Upper bound and shareability of quantum discord based on the uncertainty principle

By using the quantum-memory-assisted entropic uncertainty relation (EUR), we derive a computable tight upper bound for quantum discord, which applies to 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 and a class of tripartite mixed states, 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.