  Zero knowledge plays a central role in cryptography and complexity. The
seminal work of Ben-Or et al. (STOC 1988) shows that zero knowledge can be
achieved unconditionally for any language in NEXP, as long as one is willing to
make a suitable physical assumption: if the provers are spatially isolated,
then they can be assumed to be playing independent strategies. Quantum
mechanics, however, tells us that this assumption is unrealistic, because
spatially-isolated provers could share a quantum entangled state and realize a
non-local correlated strategy. The MIP* model captures this setting. In this
work we study the following question: does spatial isolation still suffice to
unconditionally achieve zero knowledge even in the presence of quantum
entanglement? We answer this question in the affirmative: we prove that every
language in NEXP has a 2-prover zero knowledge interactive proof that is sound
against entangled provers; that is, NEXP \subseteq ZK-MIP*. Our proof consists
of constructing a zero knowledge interactive PCP with a strong algebraic
structure, and then lifting it to the MIP* model. This lifting relies on a new
framework that builds on recent advances in low-degree testing against
entangled strategies, and clearly separates classical and quantum tools. Our
main technical contribution consists of developing new algebraic techniques for
obtaining unconditional zero knowledge; this includes a zero knowledge variant
of the celebrated sumcheck protocol, a key building block in many probabilistic
proof systems. A core component of our sumcheck protocol is a new algebraic
commitment scheme, whose analysis relies on algebraic complexity theory.
