The 46 carat Hope Diamond on which the fictional Heart of the Ocean is based, is estimated at $200 - $300 million today.
The white gold and zirconia prop used in the movie cost around $8,000 but if it were real at 56 carats, it would be valued at more than twice what the Hope Diamond is. Leave it up to Hollywood to invent fictional jewelry and then assign a value it.
Although, since the diving vessel is directly on top of where the heavy metal necklace would conceivably fall, it might not take too long to locate it on the sea floor:
The original search area for the Titanic was about 150 square miles, and the Titanic is only about 90 feet wide. So, for every Titanic width-sized object, you would need to search about 1.32 million positions.
If the search area for the necklace were 1/4 square mile to allow for drift, and the necklace is effectively 4 inches wide, you would only need to search about 435,000 necklace-width positions. Although, being directly over the Titanic wreck could hamper metal detecting. It would be pretty ironic if the necklace fell back on to the deck of the wreck.
So, suck on that ya old entitled bitch!