The basic idea
The basic idea is the following: user A publishes some identifier (usually a public key), and user B combines his private key with the published key of A and creates a unique address from which only A can spend. User C can also send money to user A by combining his private key with an address of A and deriving another unique address. User A will know that both users B and C sent him money, but B and C won't know about each other. Therefore, that allows user A to receive payments on completely delinked addresses using only one public address.
I think this is a lovely idea but, one of the many things the blockchain technology is known for is the level of transparency that is about the network.
I think to some extent, it’s the role in which mixers operated, given that you lose traces to the source of Bitcoin deposits except for one who is really keen to observe the inputs and outputs.
This silent system, does it also applies to the balance that might be available on an address?
I see this as one key aspect to privacy that we aren’t getting on the network just yet. Having just anyone to see how much is available on an address isn’t a best way to security. Tie that address to a person like we have on the forum, even though to some we are anonymous, it means trouble. The mixers case came close to some of these uneasiness.
It would be a nice incorporation into the system but, one that would be exploited for sure.
(Or, you can keep it the way you like, that is okay too 
One large difference is that in Bitcoin, you can choose your own denomination. I've seen altcoins (BlackBytes) that have fixed denominations (like banknotes). In Bitcoin, unlike banknotes, your change is always one input.
