  We establish a strong monogamy-of-entanglement property for subspace coset
states, which are uniform superpositions of vectors in a linear subspace of
$\mathbb{F}_2^n$ to which has been applied a quantum one-time pad. This
property was conjectured recently by [Coladangelo, Liu, Liu, and Zhandry,
Crypto'21] and shown to have applications to unclonable decryption and
copy-protection of pseudorandom functions. We present two proofs, one which
directly follows the method of the original paper and the other which uses an
observation from [Vidick and Zhang, Eurocrypt'20] to reduce the analysis to a
simpler monogamy game based on BB'84 states. Both proofs ultimately rely on the
same proof technique, introduced in [Tomamichel, Fehr, Kaniewski and Wehner,
New Journal of Physics '13].
