Learn English – A formal way to request for updated information in business email writing

In the Cambridge Encyclopedia of the English Language (2003), thanks is considered a minor sentence, or more specifically, a type of minor sentence that is a "formula for stereotyped social situations."

In chapter 8 of "An Advanced English Grammar with Exercises" (1913):

Good usage does not demand that all sentences shall be absolutely complete. It often allows (and sometimes requires) the omission of words that, though necessary to the construction, are so easily supplied by the mind that it would be mere waste of time to utter them.

The first example of such an elliptical sentence is:

[I] thank you.

"Thank you" without an explicit subject has been used since at least the 15th century, according to an article in the ICAME Journal (vol. 26:63–80):

Interestingly, the shift from a clearly performative speech act with a subject, e.g. I thank you or I give thanks to you to the shortened forms thank you and thanks, had not gone far in Early Modern English. The shortened forms appeared in the 15th century and there are only five examples in my material [Corpus of English Dialogues].

So, although it is generally regarded as grammatically correct, it might sound too informal for business communications. That is entirely subjective, though. Of the alternatives you provided, I think the one beginning with "we" sounds best (see edit below):

We thank you for the information...

Alternatives to thank you can also give the letter a more professional tone:

We appreciate the information...

We are [very] appreciative of the information...

Our company is [very] grateful for the information...

Edit:
Rather than rely on my own assumptions, I tried to find more references for business writing etiquette with regard to thank-you letters or letters of appreciation. I think now that my opinion was wrong about the implied subject for thank you being too informal for business communications.

I found a reference from the American Management Association, The AMA Handbook of Business Writing (2010), which gives examples of several types of business letters. In it, there is an 8:3 ratio in favor of using the implied subject form, "Thank you," rather than for example, "I want to personally thank you..."

In another book with business letter examples, 300+ Successful Business Letters for All Occasions, the first example of a Thank-you letter (pg 51), begins with "Thank you..." The second example on page 52 also starts with the implied subject form, although the last sentence uses an explicit subject "We thank you..." The examples of other types of letters often use of the implied subject form, too.

The first is more polite while the second is more impersonal and better suited to a corporate or institutional setting where the recipient might not have a relationship with the writer.

Both are however too wordy; the recipient knows you're informing her by the fact that you're sending her a message. 'Asked for' is also too colloquial for a business or academic setting. I'd use 'requested'.

Also, the word 'completed' is ambiguous and not idiomatic (it could mean that it's been scanned but not made available for download, for instance). I would suggest instead:

"The document you requested is ready for pickup."

or if it is to be downloaded,

"The document you requested is available for download at [URL]."

or if you're sending this message with a PDF or other electronic copy of the document,

"Please find enclosed XXXXXX, per your request."