Hydrolyzes diadenosine 5',5'''-P1,P4-tetraphosphate (Ap4A) to yield ADP (PubMed:32152217). Can also hydrolyze Ap3A, Ap5A, Ap4G, Ap4U and Gp4G, always releasing ADP or GDP as one of the products, but it exhibits a marked preference for Ap4A, which is mainly exerted at the substrate affinity level (PubMed:32152217). H2O + P(1),P(4)-bis(5'-adenosyl) tetraphosphate = 2 ADP + 2 H(+) Inhibited by EDTA. kcat is 107 sec(-1) with Ap4A as substrate. kcat is 32 sec(-1) with Ap5A as substrate. kcat is 210 sec(-1) with Ap4G as substrate. kcat is 324 sec(-1) with Ap4U as substrate. kcat is 1002 sec(-1) with Gp4G as substrate. Homodimer. Belongs to the Ap4A hydrolase YqeK family.