We review concepts and methods associated with quantum discord and related topics. We also describe their possible connections with other aspects of quantum information and beyond, including quantum communication, quantum computation, many-body physics, and open quantum dynamics. Quantum discord in the multiparty regime and its applications are also discussed.

Multiparty quantum states are useful for a variety of quantum information and computation protocols. We define a multiparty entanglement measure based on local measurements on a multiparty quantum state, and an entanglement measure averaged on the post-measurement ensemble. Using the generalized geometric measure as the measure of multipartite entanglement for the ensemble, we demonstrate, in the case of several well-known classes of multipartite pure states, that the localized multipartite entanglement can exceed the entanglement present in the original state. We also show that measurement over multiple parties may be beneficial in enhancing localizable multipartite entanglement. We point out that localizable generalized geometric measure faithfully signals quantum critical phenomena in well-known quantum spin models even when considerable finite-size effect is present in the system.

Computing entanglement of an arbitrary bipartite or multipartite mixed state is in general not an easy task as it usually involves complex optimization. Here we show that exploiting symmetries of certain multiqudit mixed states, we can compute a genuine multiparty entanglement measure, the generalized geometric measure, for these classes of mixed states. The chosen states have different ranks and consist of an arbitrary number of parties. I. INTRODUCTIONCharacterization and quantification of quantum entanglement [1] lies at the heart of quantum information theory, since its early recognition as "spooky action at a distance" [2] in the Einstein-Podolsky-Rosen article [3]. Moreover, it has been successfully identified as a key resource in several quantum communication protocols including superdense coding [4], teleportation [5], and quantum cryptography [6]. Entanglement has been shown to be a necessary ingredient in studying quantum state tomography [7], quantum metrology [8], cooperative quantum phenomena in many body systems like quantum phase transitions [9], etc. Quantification of entanglement is also essential for characterization of successful preparations of quantum states, both in two party and multiparty domains, in the laboratories [10].The notion of entanglement is rather well-understood in the bipartite regime, especially for pure states [11][12][13][14][15]. While several entanglement measure can be computed for bipartite pure states, the situation for mixed states is difficult, and there are only few entanglement measures which can be computed efficiently. The logarithmic negativity [14] can be obtained for arbitrary bipartite states, while the entanglement of formation [12,13] can be computed for all two-qubit states. The situation becomes complicated even for the pure states when the number of parties increase. However, there have been significant advances in recent times to quantify multipartite entanglement of pure quantum states in arbitrary dimensions [1]. They are broadly classified in two catagories − distance-based measures [16][17][18][19] and monogamy-based ones [6,11,20,21]. On the other hand, quantifying entanglement for arbitrary multiparty mixed states is still an arduous task. Recently, experiments by using photon polarization [22] and ions [23] have been reported in which multiparty states of the order of ten parties have been created successfully. Such physical implementations demand a general tool to compute multiparty entanglement measures for arbitrary mixed states. Recently there have been notable advancements in this direction [24]. Moreover, when an entanglement measure can only be evaluated for pure states, the entanglement-assisted study of cooperative phenomena becomes restricted to only a system which is at zero temperature.We address here the question of computing the generalized geometric measure (GGM) [19], a genuine multiparty entanglement quantifier, for mixed states. The GGM of pure states has already been computed efficiently in several systems for arbitrary number ...

We investigate the action of local and global noise on monogamy of quantum correlations, when monogamy scores are considered as observables, and three-qubit systems are subjected to global noise and various local noisy channels, namely, amplitude-damping, phase-damping, and depolarizing channels. We show that the dynamics of monogamy scores corresponding to negativity and quantum discord, in the case of generalized W states, as inputs to the noisy channels, can exhibit non-monotonic dynamics with respect to increasing noise parameter, which is in contrast to the monotonic decay of monogamy scores when generalized Greenberger-Horne-Zeilinger states are exposed to noise. We quantify the persistence of monogamy against noise via a characteristic value of the noise parameter, and show that depolarizing noise destroys monogamy of quantum correlation faster compared to other noisy channels. We demonstrate that the negativity monogamy score is more robust than the quantum discord monogamy score, when the noise is of the phase-damping type. We also investigate the variation of monogamy with increasing noise for arbitrary three-qubit pure states as inputs. Finally, depending on these results, we propose a two-step protocol, which can conclusively identify the type of noise applied to the quantum system, by using generalized Greenberger-Horne-Zeilinger and generalized W states as resource states. We discuss a possible generalization of the results to higher number of parties.