We investigate the non-Markovian quantum dynamics of a hybrid open system consisting of one qubit and one qutrit by employing a stochastic Schrödinger equation to generate diffusive quantum trajectories. We have established an exact quantum state diffusion (QSD) equation for the dissipative qubit-qutrit system coupled to a bosonic heat bath at zero temperature. As an important application, the non-Markovian QSD equation is employed to simulate the entanglement decay and generation measured by negativity. Finally, some steady-state properties of the hybrid system are also discussed.We investigate the non-Markovian quantum dynamics of a hybrid open system consisting of one qubit and one qutrit by employing a stochastic Schrödinger equation to generate diffusive quantum trajectories. We have established an exact quantum state diffusion (QSD) equation for the dissipative qubit-qutrit system coupled to a bosonic heat bath at zero temperature. As an important application, the non-Markovian QSD equation is employed to simulate the entanglement decay and generation measured by negativity. Finally, some steady-state properties of the hybrid system are also discussed.

arXiv:1110.6157Europhysics Letters (EPL)Nov 1, 20116 citations

Maximally entangled states for qubit- qutrit systems

Mohsen Sarbishaei

Indian Journal of PhysicsMar 12, 20050 citations

Maximally entangled mixed states for qubit-qutrit systems

Paulo E. M. F. Mendonça, Marcelo A. Marchiolli, Samuel R. Hedemann

We consider the problems of maximizing the entanglement negativity of X-form qubit-qutrit density matrices with (i) a fixed spectrum and (ii) a fixed purity. In the first case, the problem is solved in full generality whereas, in the latter, partial solutions are obtained by imposing extra spectral constraints such as rank deficiency and degeneracy, which enable a semidefinite programming treatment for the optimization problem at hand. Despite the technically motivated assumptions, we provide strong numerical evidence that threefold degenerate X states of purity $P$ reach the highest entanglement negativity accessible to arbitrary qubit-qutrit density matrices of the same purity, hence characterizing a sparse family of likely qubit-qutrit maximally entangled mixed states.We consider the problems of maximizing the entanglement negativity of X-form qubit-qutrit density matrices with (i) a fixed spectrum and (ii) a fixed purity. In the first case, the problem is solved in full generality whereas, in the latter, partial solutions are obtained by imposing extra spectral constraints such as rank deficiency and degeneracy, which enable a semidefinite programming treatment for the optimization problem at hand. Despite the technically motivated assumptions, we provide strong numerical evidence that threefold degenerate X states of purity $P$ reach the highest entanglement negativity accessible to arbitrary qubit-qutrit density matrices of the same purity, hence characterizing a sparse family of likely qubit-qutrit maximally entangled mixed states.

arXiv:1612.01214Physical Review AFeb 21, 201723 citations

Recycling Non-locality Using Minimal Resources

Joel Johansen

The thesis aims to characterize the scenario in which the non-locality of an entangled state shared between sequential observers can be recycled utilizing as few resources as possible. This is accomplished by stochastically combining standard projective measurements using locally generated randomness. Using an entangled two-qubit state, we analytically minimize the number of parameters necessary to specify two Clauser-Horne-Shimony-Holt inequalities. Moreover, employing the Collins-Gisin-Linden-Massar-Popescu inequality, the protocol is then further extended to the higher-dimensional case in which the non-locality of pair of entangled qutrits is recycled. The trade-off in the violation magnitudes between Bell parameters is then investigated numerically, both for qubits and qutrits, and it is found that the optimal trade-off is enabled by non-maximally entangled states and that qutrits allows for larger sequential violations than does qubits.The thesis aims to characterize the scenario in which the non-locality of an entangled state shared between sequential observers can be recycled utilizing as few resources as possible. This is accomplished by stochastically combining standard projective measurements using locally generated randomness. Using an entangled two-qubit state, we analytically minimize the number of parameters necessary to specify two Clauser-Horne-Shimony-Holt inequalities. Moreover, employing the Collins-Gisin-Linden-Massar-Popescu inequality, the protocol is then further extended to the higher-dimensional case in which the non-locality of pair of entangled qutrits is recycled. The trade-off in the violation magnitudes between Bell parameters is then investigated numerically, both for qubits and qutrits, and it is found that the optimal trade-off is enabled by non-maximally entangled states and that qutrits allows for larger sequential violations than does qubits.

Jan 1, 20260 citations

Uncertainty Relations for the Entanglement Between a Qubit and a Qutrit

Manuél Ávila, Juvenal Rueda-Paz

International Journal of Theoretical PhysicsDec 2, 20190 citations

P

reach the highest entanglement negativity accessible to arbitrary qubit-qutrit density matrices of the same purity, hence characterizing a sparse family of likely qubit-qutrit maximally entangled mixed states.