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A simple relation is established for the evolution equation of quantum-information-processing protocols such as quantum teleportation, remote state preparation, Bell-inequality violation, and particularly the dynamics of geometric quantum correlation measures. This relation shows that when the system traverses the local quantum channel, various figures of merit of the quantum correlations for different protocols demonstrate a factorization decay behavior for dynamics. We identified the family of quantum states for different kinds of quantum channels under the action of which the relation holds. This relation simplifies the assessment of many quantum tasks. [ABSTRACT FROM AUTHOR]

By using the quantum-memory-assisted entropie uncertainty relation (EUR), we derive a computable tight upper bound for quantum discord, which applies to an arbitrary bipartite state. Detailed examples show that this upper bound is tighter than other known bounds in a wide regime. Furthermore, we show that for any tripartite pure state, the quantum-memory-assisted EUR imposes a constraint on the shareability of quantum correlations among the constituent parties. This conclusion amends the well-accepted result that quantum discord is not monogamous. [ABSTRACT FROM AUTHOR]

With the aid of a quantum memory, the uncertainty about the measurement outcomes of two incompatible observables of a quantum system can be reduced. We investigate this measurement uncertainty bound by considering an additional quantum system connected with both the quantum memory and the measured quantum system. We find that the reduction of the uncertainty bound induced by a quantum memory, on the other hand, implies it is increasing for a third participant. We also show that the properties of the uncertainty bound can be viewed from perspectives of both quantum and classical correlations, in particular, that the behavior of the uncertainty bound is a result of competitions of various correlations between different parties. [ABSTRACT FROM AUTHOR]

Quantum coherence, incompatibility, and quantum correlations are fundamental features of quantum physics. A unified view of those features is crucial for revealing quantitatively their intrinsic connections. We define the relative quantum coherence of two states as the coherence of one state in the reference basis spanned by the eigenvectors of another one and establish its quantitative connections with the extent of mutual incompatibility of two states. We also show that the proposed relative quantum coherence, which can take any form of measures such as l¹ norm and relative entropy, can be interpreted as or connected to various quantum correlations such as quantum discord, symmetric discord, entanglement of formation, and quantum deficits. Our results reveal conceptual implications and basic connections of quantum coherence, mutual incompatibility, and quantum correlations. [ABSTRACT FROM AUTHOR]