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If a person 'knew' the coin, they might be able to surmise its potential
faces.  But if a coin is tossed by another person, there is also the
possibility of a two-headed or two-tailed coin. ;-)

Capturing a quantum does not reduce either players' potentials, just
reduce the possible number of expressions of these potentials on the
playing field.  By capturing a neutral quantum, a player not only reduces
their opponent's possibles but also their own.

Question:  If there are two quantum on the field and the player has two 
potential Rooks, would they both then be considered defined?  Thus ending 
the cycle rather pre-maturely.

I continue to advocate that all the quantum must be actually moved for a 
new cycle to begin.  Whether this cycle is predicated on one or both 
players.  If determined by one player, this should only apply to those 
quantum which are under their control.  This would allow the opposing 
player the opportunity to express all their potentials.  But does not 
guarantee such.

Of course, a new cycle can be initiated by the following:

1. One player has expressed all their potentials on the field.  Those 
particular quantum are re-cycled, or all the quantum are re-cycled.  (The
latter case would be very punitive for the player who has not had the 
opportunity to express all their potentials.  I would advocate the effect 
for the player's pieces, giving the opponent opportunity to gain 
advantage. This does not reduce the player's potential on the field, 
expect in the possible number of expressions.)

2. All the quantum have been defined and all quantum are recycled. (This 
might mean that the players have additional potentials in hand.  This 
could also be initiated by the capture of a remaining quantum when both 
players still have potential in hand.)