Master equations for two qubits coupled via a nonlinear mode

A microscopic master equation describing the dynamics of two qubits coupled via a nonlinear mediator is constructed supposing that the two qubits, as well as the nonlinear mode, interact, each with its own independent bosonic bath. Generally speaking the master equation derived in this way represents a more appropriate tool for studying the dynamics of open quantum systems. Indeed we showthat it is more complex than the phenomenological master equation, constructed simply adding ad hoc dissipative terms

Dissipation and entanglement dynamics for two interacting qubits coupled to independent reservoirs

We derive the master equation of a system of two coupled qubits by taking into account their interaction with two independent bosonic baths. Important features of the dynamics are brought to light, such as the structure of the stationary state at general temperatures and the behaviour of the entanglement at zero temperature, showing the phenomena of sudden death and sudden birth as well as the presence of stationary entanglement for long times. The model here presented is quite versatile and can be of interest in the study of both Josephson junction architectures and cavity-QED.Comment: 14 pages, 3 figures, submitted to Journal of Physics A: Mathematical and Theoretica

Asymptotic Entanglement Dynamics and Geometry of Quantum States

A given dynamics for a composite quantum system can exhibit several distinct properties for the asymptotic entanglement behavior, like entanglement sudden death, asymptotic death of entanglement, sudden birth of entanglement, etc. A classification of the possible situations was given in [M. O. Terra Cunha, {\emph{New J. Phys}} {\bf{9}}, 237 (2007)] but for some classes there were no known examples. In this work we give a better classification for the possibile relaxing dynamics at the light of the geometry of their set of asymptotic states and give explicit examples for all the classes. Although the classification is completely general, in the search of examples it is sufficient to use two qubits with dynamics given by differential equations in Lindblad form (some of them non-autonomous). We also investigate, in each case, the probabilities to find each possible behavior for random initial states.Comment: 9 pages, 2 figures; revised version accepted for publication in J. Phys. A: Math. Theo

Robust stationary entanglement of two coupled qubits in independent environments

The dissipative dynamics of two interacting qubits coupled to independent reservoirs at nonzero temperatures is investigated, paying special attention to the entanglement evolution. The counter-rotating terms in the qubit-qubit interaction give rise to stationary entanglement, traceable back to the ground state structure. The robustness of this entanglement against thermal noise is thoroughly analyzed, establishing that it can be detected at reasonable experimental temperatures. Some effects linked to a possible reservoir asymmetry are brought to light.Comment: 8 pages, 6 figures; version accepted for publication on Eur. Phys. J.

Dissipative effects on a generation scheme of a W state in an array of coupled Josephson junctions

International audienceThe dynamics of an open quantum system, consisting of three superconducting qubits interacting with independent reservoirs, is investigated to elucidate the effects of the environment on a unitary generation scheme of W states [ Migliore R. et al. (2006) Phys. Rev. B 74, 104503 ]. To this end a microscopic master equation is constructed and its exact resolution predicts the generation of a Werner-like state instead of the W state. A comparison between our model and a more intuitive phenomenological model is also considered, in order to find the limits of the latter approach in the case of structured reservoirs. Dissipative effects on a scheme of generation of a W state in an array of coupled Josephson junctions

Dissipative effects on a scheme of generation of a W state in an array of coupled Josephson junctions

The dynamics of an open quantum system, consisting of three superconducting qubits interacting with independent reservoirs, is investigated to elucidate the effects of the environment on a unitary generation scheme of W states (Migliore R et al 2006 Phys. Rev. B 74 104503). To this end a microscopic master equation is constructed and its exact resolution predicts the generation of a Werner-like state instead of the W state. A comparison between our model and a more intuitive phenomenological model is also considered, in order to find the limits of the latter approach in the case of structured reservoirs

Dissipative dynamics of two coupled qubits: a short review of some recent results

In this paper, we review some results concerning the dissipative dynamics of two coupled qubits interacting with independent reservoirs. In particular, we focus on the role of counter-rotating terms in the qubit-qubit coupling, showing that their presence is the origin of stationary entanglement, which also turns out to be robust with respect to temperature. We also discuss the performances of different non-Markovian approaches in the description of the qubit-qubit dynamics, by considering a simplified exactly solvable Hamiltonian model