Is entropy a meaningful concept on a quantum level? My naive assumptions, as I really am at a pretty basic stage in QM,  are as follows:
Classically, entropy gives us a practical measure of the direction of time, as opposed to our physical laws which, as far as I know, are time independent.
On a quantum level, time seems to be, again at my basic level of QM, to be treated as something with much less "importance" attached to it, say for example Feynman diagrams, where a positron can be treated as an electron moving backwards in time.
I do believe I am far from fully correct here though, and this is a very general assumption, based on my own ignorance of the subject.
I ask this question to find out if my assumption is correct. EDIT. It's not.
I realise, as usual in my physics knowledge, there are far more subtle aspects to the role of entropy that I know about currently. I can follow these for classical systems in any good thermodynamics text, but it is the microworld use of entropy concepts that I would like to know more about.
This question is now answered, as I made a completely wrong assumption and based the question upon that. 
 A: I am not sure this is the answer you are looking for but you may have heard, in QM especially, that an excited system eventually goes back to its ground state. This is true of subatomic particles like neutrons decaying into proton + extra stuff and of atoms too which, once in an excited electronic state, eventually release this extra energy as a photon. The reason "why" this is so does not lie in QM but in the second principle of thermodynamics: the entropy of the universe essentially always increases when a decay process $A^* \rightarrow A + B + C..$ of any sort occurs "alone" in the universe. Depending on your current level in QM, you may have seen already that such processes, where the products and reactants are assumed alone in the universe and the process irreversible, are described by the Golden Fermi Rule which relies on the assumption of infinitely many more ways of getting the reaction in one way than in the other.
A: Entropy is from statistical physics, a single particle or a single degree of freedom does not have an entropy.
Edit: There are a lot of different things that are called entropy. So I'm not sure I feel comfortable with the above as a blanket statement. And there is a way to see time from the dynamics of quantum mechanical systems, so if the above statement makes you think otherwise, then I should retract it. The below is still some good perspective.
Since you said there could be subtle issues you aren't even aware of I do want to make sure you see the broadest strokes and biggest picture so the size of what you miss isn't too huge.
And statistical physics has two main fields: classical statistical mechanics and quantum statistical mechanics. And they are pretty different fields so don't ignore one because you think the other one will cover it or mostly cover it. And the difference isn't a small tweak.
That said, I'm not even sure if that is what you are asking about.
So there is a field (and maybe the name hasn't fully stuck yet) however it goes by the name nanothermodynamics and it deals with smaller sized systems than is normally considered.
Which is nice. So many times in regular statistical mechanics they go straight to focusing on extensive and intensive properties. Nanothermodynamics is more focused on doing what you need to to correctly model small sized feature of smaller collections.
And I don't think you were asking about nonequilibrium statistical mechanics but if you want to see short range effects those can happen in short times so maybe you do want to check that out.
So those are the kinds of things that are out there that could help you see where entropy is used in physics and in particularly when quantum effects are involved.
Edit
As for time and quantum mechanics. Indeed the fundamental equations are time symmetric, at least if you don't worry about it being a mirror image of an antiparticle.
But the sense of time that subsystems of many particles notice is based on an insensitivity to which of many systems of which they could be a part. So it is about how the state of a subsystem can be interpreted as correlated to many different larger states. So it is about that relation.
If you've ever heard of a Boltzmann brain it is entirely possible that your personal subjective idea of the entropy of the universe or even your surroundings is massively and terribly wrong. But when you think your state is actually connected to the state of the wider world in a particular way, then you also realize you still don't know everything about this wider world and thus there are many possibilities. This is generally where entropy comes in.
And it doesn't answer anything about a flow of time per se because it is an opinion. An opinion that a Boltzmann brain could have and be very wrong about. To address time you could enlarge that opinion about the state to an opinion about how the state evolves. And then you can see how your ignorance can grow. And yes you can learn more about one thing, at the expense of now being less certain about other (new) things. But this is still tied to your assumption that the laws are right, so the Boltzmann brain could be wrong about that too.
It is a relational thing. It is not that each thing carries around some entropy and the entropy of the universe is the sum of all the entropy of all the parts.
