dorsal/arxiv
View SchemaTowards the theory of control in observable quantum systems
| Authors | V P Belavkin |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0408003 |
| URL | https://arxiv.org/abs/quant-ph/0408003 |
| Journal | Automatica and Remote Control, v 44, pp 178-188 (1983) |
Abstract
An operational description of the controlled Markov dynamics of quantum-mechanical system is introduced. The feedback control strategies with regard to the dynamical reduction of quantum states in the course of quantum real-time measurements are discribed in terms of quantum filtering of these states. The concept of sufficient coordinates for the description of the a posteriori quantum states from a given class is introduced, and it is proved that they form a classical Markov process with values in either state operators or state vector space. The general problem of optimal control of a quantum-mechanical system is discussed and the corresponding Bellman equation in the space of sufficient coordinates is derived. The results are illustrated in the example of control of the semigroup dynamics of a quantum system that is instantaneously observed at discrete times and evolves between measurement times according to the Schroedinger equation.
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"abstract": "An operational description of the controlled Markov dynamics of\nquantum-mechanical system is introduced. The feedback control strategies with\nregard to the dynamical reduction of quantum states in the course of quantum\nreal-time measurements are discribed in terms of quantum filtering of these\nstates. The concept of sufficient coordinates for the description of the a\nposteriori quantum states from a given class is introduced, and it is proved\nthat they form a classical Markov process with values in either state operators\nor state vector space. The general problem of optimal control of a\nquantum-mechanical system is discussed and the corresponding Bellman equation\nin the space of sufficient coordinates is derived. The results are illustrated\nin the example of control of the semigroup dynamics of a quantum system that is\ninstantaneously observed at discrete times and evolves between measurement\ntimes according to the Schroedinger equation.",
"arxiv_id": "quant-ph/0408003",
"authors": [
"V P Belavkin"
],
"categories": [
"quant-ph"
],
"journal_ref": "Automatica and Remote Control, v 44, pp 178-188 (1983)",
"title": "Towards the theory of control in observable quantum systems",
"url": "https://arxiv.org/abs/quant-ph/0408003"
},
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