I think the diamond must belong to the Queen for a couple of reasons - mainly Prince William's salary is that of an RAF officer, which is about £40,000 a year; his office costs are paid for by the Prince of Wales' office, so it would be difficult to justify buying new stones, esp in this economic era. Also, the Queen most probably has literally hundreds of gems etc given to her by various Commonwealth and other nations, so it would be appropriate to use them rather than let them linger in the dark.