$SU(N)$ Fidelity and Maximally Entangled States of Qubit and Qutrit Bipartite Systems

Mohsen Sarbishaei

P. Dasgupta, Debashis Gangopadhyay

Based on the Schmidt decomposition new convenient thumbrules are obtained to test entanglement of wavefunctions for bipartite qubit and qutrit systems. For the qubit system there is an underlying SU(2) algebra , while the same for a qutrit system is SU(3).

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.

K. Berrada, Y. Hassouni

Surajit Sen, Dey, Tushar Kanti

We develop a systematic method to construct the Bell states of a qubit bipartite system while taking $SU(2)$ group as the basis group. An alternative formulation of fidelity, called $SU(2)$ fidelity, is proposed which gives the Bell-CHSH inequality. Taking analogy from the octet theory governed by the $SU(3)$ group, it is shown that the method can be easily generalized to derive all possible entangled states and the $SU(3)$ fidelity of the higher dimensional bipartite qutrit system. The properties of these states are studied which reveal the existence of some inequalities for the qutrit bipartite system.

S. Shelly Sharma, Naresh Kumar Sharma