|
| related topics |
| {time, decoherence, evolution} |
| {states, state, optimal} |
| {operator, operators, space} |
| {qubit, qubits, gate} |
| {equation, function, exp} |
| {measurement, state, measurements} |
| {cos, sin, state} |
| {phase, path, phys} |
| {time, wave, function} |
| {spin, pulse, spins} |
|
Quantum Brachistochrone for Mixed States
A. Carlini, A. Hosoya, T. Koike, Y. Okudaira
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.
- oai_identifier:
- oai:arXiv.org:quant-ph/0703047
- categories:
- quant-ph
- comments:
- 8 pages, 3 figures
- arxiv_id:
- quant-ph/0703047
- created:
- 2007-03-06
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