Can I transfer Pokemon from XD to Pokemon white?

No, why would you think that?

There is a way to transfer the Pokemon you catch in Pokemon XD Gale of Darkness to Pokemon White, but not vice versa.

First, you need to trade over the desired Pokemon from the Gamecube game to the GBA game (I.e. Firered, Leafgreen, Sapphire, Emerald or Ruby).

Next step, you have to transfer over the Pokemon you traded into your GBA game, over to one of the 4th generation DS games (I.e. Diamond, Pearl, Platinum, Heartgold, SoulSilver). The way that works is basically you have your gameboy advance game in the gameboy advance slot of your DS (Lite), with your Pokemon DS game in the DS slot. Turn on the DS game, go to the main menu where you have options, your saved file, etc. Tap or select the option that says "migrate Pokemon from GBA game" or something to that effect. If you have more than 6 desired Pokemon to transfer over, this could take a few days, because you can only migrate up to 6 Pokemon at a time. The migrated Pokemon go into the Safari Zone of your game (not the one that limits you on time with 30 special Pokeballs) that allows you to automatically capture the migrated Pokemon when you do the Safari game.

Once you've done that, you're almost there!

Last step gets a little tricky. Depending on the version of your games you're using, you may/may not be able to do this (for example, if you own a Japanese version of Pokemon White, and an English version of your 4th generation game, the games won't recognize each other. They both have to be the same version, I.e. Japanese w/ Japanese, English w/ English). In your Pokemon White, you need to have the Transfer Machine/Relocator unlocked as a main menu option when you turn on the game. In order to unlock it, you need to have talked to the scientist in Castelia City and answer his two questions. First question answer "EVERYONE HAPPY" and the second one answer "SIMPLE CONNECTION" Once you've got the Transfer Machine/Relocator, use that option on the main menu screen where your file and such are located, follow the instructions it gives you and you shouldn't have any issues with transferring your Pokmemon you've had to send through a monstrous roller coaster ride just to get there.

Good luck!