We show how to encode $2^n$ (classical) bits $a_1,...,a_{2^n}$
by a single quantum state $|\Psi \rangle$ of size $O(n)$ qubits,
such that:
for any constant $k$ and any $i_1,...,i_k \in \{1,...,2^n\}$,
the values of the bits $a_{i_1},...,a_{i_k}$ can be retrieved
from $|\Psi \rangle$ by a one-round Arthur-Merlin interactive ... more >>>

We prove a strong limitation on the ability of entangled provers to collude in a multiplayer game. Our main result is the first nontrivial lower bound on the class MIP* of languages having multi-prover interactive proofs with entangled provers; namely MIP* contains NEXP, the class of languages decidable in non-deterministic ... more >>>

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, ... more >>>

We introduce two models of space-bounded quantum interactive proof systems, $\mathbf{QIPL}$ and $\mathbf{QIP_\mathrm{U}L}$. The $\mathbf{QIP_\mathrm{U}L}$ model, a space-bounded variant of quantum interactive proofs ($\mathbf{QIP}$) introduced by Watrous (CC 2003) and Kitaev and Watrous (STOC 2000), restricts verifier actions to unitary circuits. In contrast, $\mathbf{QIPL}$ allows logarithmically many intermediate measurements per ... more >>>