limit |
| title_fullStr | The Underlying Order Induced by Orthogonality and the Quantum Speed Limit |
| title_full_unstemmed | The Underlying Order Induced by Orthogonality and the Quantum Speed Limit |
| title_short | The Underlying Order Induced by Orthogonality and the Quantum Speed Limit |
| title_sort | underlying order induced by orthogonality and the quantum speed limit |
| topic | quantum speed limit orthogonality time three-level systems dynamics towards orthogonality |
| url | https://www.mdpi.com/2624-960X/3/3/24 |
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