Maximally entangled states for qubit- qutrit systems

S. Kanmani, S. V. M. Satyanarayana

Xin-Wei Zha, Irfan Ahmed, Yanpeng Zhang

Abstract Recently, Che et al presented a recurrence relation of multi-qubit states. Regarding this inspiration, we give and extend the recurrence relation of multi-qubit states to the recurrence relation of maximally qutrit entangled states. We also establish absolutely maximally entangled five qutrits states via maximally entangled four qutrits states. We also demonstrate that such a state is the 2-uniform state of five qutrits states.

Manu Pratap Singh, B. S. Rajput

최정운

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.

P. Dasgupta, Debashis Gangopadhyay

New convenient thumbrules are obtained to test entanglement of wavefunctions for bipartite qubit and qutrit systems. All results are analytic. The new results are: (a) For bipartite qubit systems there exists a matrix $A$ for which $\det A = 0$ implies unentanglement while $\det A \ne 0$ implies entanglement. There is an underlying SU(2) algebra. (2) Teleportation for a general qubit state is possible by using non-maximally entangled bipartite qubit states. This protocol has an additional parameter, viz., $\det A$, which enhances the cryptographic security of the teleportation. (c) For qutrits there is a matrix $P$ for which $\det P = 0$ simultaneously with ${\rm tr}P=\pm 1$ imply unentanglement. Any departure from these conditions implies entanglement. There exists an underlying SU(3) algebra. (d) Physical interpretation of the underlying algebras are given and plausible experimental scenarios are proposed for the SU(2) case in the context of two entangled electrons. (e) The entanglement entropy in both cases, viz., for qubits and qutrits respectively, are expressed in terms of the determinants and trace of the matrices mentioned above.