Steerability is a characteristic of quantum correlations lying between entanglement and Bell nonlocality. Understanding how these steering correlations can be shared between different parties has profound applications in ensuring the security of quantum communication protocols. Here we show that at most two bipartite reduced states of a three-qubit state can violate the three-setting CJWR linear steering inequality, contrary to the two-setting linear steering inequality. This result explains that quantum steering correlations have limited shareability properties apart from the conventional 'nonshareable' monogamy constraint. In contrast to the two-measurement-setting scenario, the three-setting scenario turns out to be more useful for developing a deeper understanding of the shareability of tripartite steering correlations. Apart from the distribution of steering correlations, several relations between reduced bipartite steering, different measures of bipartite entanglement of reduced states, and genuine tripartite entanglement are presented here. The results enable the detection of different kinds of tripartite entanglement.
Quantum coherence and quantum entanglement are two strong pillars in quantum information theory. We study here for the possibility of any connection between these two important aspects of quantum mechanics while studying the entanglement detection problem for the detection of bipartite higher dimensional entangled states and multipartite entangled states. To achieve our goal, we derive the lower bound
L of
l1 norm of coherence of bipartite qubit-qudit system using the criterion that detect entanglement. Furthermore, we deduce the upper bound
U of
l1 norm of coherence of separable bipartite qubit-qudit system using the separability criterion. Thus, we find that if any
l1 norm of coherence of bipartite qubit-qudit system is greater than the upper bound
U then the given qubit-qudit state is entangled. Finally, we obtained the upper bound
U1 of
l1 norm of coherence of separable tripartite state lies either in
2⊗d⊗d or
d⊗2⊗d or
d⊗d⊗2 dimensional Hilbert space using the upper bound
U. We have shown that if the
l1 norm of coherence of any tripartite
qubit−qudit−qudit or
qudit−qubit−qudit or
qudit−qudit−qubit system is greater than the derived upper bound
U1 then the given tripartite system represent an entangled state.
For pure bipartite superposed states, the entanglement quantified by negativity is studied. If the entanglement is quantified by concurrence, we show that two pure states with high fidelity to one another have nearly the same entanglement. We deduce an inequality in which the concurrence is known to be a continuous function in infinite dimensions. The main result of this paper is to give the bounds on the negativity of a bipartite state in terms of the entanglement of the states being superposed. These bounds may be used in estimating the entanglement of a given state.