Abstract
Quantum discord and quantum uncertainty are two important features of the quantum world. In this work, the relation between entropic uncertainty relation and the shareability of quantum discord is studied. By using tripartite quantum-memory-assisted entropic uncertainty relation, an upper bound for the shareability of quantum discord among different parties of a composite system is obtained. It is also shown that, for a specific class of tripartite states, the obtained relation could be expressed as monogamy of quantum discord. Moreover, it is illustrated that the relation could be generalized and an upper bound for the shareability of quantum discord for multipartite states is derived.
Highlights
Quantum discord and quantum uncertainty are two important features of the quantum world
In “Tripartite QMA-entropic uncertainty relation (EUR) and shareability of quantum discord (QD)”section, the new relation for the tripartite quantum-memoryassisted entropic uncertainty relation (QMA-EUR) is expressed and an upper bound for the shareability of QD is extracted
We introduce new tripartite QMA-EURs, which depend on the incompatibility of two quantum measurements, the strong subadditivity (SSA) inequality, the QD, and the classical correlations of a state shared between the observed system and quantum memories
Summary
QD is another important concept within the field of quantum information. Considerable attention has been paid to QD due to its potential connection with other aspects of quantum information and beyond, including quantum communication, quantum computation, many-body physics, and open quantum dynamics ( see[84] for further details). Hu and Fan have investigated a relation between QD and bipartite QMA-EUR53 Their consideration led to an improvement on the upper bounds for Q D53. They considered the effects of the bipartite QMA-EUR on the shearability of quantum correlation among different subsystems. In which δT = S(X|B) + S(Z|B) − qMU − S(A|B) They showed that for any tripartite state ρABC with S(ρA) = −S(A|BC) , the above relation can be written as: DA(ρAB) + DA(ρAC ) ≤ DA(ρA:BC ) + δT. Proof The theorem is proved using the definition of classical correlation, QD, and tripartite QMA-EUR, Eq (6). S(X|B) + S(Z|C) − qMU − 1 [S(A|B) + S(A|C)] + 1 [I(A : B) + I(A : C)] ≥ DA(ρAB) + DA(ρAC)
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