dorsal/arxiv
View SchemaQuantum Brachistochrone for Mixed States
| Authors | A. Carlini, A. Hosoya, T. Koike, Y. Okudaira |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0703047 |
| URL | https://arxiv.org/abs/quant-ph/0703047 |
| DOI | 10.1088/1751-8113/41/4/045303 |
| Journal | J. Phys. A: Math. Theor. 41 (2008), 045303 |
Abstract
We present a general formalism based on the variational principle for finding the time-optimal quantum evolution of mixed states governed by a master equation, when the Hamiltonian and the Lindblad operators are subject to certain constraints. The problem reduces to solving first a fundamental equation (the {\it quantum brachistochrone}) for the Hamiltonian, which can be written down once the constraints are specified, and then solving the constraints and the master equation for the Lindblad and the density operators. As an application of our formalism, we study a simple one-qubit model where the optimal Lindblad operators control decoherence and can be simulated by a tunable coupling with an ancillary qubit. It is found that the evolution through mixed states can be more efficient than the unitary evolution between given pure states. We also discuss the mixed state evolution as a finite time unitary evolution of the system plus an environment followed by a single measurement. For the simplest choice of the constraints, the optimal duration time for the evolution is an exponentially decreasing function of the environment's degrees of freedom.
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"abstract": "We present a general formalism based on the variational principle for finding\nthe time-optimal quantum evolution of mixed states governed by a master\nequation, when the Hamiltonian and the Lindblad operators are subject to\ncertain constraints. The problem reduces to solving first a fundamental\nequation (the {\\it quantum brachistochrone}) for the Hamiltonian, which can be\nwritten down once the constraints are specified, and then solving the\nconstraints and the master equation for the Lindblad and the density operators.\nAs an application of our formalism, we study a simple one-qubit model where the\noptimal Lindblad operators control decoherence and can be simulated by a\ntunable coupling with an ancillary qubit. It is found that the evolution\nthrough mixed states can be more efficient than the unitary evolution between\ngiven pure states. We also discuss the mixed state evolution as a finite time\nunitary evolution of the system plus an environment followed by a single\nmeasurement. For the simplest choice of the constraints, the optimal duration\ntime for the evolution is an exponentially decreasing function of the\nenvironment\u0027s degrees of freedom.",
"arxiv_id": "quant-ph/0703047",
"authors": [
"A. Carlini",
"A. Hosoya",
"T. Koike",
"Y. Okudaira"
],
"categories": [
"quant-ph"
],
"doi": "10.1088/1751-8113/41/4/045303",
"journal_ref": "J. Phys. A: Math. Theor. 41 (2008), 045303",
"title": "Quantum Brachistochrone for Mixed States",
"url": "https://arxiv.org/abs/quant-ph/0703047"
},
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