  Unclonable cryptography is concerned with leveraging the no-cloning principle
to build cryptographic primitives that are otherwise impossible to achieve
classically. Understanding the feasibility of unclonable encryption, one of the
key unclonable primitives, satisfying indistinguishability security in the
plain model has been a major open question in the area. So far, the existing
constructions of unclonable encryption are either in the quantum random oracle
model or are based on new conjectures.
  We present a new approach to unclonable encryption via a reduction to a novel
question about nonlocal quantum state discrimination: how well can
non-communicating -- but entangled -- players distinguish between different
distributions over quantum states? We call this task simultaneous state
indistinguishability. Our main technical result is showing that the players
cannot distinguish between each player receiving independently-chosen Haar
random states versus all players receiving the same Haar random state.
  We leverage this result to present the first construction of unclonable
encryption satisfying indistinguishability security, with quantum decryption
keys, in the plain model. We also show other implications to single-decryptor
encryption and leakage-resilient secret sharing.
