dorsal/arxiv
View SchemaQuantum control without access to the controlling interaction
| Authors | Dominik Janzing, Frederik Armknecht, Robert Zeier, Thomas Beth |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0103022 |
| URL | https://arxiv.org/abs/quant-ph/0103022 |
| DOI | 10.1103/PhysRevA.65.022104 |
| Journal | Phsy. Rev. A, 65:022104, 2002 |
Abstract
In our model a fixed Hamiltonian acts on the joint Hilbert space of a quantum system and its controller. We show under which conditions measurements, state preparations, and unitary implementations on the system can be performed by quantum operations on the controller only. It turns out that a measurement of the observable A and an implementation of the one-parameter group exp(iAr) can be performed by almost the same sequence of control operations. Furthermore measurement procedures for A+B, for (AB+BA), and for i[A,B] can be constructed from measurements of A and B. This shows that the algebraic structure of the set of observables can be explained by the Lie group structure of the unitary evolutions on the joint Hilbert space of the measuring device and the measured system. A spin chain model with nearest neighborhood coupling shows that the border line between controller and system can be shifted consistently.
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"abstract": "In our model a fixed Hamiltonian acts on the joint Hilbert space of a quantum\nsystem and its controller. We show under which conditions measurements, state\npreparations, and unitary implementations on the system can be performed by\nquantum operations on the controller only.\n It turns out that a measurement of the observable A and an implementation of\nthe one-parameter group exp(iAr) can be performed by almost the same sequence\nof control operations. Furthermore measurement procedures for A+B, for (AB+BA),\nand for i[A,B] can be constructed from measurements of A and B. This shows that\nthe algebraic structure of the set of observables can be explained by the Lie\ngroup structure of the unitary evolutions on the joint Hilbert space of the\nmeasuring device and the measured system.\n A spin chain model with nearest neighborhood coupling shows that the border\nline between controller and system can be shifted consistently.",
"arxiv_id": "quant-ph/0103022",
"authors": [
"Dominik Janzing",
"Frederik Armknecht",
"Robert Zeier",
"Thomas Beth"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevA.65.022104",
"journal_ref": "Phsy. Rev. A, 65:022104, 2002",
"title": "Quantum control without access to the controlling interaction",
"url": "https://arxiv.org/abs/quant-ph/0103022"
},
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