I'm the author of the Apple SSD article that klanomath linked to in their comment and I wanted to clarify some things that seem to have been misinterpreted.
First of all, the Mid 2013 release of the MacBook Air 11" absolutely can use the faster PCIe 3.0 x4 drives from the 2015-2017 MacBook Air 13", which I refer to in the article as the Gen. 4A SSDs.
Allan's answer mentions that the 2015-2017 MacBook Air 13" drives are PCIe 2.0 x4, but they're in fact PCIe 3.0 x4 drives. It's the PCIe interface of the MacBook Airs logic board that is limited to PCIe 2.0 x4.
And the quirky firmware changes that prevent compatibility with earlier MacBook Airs were only present in the 128GB and 256GB PCIe 2.0 x2 drives (referred to as Gen. 4C in the article) found in the Early 2015 release of the MacBook Air 11". All of the drives found in Early 2015 and later MacBook Air 13" laptops are 100% compatible with earlier Mid 2013 and Early 2014 MacBook Airs, as is the 512GB drive from the Early 2015 release of the MacBook Air 11".
Everyone in this discussion missed this paragraph from the article:
Despite the two channel drive, the 11″ MacBook Air actually supports
four channel PCIe connections, and they can be upgraded with the Gen.
4A drives found in other devices. In fact, if the 11″ MacBook Air was
configured with a 512GB SSD from the factory, it already included the
same Gen. 4A drive found in the other Apple computers of the era.
Despite all the good info in that article, it's a bit dense to read in places and I think much of the information could have been conveyed in a better way. I've recently started working on some improvements that should make it easier to quickly grasp the most important details and should be publishing those changes in the next couple weeks.