The unseeded pair beat third seeds Julien Cagnina of Belgium and Luke Saville of Australia [ Images ] 6-3, 7-6 (7-4).
The 19-year-old Kadhe, India's senior national doubles champion, and Herreros dominated the first set and wrapped it up in just 20 minutes.
However, their higher-ranked Australian opponents fought back in the second as both teams effected two breaks each.
But just when it looked like the third seeds were getting into a rhythm, Kadhe and Herreros raised their game in the tie-breaker to set up a last eight clash against another Australian combination of Andrew Harris and Nick Kyrgios.
Arjun is a 12th standard student of Symbiosis college and member of MSLTA Vision Programme, and trained by Hemant Bendrey at PYC Gymkhana in Pune. He is supported by LAKSHYA-Bharat Forge.