XXXVIII Workshop on Geometric Methods in Physics | 30.06-6.07.2019 |

VIII School on Geometry and Physics | 24-28.06.2019 |

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## Claudia Quintana## Entangled bipartite qubit systems coupled to photon baths: in search of the master equationThe time-evolution of pure states ($\rho ^2 = \rho$) associated with a closed bipartite system $\mathcal{S} = \mathcal{S}_A + \mathcal{S}_B$ is unitary and obeys the Heisenberg equation. By summing the degrees of freedom of the subsystem $B$ we obtain the reduced state $\rho_A$ of subsystem $A$, which is a mixed state ($\rho^2_A \neq \rho_A$) in general. One may consider $\mathcal{S}_A$ as an open system that interacts with $\mathcal{S}_B$ in controlled form. The law of motion for $\mathcal{S}_A$ is not represented by the Heisenberg equation anymore, so that a master equation is necessary. We consider a closed tetra-partite system $\mathcal{S}$ composited by two entangled qubits and two quantized single-mode radiation fields; two isolated QED cavities contain a pair (qubit + field) each one. Our interest is addressed to investigate the master equation for the different configurations of subsystems $\mathcal{S}_A$ and $\mathcal{S}_B$ that can be obtained from $\mathcal{S}$. For instance, one of the configurations identifies $\mathcal{S}_A$ and $\mathcal{S}_B$ with the systems (qubit + field) in the cavities, other considers $\mathcal{S}_A$ as the subsystem qubit + qubit and $\mathcal{S}_B$ as the subsystem field + field, and so on. That is, we look for the master equation that provides $\rho_A$ in agreement with the reduction of the pure states of $\mathcal{S}$ for each of the above mentioned configurations. |

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University of Bialystok |

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