One of the fundamental results in quantum foundations is the Kochen-Specker no-go theorem. For the quantum theory, the no-go theorem excludes the possibility of a class of hidden variable models where value attribution is context independent. Recently, the notion of contextuality has been generalized for different operational procedures and it has been shown that preparation contextuality of mixed quantum states can be a useful resource in an information-processing task called parityoblivious multiplexing. Here, we introduce a new class of information processing tasks, namely d-level parity oblivious random access codes and obtain bounds on the success probabilities of performing such tasks in any preparation noncontextual theory. These bounds constitute noncontextuality inequalities for any value of d. For d = 3, using a set of mutually asymmetric biased bases we show that the corresponding noncontextual bound is violated by quantum theory. We also show quantum violation of the inequalities for some other higher values of d. This reveals operational usefulness of preparation contextuality of higher level quantum systems.
Abstract. Unresolved indirect branch instructions are a major obstacle for statically reconstructing a control flow graph (CFG) from machine code. If static analysis cannot compute a precise set of possible targets for a branch, the necessary conservative over-approximation introduces a large amount of spurious edges, leading to even more imprecision and a degenerate CFG. In this paper, we propose to leverage under-approximation to handle this problem. We provide an abstract interpretation framework for control flow reconstruction that alternates between over-and under-approximation. Effectively, the framework imposes additional preconditions on the program on demand, allowing to avoid conservative over-approximation of indirect branches. We give an example instantiation of our framework using dynamically observed execution traces and constant propagation. We report preliminary experimental results confirming that our alternating analysis yields CFGs closer to the concrete CFG than pure over-or under-approximation.
Non-local games are widely studied as a model to investigate the properties of quantum mechanics as opposed to classical mechanics. In this paper, we consider a subset of non-local games: symmetric XOR games of n players with 0-1 valued questions. For this class of games, each player receives an input bit and responds with an output bit without communicating to the other players. The winning condition only depends on XOR of output bits and is constant w.r.t. permutation of players. We prove that for almost any n-player symmetric XOR game the entangled value of the game is Θ √ ln n n 1/4 adapting an old result by Salem and Zygmund on the asymptotics of random trigonometric polynomials. Consequently, we show that the classical-quantum gap is Θ( √ ln n) for almost any symmetric XOR game.
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