Generalizing Wave-Particle Duality: Two-Qubit Extension of the Polarization Coherence Theorem
We present an extension of the polarization coherence theorem (PCT) for the case in which two qubits play similarly important roles. The standard version of the PCT: <inline-formula><math display="inline"><semantics><mrow><msup><mi mathvariant="script&...
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| Format: | Article |
| Language: | English |
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MDPI AG
2020-10-01
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| Series: | Quantum Reports |
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| Online Access: | https://www.mdpi.com/2624-960X/2/4/35 |
| _version_ | 1797549830534332416 |
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| author | Francisco De Zela |
| author_facet | Francisco De Zela |
| author_sort | Francisco De Zela |
| collection | DOAJ |
| description | We present an extension of the polarization coherence theorem (PCT) for the case in which two qubits play similarly important roles. The standard version of the PCT: <inline-formula><math display="inline"><semantics><mrow><msup><mi mathvariant="script">V</mi><mn>2</mn></msup><mo>+</mo><msup><mi mathvariant="script">D</mi><mn>2</mn></msup><mo>=</mo><msup><mi mathvariant="script">P</mi><mn>2</mn></msup></mrow></semantics></math></inline-formula>, involves three measures, visibility <inline-formula><math display="inline"><semantics><mi mathvariant="script">V</mi></semantics></math></inline-formula>, distinguishability <inline-formula><math display="inline"><semantics><mi mathvariant="script">D</mi></semantics></math></inline-formula>, and the degree of polarization <inline-formula><math display="inline"><semantics><mi mathvariant="script">P</mi></semantics></math></inline-formula>, all of which refer to a single qubit, regardless of its physical realization. This is also the case with the inequality that is implied by the PCT: <inline-formula><math display="inline"><semantics><mrow><msup><mi mathvariant="script">V</mi><mn>2</mn></msup><mo>+</mo><msup><mi mathvariant="script">D</mi><mn>2</mn></msup><mo>≤</mo><mn>1</mn></mrow></semantics></math></inline-formula>, which was originally derived in an attempt to quantify Bohr’s complementarity principle. We show that all of these constraints hold true, no matter how the involved qubits are physically realized, either as quantum or else as classical objects. |
| first_indexed | 2024-03-10T15:19:59Z |
| format | Article |
| id | doaj.art-a9cf5b81d87944d4aa9f7421f1eef6a6 |
| institution | Directory Open Access Journal |
| issn | 2624-960X |
| language | English |
| last_indexed | 2024-03-10T15:19:59Z |
| publishDate | 2020-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Quantum Reports |
| spelling | doaj.art-a9cf5b81d87944d4aa9f7421f1eef6a62023-11-20T18:33:39ZengMDPI AGQuantum Reports2624-960X2020-10-012450151310.3390/quantum2040035Generalizing Wave-Particle Duality: Two-Qubit Extension of the Polarization Coherence TheoremFrancisco De Zela0Departamento de Ciencias, Sección Física, Pontificia Universidad Católica del Perú Apartado, Lima 1761, PeruWe present an extension of the polarization coherence theorem (PCT) for the case in which two qubits play similarly important roles. The standard version of the PCT: <inline-formula><math display="inline"><semantics><mrow><msup><mi mathvariant="script">V</mi><mn>2</mn></msup><mo>+</mo><msup><mi mathvariant="script">D</mi><mn>2</mn></msup><mo>=</mo><msup><mi mathvariant="script">P</mi><mn>2</mn></msup></mrow></semantics></math></inline-formula>, involves three measures, visibility <inline-formula><math display="inline"><semantics><mi mathvariant="script">V</mi></semantics></math></inline-formula>, distinguishability <inline-formula><math display="inline"><semantics><mi mathvariant="script">D</mi></semantics></math></inline-formula>, and the degree of polarization <inline-formula><math display="inline"><semantics><mi mathvariant="script">P</mi></semantics></math></inline-formula>, all of which refer to a single qubit, regardless of its physical realization. This is also the case with the inequality that is implied by the PCT: <inline-formula><math display="inline"><semantics><mrow><msup><mi mathvariant="script">V</mi><mn>2</mn></msup><mo>+</mo><msup><mi mathvariant="script">D</mi><mn>2</mn></msup><mo>≤</mo><mn>1</mn></mrow></semantics></math></inline-formula>, which was originally derived in an attempt to quantify Bohr’s complementarity principle. We show that all of these constraints hold true, no matter how the involved qubits are physically realized, either as quantum or else as classical objects.https://www.mdpi.com/2624-960X/2/4/35Bohr’s complementaritywave-particle dualitycoherencepolarization |
| spellingShingle | Francisco De Zela Generalizing Wave-Particle Duality: Two-Qubit Extension of the Polarization Coherence Theorem Quantum Reports Bohr’s complementarity wave-particle duality coherence polarization |
| title | Generalizing Wave-Particle Duality: Two-Qubit Extension of the Polarization Coherence Theorem |
| title_full | Generalizing Wave-Particle Duality: Two-Qubit Extension of the Polarization Coherence Theorem |
| title_fullStr | Generalizing Wave-Particle Duality: Two-Qubit Extension of the Polarization Coherence Theorem |
| title_full_unstemmed | Generalizing Wave-Particle Duality: Two-Qubit Extension of the Polarization Coherence Theorem |
| title_short | Generalizing Wave-Particle Duality: Two-Qubit Extension of the Polarization Coherence Theorem |
| title_sort | generalizing wave particle duality two qubit extension of the polarization coherence theorem |
| topic | Bohr’s complementarity wave-particle duality coherence polarization |
| url | https://www.mdpi.com/2624-960X/2/4/35 |
| work_keys_str_mv | AT franciscodezela generalizingwaveparticledualitytwoqubitextensionofthepolarizationcoherencetheorem |