dorsal/arxiv
View SchemaQuantum control and the Strocchi map
| Authors | R. Vilela Mendes, V. I. Man'ko |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0212006 |
| URL | https://arxiv.org/abs/quant-ph/0212006 |
| DOI | 10.1103/PhysRevA.67.053404 |
| Journal | Physical Review A 67 (2003) 053404 |
Abstract
Identifying the real and imaginary parts of wave functions with coordinates and momenta, quantum evolution may be mapped onto a classical Hamiltonian system. In addition to the symplectic form, quantum mechanics also has a positive-definite real inner product which provides a geometrical interpretation of the measurement process. Together they endow the quantum Hilbert space with the structure of a K\"{a}ller manifold. Quantum control is discussed in this setting. Quantum time-evolution corresponds to smooth Hamiltonian dynamics and measurements to jumps in the phase space. This adds additional power to quantum control, non unitarily controllable systems becoming controllable by ``measurement plus evolution''. A picture of quantum evolution as Hamiltonian dynamics in a classical-like phase-space is the appropriate setting to carry over techniques from classical to quantum control. This is illustrated by a discussion of optimal control and sliding mode techniques.
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"abstract": "Identifying the real and imaginary parts of wave functions with coordinates\nand momenta, quantum evolution may be mapped onto a classical Hamiltonian\nsystem. In addition to the symplectic form, quantum mechanics also has a\npositive-definite real inner product which provides a geometrical\ninterpretation of the measurement process. Together they endow the quantum\nHilbert space with the structure of a K\\\"{a}ller manifold. Quantum control is\ndiscussed in this setting. Quantum time-evolution corresponds to smooth\nHamiltonian dynamics and measurements to jumps in the phase space. This adds\nadditional power to quantum control, non unitarily controllable systems\nbecoming controllable by ``measurement plus evolution\u0027\u0027. A picture of quantum\nevolution as Hamiltonian dynamics in a classical-like phase-space is the\nappropriate setting to carry over techniques from classical to quantum control.\nThis is illustrated by a discussion of optimal control and sliding mode\ntechniques.",
"arxiv_id": "quant-ph/0212006",
"authors": [
"R. Vilela Mendes",
"V. I. Man\u0027ko"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevA.67.053404",
"journal_ref": "Physical Review A 67 (2003) 053404",
"title": "Quantum control and the Strocchi map",
"url": "https://arxiv.org/abs/quant-ph/0212006"
},
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