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Absolute separable states is a kind of separable state that remain separableunder the action of any global unitary transformation. These states may or maynot have quantum correlation and these correlations can be measured by quantumdiscord. We find that the absolute separable states are useful in quantumcomputation even if it contains infinitesimal quantum correlation in it. Thusto search for the class of two-qubit absolute separable states with zerodiscord, we have derived an upper bound for $Tr(\varrho^{2})$, where $\varrho$denoting all zero discord states. In general, the upper bound depends on thestate under consideration but if the state belong to some particular class ofzero discord states then we found that the upper bound is state independent.Later, it is shown that among these particular classes of zero discord states,there exist sub-classes which are absolutely separable. Furthermore, we havederived necessary conditions for the separability of a given qubit-quditstates. Then we used the derived conditions to construct a ball for $2\otimesd$ quantum system described by $Tr(\rho^{2})\leq Tr(X^{2})+2Tr(XZ)+Tr(Z^{2})$,where the $2\otimes d$ quantum system is described by the density operator$\rho$ which can be expressed by block matrices $X,Y$ and $Z$ with $X,Z\geq 0$.In particular, for qubit-qubit system, we show that the newly constructed ballcontain larger class of absolute separable states compared to the balldescribed by $Tr(\rho^{2})\leq \frac{1}{3}$. Lastly, we have derived thenecessary condition in terms of purity for the absolute separability of aqubit-qudit system under investigation.

the european physical journal. d, atomic, molecular and optical physics/the european physical journal. d, atomic, molecular, optical and plasma physics

Constructing a ball of separable and absolutely separable states for $2\otimes d$ quantum system