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The work is intended to represent some interesting and apparently peculiarfeatures of entangled system in both pure as well as mixed states level. In thepure state level, we are largely concerned about the existence andcharacteristics of bipartite incomparable pair of states. We have found someschemes for local transformation of one pure bipartite state to another,incomparable in nature, by exploiting free unpreserved entanglement. Also, weobserved that different incomparable pair of states in $3\times 3$ mayco-operate with each other to cross the barrier of incomparability. Our nextgoal was to probe critically the roots of the existence of incomparable states.We have succeeded in connecting incomparability with some famous no-go theoremsof quantum mechanics. We have established it with no-flipping principle,general anti-unitary operators and lastly with inner product preservingoperations. Thus we are able to pose incomparability as a good detector of somenon-physical operations. In the next part, we provide a new class ofmultipartite bound entanglement in mixed state level. The class of states areactivable bound entangled. There are exactly four orthogonal activable boundentangled states in any even number of qubit system. They have some interestingfeatures like Bell correlation, permutation symmetry, local Pauli connection,non-compatibility, etc. Apart from those properties, the class of boundentangled states have the remarkable feature of local indistinguishability inquantum systems.

Entanglement - A Queer In The World Of Quantum : Some Perspectives