Definition 1 Sample Clauses

Definition 1. Given a (hash) function H, we play the following game. An adversary A generates a quantum state |φ) = x X αx |x) such that H(x) = c for all x ∈ X for some c. Then, one of the following happens: 1. The state |φ) gets measured in the computational basis. 2. The state |φ) is left untouched. The adversary does not know which one happened, but it tries to determine it. It returns a bit b, indicating which case it thinks has happened. Its advantage is given by . . cAdv[H](A) = P[b = 1 : Case (1)] − P[b = 1 : Case (2)] . 3.1. This allows us to give a definition of collapseability that maximizes over adversaries. Then we look at the composability of collapseability in Sect. 3.2. These lemmas allow us to reason classically about the collapsing advantage. Finally, in Sect. 3.3 we explain why collapseability is a stronger notion than collision resistance.

Definition 1. (Action). An action is a tuple consisting of three elements p, an, d , where p is the principal, an is an action name, and d is the data.

Definition 1. 3.1. A unital C∗-algebra is called a C∗-algebra of real rank zero if any its self-adjoint element can be approximated by elements with finite spectra.

Definition 1. Suppose we are given an optimization problem defined by a cost function R(c, X) R, where c is a solution from the finite solution space and X is a random data instance. Then the Xxxxx posterior distribution pβ(c|X) is defined as Σ| − − p (c X) = 1 exp( βR(c, X)) with Z(β, X) = exp( βR(cj, X)) . β Z(β, X) ct∈C