Go to fastboot, conect phone to pc and in terminal type:
fastboot oem device-info
Watch for devices unlocked, true or false. I guest you activate developer mode, with enable oem unlock and usb debugging?
Wheu you have permission for unlock, it`s really simple:
http://xiaomitips.com/guide/how-to-fix-couldnt-verify-device-error-during-bootloader-unlock-process/
My phone came with 6.5.19, which is global dev. Unlock with MiUnlock work like a charm. Unlock official work with any China ROM and global devel, but not with global stable. Still, why you need unlock, for EU ROMS? Or for twrp/root?
You can unlock unofficially, but is tricky and somehow risky.
http://xiaomitips.com/guide/unlock-redmi-note-3-bootloader-without-official-permission/
http://forum.xda-developers.com/redmi-note-3/how-to/unlock-bootloader-waiting-permission-t3349886
HIGHLY RECOMMEND you to try this tutorial...
http://forum.xda-developers.com/showthread.php?t=3034811
http://dl-xda.xposed.info/framework/sdk23/arm64/xposed-v86-sdk23-arm64.zip
Copy unninstaler to phone, just in case.