The CanPickUpLoot tag doesn't do anything if gamerule mobGriefing is off

Use this command:

/summon Zombie ~ ~1 ~ {CustomName:Clone,CustomNameVisible:1,At­tributes:[{Name:generic.movementSpeed,Ba­se:0.01}],CanPickUpLoot:true} 

Which is proved it works by this video: https://www.youtube.com/watch?v=VDiI9NR9c1A

Then throw any item on the zombie. The zombie won't grab it!

If the gamerule is off