Monogamy is a non-classical property that restricts the sharability of quantum correlation among the constituents of a multipartite quantum system. Quantum correlations may satisfy or violate monogamy for quantum states. Here we provide evidence that almost all pure quantum states of systems consisting of a large number of subsystems are monogamous with respect to all quantum correlation measures of both the entanglement-separability and the information-theoretic paradigms, indicating that the volume of the monogamous pure quantum states increases with an increasing number of parties. Nonetheless, we identify important classes of pure states that remain nonmonogamous with respect to quantum discord and quantum work-deficit, irrespective of the number of qubits. We find conditions for which a given quantum correlation measure satisfies vis-à-vis violates monogamy.

A highly entangled bipartite quantum state is more advantageous for the quantum dense coding protocol than states with low entanglement. Such a correspondence, however, does not exist even for pure quantum states in the multipartite domain. We establish a connection between the multiparty capacity of classical information transmission in quantum dense coding and several multipartite quantum correlation measures of the shared state, used in the dense coding protocol. In particular, we show that for the noiseless channel, if multipartite quantum correlations of an arbitrary multipartite state of arbitrary number of qubits is the same as that of the corresponding generalized Greenberger-Horne-Zeilinger state, then the multipartite dense coding capability of former is the same or better than that of the generalized Greenberger-Horne-Zeilinger state. Interestingly, in a noisy channel scenario, where we consider both uncorrelated and correlated noise models, the relative abilities of the quantum channels to transfer classical information can get inverted by administering a sufficient amount of noise. When the shared state is an arbitrary multipartite mixed state, we also establish a link between the classical capacity for the noiseless case and multipartite quantum correlation measures.

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 ...

Fidelity plays an important role in measuring distances between pairs of quantum states, of single as well as multiparty systems. Based on the concept of fidelity, we introduce a physical quantity, shared purity, for arbitrary pure or mixed quantum states of shared systems of an arbitrary number of parties in arbitrary dimensions. We find that it is different from quantum correlations. However, we prove that a maximal shared purity between two parties excludes any shared purity of these parties with a third party, thus ensuring its quantum nature. Moreover, we show that all generalized GHZ states are monogamous, while all generalized W states are non-monogamous with respect to this measure. We apply the quantity to investigate the quantum XY spin models, and observe that it can faithfully detect the quantum phase transition present in these models. We perform a finite-size scaling analysis and find the scaling exponent for this quantity.