Does entanglement allow communication of user specified information or not?

An entangled quantum state, where one subsystem is held by each party, and there is no other communication, cannot be used to achieve communication.

The two classes of operation that one party could perform on their quantum system are unitaries and measurements.

• A unitary performed on one quantum subsystem (Alice) does not change the other one (Bob), so that cannot give you communication

• A measurement performed on Alice's subsystem gives a random outcome. While that outcome is effectively communicated to Bob's subsystem, since Alice could not choose the outcome, she cannot choose what is communicated. Moreover, Bob needs to know what basis Alice used if he is to access that result, so she cannot use that choice to communicate anything.

However, to be clear, there are other settings in which entanglement can be used to communicate information, such as superdense coding. This is where Alice manipulates her quantum system, and then physically sends her part of the quantum state to Bob (in the previous scenario, she kept hold of it the whole time). This gives you double the communication rate of a classical channel. Theoretically, the data can be transmitted at the speed of light (as can classical), giving you trivial latency.

This method can be perfectly secure (although it is not usually talked about in this context) in the sense that an eavesdropper cannot access the information that Alice encoded (because that can only be done if you can access both halves, but Bob never lets his half out of his possession). However, Eve would be able to scramble the message by manipulating Alice's qubit during transmission. Build in some authentication and it would probably be OK.

You cannot directly send information using only entanglement like DaftWullie excellently explained.

But here's what you can do

1. Superdense coding: a) pre-share 2 entangled qubits between you and a friend b) then by sending a single qubit you can send 2 classical bits
2. Teleportation: a) pre-share 2 entangled qubits between you and a friend b) when you want to send an arbitrary qubit you process it together with your entangled qubit then measure it and get two classical bits. c) send those classical bits to your friend and he will be able to recreate the arbitrary qubit you wanted to send. (You have to destroy the information in order ho send it that's why it's called teleportation)
3. Use quantum cryptographic protocols like Quantum key distribution to encode/decode messages sent over a classical channel.

Mathematically, if Alice measures her part of an entangled bipartite state (or does whatever she likes with her part), the local state of the Bob's part (described by density matrix) does not change. This means that no information is transferred from Alice to Bob by Alice manipulating her part of an entangled state, at all.