We study the properties of a general quantum correlation known as quantum discord, which has recently been studied as a resource for quantum computation. We investigate the relations between discord, entanglement and entropy.
Measurements of quantum systems disturb their states. To quantify this nonclassical characteristic, Zurek and Ollivier [Phys. Rev. Lett. 88, 017901 (2001)] introduced the quantum discord, a quantum correlation that can be nonzero even when entanglement in the system is zero. Discord has aroused great interest as a resource that is more robust against the effects of decoherence and offers the exponential speed-up of certain computational algorithms. Here, we study general two-level bipartite systems and give general results on the relationship between discord, entanglement, and linear entropy. We also identify the states for which discord takes a maximal value for a given entropy or entanglement, thus placing strong bounds on entanglement-discord and entropy-discord relations. We find out that although discord and entanglement are identical for pure states, they differ when generalized to mixed states as a result of the difference in the method of generalization.
Measurements of Quantum Systems disturb their states. To quantify this non-classical characteristic, Zurek and Ollivier introduced the quantum discord, a quantum correlation which can be nonzero even when entanglement in the system is zero. Discord has aroused great interest as a resource that is more robust against the effects of decoherence and offers exponential speed up of certain computational algorithms. Here, we study general two-level bipartite systems and give general results on the relationship between discord, entanglement, and linear entropy, and identify the states for which discord takes a maximal value for a given entropy or entanglement, thus placing strong bounds on entanglement-discord and entropy-discord relations. We find out that although discord and entanglement are identical for pure states, they differ when generalized to mixed states as a result of the difference in the method of generalization.
Quantum information and computation, based on quantum correlations of quantum systems, is one of the promising new fields of physics and information science. Entanglement is the key resource of quantum information processing. However, it is shown recently that quantum entanglement is not the only kind of quantum correlations useful for quantum information processing. Quantum systems without any entanglement can still be helpful for quantum information processing since unentangled systems could have another kind of quantum correlations - quantum discord. Thus, quantum discord has drawn much attention in recent years. Here, we briefly review the concepts and properties of quantum discord. Several measures of discord including the original measure of discord, relative entropy-based discord, geometric discord, global discord, Gaussian discord, are reviewed and discussed.
Quantum coherence and quantum correlations are important quantum resources for quantum computation and quantum information. In this paper, using entropy-based measures, we investigate the relationships between quantum correlated coherence, which is the coherence between subsystems, and two main kinds of quantum correlations as defined by quantum discord as well as quantum entanglement. In particular, we show that quantum discord and quantum entanglement can be well characterized by quantum correlated coherence. Moreover, we prove that the entanglement measure formulated by quantum correlated coherence is lower and upper bounded by the relative entropy of entanglement and the entanglement of formation, respectively, and equal to the relative entropy of entanglement for all the maximally correlated states.
We give a pedagogical introduction to quantum discord and discuss the problem of separation of total correlations in a given quantum state into entanglement, dissonance, and classical correlations using the concept of relative entropy. This allows us to put all correlations on an equal footing. Entanglement and dissonance jointly belong to what is known as quantum discord. Our methods are completely applicable for multipartite systems of arbitrary dimensions. We finally show, using relative entropy, how different notions of quantum correlations are related to each other. This gives a single theory that incorporates all correlations, quantum and classical, and different methods of quantifying them.
entanglement generated by the far beyond intuitive pure quantum phenomena such as EPRparadox,Schr?dinger's Equation has been considered not only as one of the significant notions in quantum theorybut also a key of realizing the Super Dense Coding and the Quantum Teleportation in quantum communication.However,recent researches show that quantum entanglement is less likely to account for all the properties of quan-tum correlations.Except for the quantum entanglement,researchers find other non-classical correlations like quan-tum discord,which plays a pivotal role in quantum information and quantum computation and that's why the purequbit-decisive quantum computer possesses computational efficiency.With this clarification,quantum discord com-pletely can be a new resource of quantum computation.In this paper,basic notions and measurement methods ofnon- classical correlations(including quantum entanglement) were discussed and the quantum correlationproperties of the quantum discord in various models were analyzed and compared with the quantum entanglement.Conducting researches on the non-classical correlations in various quantum systems are not merely meritorious tothe quantum theory,in the mean time,may provide some efficient thoughts and motivations for researchers to em-ploy theoretical concepts about quantum correlations for avoiding decoherence and theoretical scenario for the exper-iments.