Will quantum computing provide any advantage for storing large amounts of data? Essentially, does superposition or entanglement provide any advantage for data storage as opposed to classical memory.
 A: No, there's no advantage in capacity.
Given N qubits, the maximum amount of retrievable information you can pack into them is N bits. This is Holevo's theorem.
There is some extra flexibility in how quantum data is stored. I'm sure cypherpunks will get a kick out of that, at least. But, realistically, the flexibility tends to be somewhat... esoteric (e.g. quantum locking).
A: Sort of.
It is almost impossible to compare the storage efficiency of different hardware on anything but the most crude metrics, like "how many bits can you store per square millimeter?", that provide absolutely no insight into anything physically interesting. So to do interesting theory here one needs the idea of qubits as being compared directly with bits.
In turn it is possible to phrase this in a question that also gives you no insight, like "how many bits would it take to represent the state space of $n$ qubits?" (Exponentially many.) 
But there is a very nice way to phrase a tightly related question which is, "someone has sent me $n$ qubits, how many classical bits could I possibly extract from this?" The answer, if you have absolutely no prior history with this person, is $n$ bits. In that sense there is nothing better you can do.
You can hear the waffling and you may be curious, "what if I have history with this other person, can I do better?" and the answer is, "yes." If you share a long-lived entangled state of $n$ bits with that other person, there is a technique called superdense coding which allows you to extract $2n$ bits from the combination of your pre-entangled bits and the $n$ bits in front of you.
However it is not too hard to see that this gives us no real advantage to storage as it still requires one qubit per bit total -- it's just that you can "store" $2n$ bits in a register of $n$ qubits if you happen to have $n$ qubits somewhere else in your quantum computer.
A: It can handle a number of information at once. This method of data processing might be advantage.
A: There's a few things being mixed here. Quantum computing is a form of computation/processing and it involves itself with transmitting, relaying, or decrypting information. The information should exist independently for a quantum computer to work with. Superpositions and entanglements allow one to perform tasks using data. Data storage would be unaffected by these quantum processes.
Edit: Elaboration
There are people working on quantum memory however. This involves using quantum mechanical processes to store and retrieve stored information, but this is still being worked on. From the aforementioned group:
"A quantum memory is an interface between light and matter that allows
for the storage and retrieval of photonic quantum information, analogous
to the memory in a normal computer"

Hope that clarifies things.
