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arXiv:1302.4690 · Physical Review Letters

Optimal Coherent Control to Counteract Dissipation

Simeon Sauer, Clemens Gneiting, Andreas Buchleitner

Published Jul 18, 2013• 40 citations
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Abstract

We study to what extent the detrimental impact of dissipation on quantum properties can be compensated by suitable coherent dynamics. To this end, we develop a general method to determine the control Hamiltonian that optimally counteracts a given dissipation mechanism, in order to sustain the desired property, and apply it to two exemplary target properties: the coherence of a decaying two-level system and the entanglement of two qubits in the presence of local dissipation.

DOI
10.1103/physrevlett.111.030405

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We study to what extent the detrimental impact of dissipation on quantum properties can be compensated by suitable coherent dynamics. To this end, we develop a general method to determine the control Hamiltonian that optimally counteracts a given dissipation mechanism, in order to sustain the desired property, and apply it to two exemplary target properties: the coherence of a decaying two-level system and the entanglement of two qubits in the presence of local dissipation.
We investigate to what extent a suitably chosen system Hamiltonian can counteract local dissipative processes and preserve entanglement in the stationary state. The results determine prospects and limitations of dissipative state preparation schemes based on natural dissipative processes---in contrast to engineered, typically nonlocal dissipative schemes. As an exemplary case, we determine the stationary state of two spontaneously decaying two-level systems with optimal entanglement properties. The corresponding system Hamiltonian is derived, and its possible experimental implementation is discussed in detail. Finally, we discuss generalizations for NNN qubits.
Decoherence represents a major obstacle towards realizing reliable quantum technologies. Identifying states that can be upheld against decoherence by purely coherent means, i.e., stabilizable states, for which the dissipation-induced decay can be completely compensated by suitable control Hamiltonians, can help to optimize the exploitation of fragile quantum resources and to understand the ultimate limits of coherent control for this purpose. In this work, we develop conditions for stabilizability based on the target state's eigendecomposition, both for general density operators and for the covariance matrix parametrization of Gaussian states. Unlike previous conditions for stabilizability, these spectral conditions are both necessary and sufficient and are typically easier to use, extending their scope of applicability. To demonstrate its viability, we use the spectral approach to derive upper bounds on stabilizability for a number of exemplary open system scenarios, including stabilization of generalized Greenberger-Horne-Zeilinger (GHZ) and W states in the presence of local dissipation and stabilization of squeezed thermal states under collective damping.