Various types of probabilistic proof systems have played
a central role in the development of computer science in the last decade.
In this exposition, we concentrate on three such proof systems ---
interactive proofs, zero-knowledge proofs,
and probabilistic checkable proofs --- stressing the essential
role of randomness in each ... more >>>

Khot formulated in 2002 the "Unique Games Conjectures" stating that, for any epsilon > 0, given a system of constraints of a certain form, and the promise that there is an assignment that satisfies a 1-epsilon fraction of constraints, it is intractable to find a solution that satisfies even an ... more >>>

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 >>>