@Luca @Peter Rabbitson
In 
Fil-PoA: Filecoin Proof of Access we described a way of implementing provable Access for Filecoin data in a way which is entangled with consensus.
We want here to clarify the relation of PoA with FIL+, as well as answering some questions on PoA itself.
What is PoA actually proving?
SP submitting a valid PoA on a sector proves that he have timely access to the clear client data associated with a particular sector. This means that efficient retrieval is provably possible.
Is PoA giving retrievability guarantee?
No.
Efficient retrievability is provably enabled by PoA but not guranateed. SP can always refuse to send data back to the client even if she proved that she has efficient access to it.
What does PoA add to the status quo?
Currently Filecoin does not give any indication of the storage strategy employed by an SP ( replica only, or clear-data / unsealed copy ). This also means that there is no way to ascertain whether efficient retrieval is possible. PoA provides a sound over-time indicator that SP has access to clear data, making efficient retrieval possible.
Does PoA prove that SP submitting PoA is storing an extra copy of the data encoded into the sector?
No.
PoA provides a guarantee that the SP has access to a clear-copy of the data. This does not mean that each SP submitting a PoA is storing a distinct copy of the data. Data in the clear can be shared among different SPs. Nevertheless, having a unique shared copy of the data among different SPs presents them with a well-defined risk: losing that unique copy would translate in failing all proofs for all participants from that moment onwards (up until a copy in the clear is obtained by some mechanism). PoA entangled with consensus implicitly encourages storing multiple copies of the file.
Does PoA mitigates current FIL+ limitations?
No.
We know that an SP pretending to be a client can open the door to FIL+ abuses, due to datacap misuse. PoA is only adding the proof of access the clear-copy of the file, but it is not preventing any of the current FIL+ potential abuses, enabled by the unsolved Sybil-problem.
Should SPs providing PoA be rewarded with QAP multipliers?
At the current stage, we are have designed any incentives, even if it is of course possible to introduce such a mechanism.
PoA sectors could be an alternative to FIL+ (inheriting the same limitations), by being a simpler system with a larger portion of its mechanisms being provable on-chain.