Kolokotronis wrote (citing a Greek Orthodox theological source): "Our prayers, which are offered for the departed, are expressions of love, devotion and a continuous association with them. Through these prayers, we beseech merciful God to forgive our departed brothers so that on Judgment Day their state may improve."
I observe that it is in that last sentence "We beseech merciful God to forgive our departed brothers so that on Judgment Day their state may improve" that lies the concept fleshed out in the West as Purgatory and Indulgences.
There are two ways to go with this: (1) to leave it as a mystery and not try to flesh it further out, and focus on the Sacraments in the here and now, or (2) to try to flesh out our understanding more fully.
I think that (1) is the more prudent option for a lot of reasons, not the least of which is that it avoids bruises and abrasions from each other on a subject whose full structures and ramifications are not revealed to us with great clarity. If we are striving for Christian unity, then we need to avoid creating controversies by asserting that a particular interpretation of what is really a mystery is Right (and by extension, every other interpretation is Wrong). We've said before that the primary difference between East and West is not the Sacraments, and is barely theological, but is primarily ecclesiological, and specifically the question of authority.
If communal Sacraments are desireable as Jesus' prayed-for unity, then we need to studiously and diplomatically avoid creating arguments that will invariably result in appeals to the ecclesial authorities that divided us in the first place. The Greek Orthodox believe that prayers for the dead change the status us of the dead. That is what that last sentence cited above means. But to what degree? How? We don't know, and can't know, but we can certainly fight with each other and sow division trying to assert more than we know on an ancillary subject. Instead, a redirect is in order: stay close to the Church, recieve the Sacraments, confess your sins and be reconciled to God. These are the things we share and that can keep us united. Determining exactly how many angels can dance on the head of a pin can only divide us, and can only lead, in about one and a half quick steps, to frank appeals to ecclesial authority...and division, while the Devil snickers.