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arXiv:1310.6537 · Physical Review A

Stabilizing entanglement in the presence of local decay processes

Simeon Sauer, Clemens Gneiting, Andreas Buchleitner

Published Feb 18, 2014• 17 citations
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Abstract

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 $N$ qubits.

DOI
10.1103/physreva.89.022327

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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.
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We characterize time-independent Markovian dynamics that drive a finite-dimensional multipartite quantum system into a target (pure) entangled steady state, subject to physical locality constraints. New control schemes are introduced in situations where the desired stabilization task {\em cannot} be attained solely based on quasi-local dissipative means, as considered in previous analysis. The new schemes either allow for Hamiltonian control or, if the latter is not an option, suitably restrict the set of admissible initial states. In both cases, we provide explicit algorithms for constructing a Markovian master equation that achieves the intended objective and show how this genuinely extends the manifold of stabilizable states. In particular, we present dissipative quasi-local control protocols for deterministically engineering multipartite GHZ ``cat'' states and W states on nnn qubits. For GHZ states, we show that no scalable procedure exists for achieving stabilization from arbitrary initial states, whereas this is possible for a target W state by a suitable combination of a two-body Hamiltonian and dissipators. Interestingly, for both entanglement classes, we show that quasi-local stabilization may be {\em scalably} achieved conditional to initialization of the system in a large, appropriately chosen subspace.
The unavoidable interaction of quantum systems with their environment usually results in the loss of desired quantum resources. Suitably chosen system Hamiltonians, however, can, to some extent, counteract such detrimental decay, giving rise to the set of stabilizable states. Here we discuss the possibility to stabilize Gaussian states in continuous-variable systems. We identify necessary and sufficient conditions for such stabilizability and elaborate these on two benchmark examples, a single, damped mode and two locally damped modes. The obtained stabilizability conditions, which are formulated in terms of the states' covariance matrices, are, more generally, also applicable to non-Gaussian states, where they may similarly help to, e.g., discuss entanglement preservation and/or detection up to the second moments.
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We investigate the control and protection of two-qubit entanglement through engineered interactions between two auxiliary harmonic oscillators. Each qubit is coupled to a local oscillator via a dephasing interaction, while the oscillators interact through independently tunable position-position and momentum-momentum couplings. Employing the characteristic-function representation, we obtain analytical solutions for the composite-system dynamics and examine how the stability properties of the coupled oscillators determine the evolution of two-qubit concurrence. Our analysis reveals distinct dynamical regimes exhibiting entanglement revivals, suppression, or decay, and identifies configurations in which oscillator interactions effectively reduce entanglement degradation. We further investigate the influence of thermal dissipation using local and global master-equation descriptions, demonstrating that suitable oscillator couplings can preserve substantial two-qubit entanglement under the dissipative conditions considered. These results establish a connection between the dynamical stability of auxiliary bosonic modes and the controllability of entanglement in discrete-variable quantum systems, providing a potential strategy for entanglement protection through engineered oscillator interactions.