  By leveraging the no-cloning principle of quantum mechanics, unclonable
cryptography enables us to achieve novel cryptographic protocols that are
otherwise impossible classically. Two most notable examples of unclonable
cryptography are copy-protection (CP) and unclonable encryption (UE). Most
known constructions rely on the QROM (as opposed to the plain model). Despite
receiving a lot of attention in recent years, two important open questions
still remain: CP for point functions in the plain model, which is usually
considered as feasibility demonstration, and UE with unclonable
indistinguishability security in the plain model. A core ingredient of these
protocols is the so-called monogamy-of-entanglement (MoE) property. Such games
allow quantifying the correlations between the outcomes of multiple
non-communicating parties sharing entanglement in a particular context.
Specifically, we define the games between a challenger and three players in
which the first player is asked to split and share a quantum state between the
two others, who are then simultaneously asked a question and need to output the
correct answer.
  In this work, by relying on previous works [CLLZ21, CV22], we establish a new
MoE property for subspace coset states, which allows us to progress towards the
aforementioned goals.
  However, it is not sufficient on its own, and we present two conjectures that
would allow first to show that CP of point functions exists in the plain model,
with different challenge distributions, and then that UE with unclonable
indistinguishability security exists in the plain model.
  We believe that our new MoE to be of independent interest, and it could be
useful in other applications as well. To highlight this last point, we leverage
our new MoE property to show the existence of a tokenized signature scheme with
a new security definition, called unclonable unforgeability.
