Measurement-Induced NonLocality was introduced by Luo and Fu (Phys. Rev. Lett. 106, 120401,(2011)) as a measure of nonlocality in a bipartite state. In this paper we will discuss monogamy property of measurement-induced nonlocality for some three-and four-qubit classes of states. Unlike discord, we find quite surprising results in this situation. Both the GHZ and W states satisfy monogamy relations in the three-qubit case, however, in general there are violations of monogamy relations in both the GHZ-class and W-class states. In case of four-qubit system, monogamy holds for most of the states in the generic class. Four qubit GHZ does not satisfy monogamy relation, but W-state does. We provide several numerical results including counterexamples regarding monogamy nature of measurement induced nonlocality. We will also extend our results of generalized W-class to n-qubit.

No-cloning and No-deleting theorems are verified with the constraint on local state transformations via the existence of incomparable states. Assuming the existence of exact cloning or deleting operation defined on a minimum number of two arbitrary states, an incomparable pair of states of the joint system between two parties can be made to compare under deterministic LOCC. We have restricted our proof with the assumption that the machine states of the cloning or deleting operations do not keep any information about the input states. We use the same setting to establish the no-cloning and no-deleting theorems via incomparability that supports the reciprocity of the two operations in their operational senses. The work associates the impossibility of operations with the evolution of an entangled system by LOCC. KEY WORDS: Local operations and classical communication; quantum cloning; quantum deleting; incomparability of quantum states. PACS: 03.67.Mn; 03.67.Hk.One of the most important task in quantum information processing is to detect the allowable set of operations performed on quantum systems. If someone wants to copy an arbitrary quantum information encoded in a quantum state then no-cloning theorem (1) restricts one to copy arbitrary quantum information exactly. Quite reverse to it, if we want to delete arbitrary quantum information then we have a similar kind of restriction. (2,3) According to the no-deletion theorem, (2,3) it is not possible to delete arbitrary quantum information encoded in a quantum state to a standard one. On the other hand, manipulation of pure state entanglement provides us some other kind of restrictions on the evolution of quantum systems.

Monogamy is a defining feature of entanglement, having far reaching applications. Recently, Regula et.al. in Phys. Rev. Lett. 113, 110501(2014) have proposed a stronger version of monogamy relation for concurrence. We have extended the strong monogamy inequality for another entanglement measure, viz., negativity. In particular, we have concentrated on four-qubit system and provided a detail study on the status of strong monogamy on pure states. Further, we have analytically provided some classes of states for which negativity and squared negativity satisfy strong monogamy. Numerical evidences have also been shown in proper places. Our analysis also provides cases where strong monogamy is violated.PACS numbers: 03.67.Mn, 03.65.Ud.; arXiv:1512.06816v1 [quant-ph]

Local quantum uncertainty (in short LQU) was introduced by Girolami et. al.(Phy. Rev. Lett. 110, 240402) as a measure of quantum uncertainty in a quantum state as achievable on single local measurement. However, such quantity do satisfy all necessary criteria to serve as measure of discord like quantum correlation and it has no closed formula except only for 2⊗n system. Here, we consider orthogonal invariant class of states which includes both the Werner and Isotropic class of states and explore the possibility of closed form formula. Further, we extend our quest to the possibility of closed form of geometric discord and measurement induced nonlocality for this class. We also provide a comparative study of the bounds of general quantum correlations with entanglement, as measured by negativity, for an interesting subclass of states.

We check the decoherence dynamics of Measurement-induced Nonlocality(in short, MIN) and compare it with geometric discord for two qubit systems. There are quantum states, on which the action of dephasing channel cannot destroy MIN in finite or infinite time. We check the additive dynamics of MIN on a qubit state under two independent noise. Geometric discord also follows such additive dynamics like quantum discord. We have further compared non-Markovian evolution of MIN and geometric discord under dephasing and amplitude damping noise for pure state and it shows distinct differences between their dynamics.