Short answer: No. This would not give you any sort of special powers.
Long answer: A device that produces quantum entanglement is a device that produces pairs of tiny particles that have opposite spin values. The ability to do this is interesting from a physics experiment point of view, but supremely lacking in practical applications. There's no known way to do mind-reading, free energy, FTL communications or any of the things you're likely thinking about using quantum anythings. It would be pretty much like having a remote control for a particle accelerator or a fume hood or some other piece of heavy and expensive lab equipment wired to your brain.
Hmmmmm. I'm very tempted to say that you could create a mind reader, if you entangled nerves and somehow duplicated memories and feelings from there.
A] Creating quantum entanglement requires that the two particles interact. This interaction requires the particles to be very close together. In order to "read" someone's mind with it, you would have to rub all of the particles in the brain of the person to be read up against an equal number of identical particles somewhere in the brain of the reader. Which is obviously all sorts of fatal for both parties.
B] Even if you did somehow get all of the particles in a person's brain quantumnly entangled with all of the particles in someone else's brain, the quantum state of the brain does not determine thoughts: It's the chemical and electrical level interaction that makes your brain think. Quantum entanglement has nothing to do with it.
C] Assuming you did get the a portion of one person's brain to physically match the corresponding portion of the other person's brain in all important respects, that would be as useful in terms of learning their thoughts as cutting out a chunk of the "mindreader's" brain and inserting a chunk of the person-to-be-read's brain. Which is to say: Not very helpful.