  Tamper-detection codes (TDCs) and non-malleable codes (NMCs) are now
fundamental objects at the intersection of cryptography and coding theory. Both
of these primitives represent natural relaxations of error-correcting codes and
offer related security guarantees in adversarial settings where error
correction is impossible. While in a TDC, the decoder is tasked with either
recovering the original message or rejecting it, in an NMC, the decoder is
additionally allowed to output a completely unrelated message.
  In this work, we study quantum analogs of one of the most well-studied
adversarial tampering models: the so-called split-state tampering model. In the
$t$-split-state model, the codeword (or code-state) is divided into $t$ shares,
and each share is tampered with "locally". Previous research has primarily
focused on settings where the adversaries' local quantum operations are
assisted by an unbounded amount of pre-shared entanglement, while the code
remains unentangled, either classical or separable.
  We construct quantum TDCs and NMCs in several $\textit{resource-restricted}$
analogs of the split-state model, which are provably impossible using just
classical codes. In particular, against split-state adversaries restricted to
local (unentangled) operations, local operations and classical communication,
as well as a "bounded storage model" where they are limited to a finite amount
of pre-shared entanglement. We complement our code constructions in two
directions. First, we present applications to designing secret sharing schemes,
which inherit similar non-malleable and tamper-detection guarantees. Second, we
discuss connections between our codes and quantum encryption schemes, which we
leverage to prove singleton-type bounds on the capacity of certain families of
quantum NMCs in the split-state model.

Quantum Physics