Local Quantum Uncertainty and Bounds on Quantumness for O ⊗O invariant class of states

Quantum mechanics shows several counter-intuitive results when we are dealing with composite systems [1–3]. There exist peculiar type of correlations between different parts of a composite system commonly known as non-classical correlations. Entanglement is one of the most powerful non-classical correlation that establishes its importance in different information processing tasks. However, several post entanglement correlation measures have generated a lot of interests in recent years. Discord, quantum deficit, measurement-induced nonlocality(in short, MIN) [4–7] are a few of them. Even there are different non equivalent versions of discord [8]. Recently Girolami et. al.[9] introduced the concept of local quantum uncertainty which quantifies the uncertainty in a quantum state due to measurement of a local observable. Nevertheless, such quantifier has strong reasons to be considered as a faithful measure of quantumness in quantum states. But due to inherent optimization, finding closed formula is a difficult problem for most of the correlations measures. The value of quantum discord is not even known for general bipartite qubit system. In higher dimensional bipartite systems, the results are known for only some special classes of states [10, 11]. Geometric discord has explicit formula for qubit-qudit system and its lower bound is calculated in [12, 13] for higher dimensions. MIN has a closed formula for qubitqudit systems and it has tight upper bound in higher dimensions [6]. It is possible to derive closed formula for MIN, geometric discord and also for quantum discord for Werner and Isotropic classes of states due to their highly inherent symmetry in the structures. However, local quantum uncertainty (LQU) has analytical form only for any qubit-qudit system. Here, we will consider orthogonal invariant class of states which is a larger class of symmetric states and it contains both Werner and Isotropic classes. We will derive closed form of LQU for this class of states in