arXiv:2408.02702

SU(N) algebras and new thumbrules for entanglement of bipartite qubit and qutrit systems

P. Dasgupta, Debashis Gangopadhyay

Published Aug 4, 2024• 0 citations

Abstract

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).

DOI: 10.48550/arxiv.2408.02702

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arXiv:2408.02702

SU(N) algebras and new thumbrules for entanglement of bipartite qubit and qutrit systems

P. Dasgupta, Debashis Gangopadhyay

Published Aug 4, 2024• 0 citations

arXiv HTML PDF

Abstract

DOI: 10.48550/arxiv.2408.02702

Related papers

Teleportation with non-maximally entangled states and underlying unitary algebras of certain bipartite systems

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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.

SU(N)

Fidelity and Maximally Entangled States of Qubit and Qutrit Bipartite Systems

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.