Timelike curves can increase entanglement with LOCC

We study the nature of entanglement in presence of Deutschian closed timelike curves (D-CTCs) and open timelike curves (OTCs) and find that existence of such physical systems in nature would allow us to increase entanglement using local operations and classical communication (LOCC). This is otherwise in direct contradiction with the fundamental definition of entanglement. We study this problem from the perspective of Bell state discrimination, and show how D-CTCs and OTCs can unambiguously distinguish between four Bell states with LOCC, that is otherwise known to be impossible.