  Non-malleable codes are fundamental objects at the intersection of
cryptography and coding theory. These codes provide security guarantees even in
settings where error correction and detection are impossible, and have found
applications to several other cryptographic tasks. One of the strongest and
most well-studied adversarial tampering models is $2$-split-state tampering.
Here, a codeword is split into two parts and the adversary can then
independently tamper with each part using arbitrary functions. This model can
be naturally extended to the secret sharing setting with several parties by
having the adversary independently tamper with each share. Previous works on
non-malleable coding and secret sharing in the split-state tampering model only
considered the encoding of \emph{classical} messages. Furthermore, until recent
work by Aggarwal, Boddu, and Jain (IEEE Trans.\ Inf.\ Theory 2024), adversaries
with quantum capabilities and \emph{shared entanglement} had not been
considered, and it is a priori not clear whether previous schemes remain secure
in this model.
  In this work, we introduce the notions of split-state non-malleable codes and
secret sharing schemes for quantum messages secure against quantum adversaries
with shared entanglement. Then, we present explicit constructions of such
schemes that achieve low-error non-malleability. More precisely, we construct
efficiently encodable and decodable split-state non-malleable codes and secret
sharing schemes for quantum messages preserving entanglement with external
systems and achieving security against quantum adversaries having shared
entanglement with codeword length $n$, any message length at most
$n^{\Omega(1)}$, and error $\epsilon=2^{-{n^{\Omega(1)}}}$. In the easier
setting of \emph{average-case} non-malleability, we achieve efficient
non-malleable coding with rate close to $1/11$.
