Monogamous nature of symmetricN-qubit states of the W class: Concurrence and negativity tangle

Abstract

Using Majorana representation of symmetric N -qubit pure states, we have examined the monogamous nature of the family of states with two-distinct spinors, the W-class of states. We have evaluated the N -concurrence tangle and showed that all the states in this family have vanishing concurrence tangle. The negativity tangle for the W-class of states is shown to be non-zero illustrating the fact that concurrence tangle underestimates the residual entanglement in a pure N -qubit state.

Monogamous nature of Dicke-class of states with two distinct Majorana spinors

“…We have noticed that the negativity tangle ξ N is non-zero for all values of N ≥ 3 [39]. This feature is seen in Fig.…”

“…It was also shown that different measures of entanglement give rise to different quantifications of residual entanglement. While it is shown that W-class of states have vanishing concurrence-tangle [1], they are shown to have non-zero negativity tangle [9,39]. It thus becomes important to choose a suitable measure of entanglement for quantifying residual entanglement and evaluating the tangle.…”

“…Here the set of all N -qubit symmetric states (invariant under the interchange of qubits) with only two distinct qubits (spinors) characterizing them is defined as the Dicke-class of states, as all Dicke states belong to this family. While the W-class of states, the symmetric multiqubit states with one of the spinors repeating only once in all possible permutations contained in the state, have vanishing concurrence tangle [39], the states with all other degeneracy configurations (SLOCC inequivalent families) are shown to have non-zero concurrence tangle. It is also shown that for all inequivalent families of states of Dicke class, the negativity tangle is greater than concurrence tangle.…”

Monogamy relations of quantum entanglement for partially coherently superposed states

“…[26], the CoA of an n-qubit pure state satisfies a polygamy inequality of entanglement, and here we present a monogamy relation with respect to CoA for PCS states. Note that according to inequality (24), we can give a lower bound of CoA for the reduced density matrices of a PCS state. Next we give an example.…”

“…Then it may be important to investigate the monogamy of these two classes of states. Recently, Geetha et al analyzed the monogamous nature for the W class of symmetric N-qubit states in terms of the squared negativity and concurrence and presented that for these states, the concurrence tangle is zero, while the negativity tangle is non-zero, [24] the authors in Ref. [25] showed the generalized monogamy for the generalized Wclass multiqubit states.…”