The quantum switch is uniquely defined by its action on unitary operations
The quantum switch is a quantum process that creates a coherent control between different unitary operations, which is often described as a quantum process which transforms a pair of unitary operations $(U_1 , U_2)$ into a controlled unitary operation that coherently applies them in different orders...
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| Format: | Article |
| Language: | English |
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Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften
2023-11-01
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| Series: | Quantum |
| Online Access: | https://quantum-journal.org/papers/q-2023-11-07-1169/pdf/ |
| _version_ | 1797634683646771200 |
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| author | Qingxiuxiong Dong Marco Túlio Quintino Akihito Soeda Mio Murao |
| author_facet | Qingxiuxiong Dong Marco Túlio Quintino Akihito Soeda Mio Murao |
| author_sort | Qingxiuxiong Dong |
| collection | DOAJ |
| description | The quantum switch is a quantum process that creates a coherent control between different unitary operations, which is often described as a quantum process which transforms a pair of unitary operations $(U_1 , U_2)$ into a controlled unitary operation that coherently applies them in different orders as $\vert {0} \rangle\langle {0} \vert \otimes U_1 U_2 + \vert {1} \rangle\langle {1} \vert \otimes U_2 U_1$. This description, however, does not directly define its action on non-unitary operations. The action of the quantum switch on non-unitary operations is then chosen to be a ``natural'' extension of its action on unitary operations. In general, the action of a process on non-unitary operations is not uniquely determined by its action on unitary operations. It may be that there could be a set of inequivalent extensions of the quantum switch for non-unitary operations. We prove, however, that the natural extension is the only possibility for the quantum switch for the 2-slot case. In other words, contrary to the general case, the action of the quantum switch on non-unitary operations (as a linear and completely CP preserving supermap) is completely determined by its action on unitary operations. We also discuss the general problem of when the complete description of a quantum process is uniquely determined by its action on unitary operations and identify a set of single-slot processes which are completely defined by their action on unitary operations. |
| first_indexed | 2024-03-11T12:12:08Z |
| format | Article |
| id | doaj.art-cbd7481d1824412bbff07cb8d3f617ad |
| institution | Directory Open Access Journal |
| issn | 2521-327X |
| language | English |
| last_indexed | 2024-03-11T12:12:08Z |
| publishDate | 2023-11-01 |
| publisher | Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften |
| record_format | Article |
| series | Quantum |
| spelling | doaj.art-cbd7481d1824412bbff07cb8d3f617ad2023-11-07T12:08:53ZengVerein zur Förderung des Open Access Publizierens in den QuantenwissenschaftenQuantum2521-327X2023-11-017116910.22331/q-2023-11-07-116910.22331/q-2023-11-07-1169The quantum switch is uniquely defined by its action on unitary operationsQingxiuxiong DongMarco Túlio QuintinoAkihito SoedaMio MuraoThe quantum switch is a quantum process that creates a coherent control between different unitary operations, which is often described as a quantum process which transforms a pair of unitary operations $(U_1 , U_2)$ into a controlled unitary operation that coherently applies them in different orders as $\vert {0} \rangle\langle {0} \vert \otimes U_1 U_2 + \vert {1} \rangle\langle {1} \vert \otimes U_2 U_1$. This description, however, does not directly define its action on non-unitary operations. The action of the quantum switch on non-unitary operations is then chosen to be a ``natural'' extension of its action on unitary operations. In general, the action of a process on non-unitary operations is not uniquely determined by its action on unitary operations. It may be that there could be a set of inequivalent extensions of the quantum switch for non-unitary operations. We prove, however, that the natural extension is the only possibility for the quantum switch for the 2-slot case. In other words, contrary to the general case, the action of the quantum switch on non-unitary operations (as a linear and completely CP preserving supermap) is completely determined by its action on unitary operations. We also discuss the general problem of when the complete description of a quantum process is uniquely determined by its action on unitary operations and identify a set of single-slot processes which are completely defined by their action on unitary operations.https://quantum-journal.org/papers/q-2023-11-07-1169/pdf/ |
| spellingShingle | Qingxiuxiong Dong Marco Túlio Quintino Akihito Soeda Mio Murao The quantum switch is uniquely defined by its action on unitary operations Quantum |
| title | The quantum switch is uniquely defined by its action on unitary operations |
| title_full | The quantum switch is uniquely defined by its action on unitary operations |
| title_fullStr | The quantum switch is uniquely defined by its action on unitary operations |
| title_full_unstemmed | The quantum switch is uniquely defined by its action on unitary operations |
| title_short | The quantum switch is uniquely defined by its action on unitary operations |
| title_sort | quantum switch is uniquely defined by its action on unitary operations |
| url | https://quantum-journal.org/papers/q-2023-11-07-1169/pdf/ |
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