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Quantum Information Processing

Squeezing and entanglement in multi-qutrit systems

Azita Naji, Mojtaba Jafarpour

Published Apr 9, 2013• 2 citations
Publisher
DOI
10.1007/s11128-013-0574-0

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Using the single SU(2) qutrit (spin-1 like system), we show that entanglement may take place for a single particle with respect to its internal degrees of freedom, in other words, beyond the conventional requirements of nonlocality and nonseparability. We show that the SU(2) or spin coherent states do not manifest entanglement, while the so-called squeezed spin states are entangled. We reveal the principle difference between the spin coherent and spin squeezed states in terms of quantum correlations. A number of physical realizations of the SU(2) qutrit is discussed.
In this paper, we investigate the entanglement of multi-partite Grassmannian coherent states (GCSs) described by Grassmann numbers for n > 2 degree of nilpotency.Choosing an appropriate weight function, we show that it is possible to construct some wellknown entangled pure states, consisting of GHZ, W, Bell, cluster type and bi-separable states, which are obtained by integrating over tensor product of GCSs.It is shown that for three level systems, the Grassmann creation and annihilation operators b and b † together with b z form a closed deformed algebra, i.e., SU q (2) with q = e 2πi 3 , which is useful to construct entangled qutrit-states.The same argument holds for three level squeezed states.Moreover combining the Grassmann and bosonic coherent states we construct maximal entangled super coherent states.
We study the correlation dynamics of a system composed of arbitrary numbers of qutrits interacting with a common environment. Initially, the system is assumed to be in a low dimensional subspace of the Hamiltonian called "decoherence-free subspace". Environment induced quantum entanglement and discord is calculated between pair of qutrits of the system as measures of non-classical correlations. Finally the steady state distribution of entanglement and discord is determined with respect to the total number of qutrits of the system.