Better Non-Local Games from Hidden Matching

Separation between Classical and Quantum Winning Strategies for the Matching Game

Communication complexity is an area of classical computer science which studies how much communication is necessary to solve various distributed computational problems. Quantum information processing can be used to reduce the amount of communication required to carry out some distributed problems. We speak of pseudo-telepathy when it is able to completely eliminate the need for communication. The matching game is the newest member of the family of pseudo-telepathy games. After introducing a general model for pseudo-telepathy games, we focus on the question what the smallest size of inputs is f…

Quantum Matching Pennies Game

A quantum version of the Matching Pennies (MP) game is proposed that is played using an Einstein-Podolsky-Rosen-Bohm (EPR-Bohm) setting. We construct the quantum game without using the state vectors, while considering only the quantum mechanical joint probabilities relevant to the EPR-Bohm setting. We embed the classical game within the quantum game such that the classical MP game results when the quantum mechanical joint probabilities become factorizable. We report new Nash equilibria in the quantum MP game that emerge when the quantum mechanical joint probabilities maximally violate the Clau…

Indeterministic Quantum Gravity and Cosmology X. Probability-Theoretic Aspect: A Hidden Selector for Quantum Jumps, or How the Universe Plays the Game of Chance

This paper is a sequel to the series of papers [gr-qc/9409010, gr-qc/9505034, gr-qc/9603022, gr-qc/9609035, gr-qc/9609046, gr-qc/9704033, gr-qc/9704038, gr-qc/9708014, gr-qc/9802016]. The problem of the meaning of objective a priori probability for individual random trials without repetition is considered. A sequence of such trials, namely quantum jumps, is realized in indeterministic dynamics of the universe. A hidden selector for the quantum jumps is constructed.

量子完美匹配

Quantum Perfect Matchings

本文通过非局域博弈定义并研究量子与非信号完美匹配，给出非信号匹配的完全组合表征，证明奇数 n≥7 的完全图具有量子完美匹配，并建立完美匹配与线图量子独立数的等价关系，同时证明超图中量子完美匹配判定不可判定。

The one-way communication complexity of the Boolean Hidden Matching Problem

We give a tight lower bound of Omega(\sqrt{n}) for the randomized one-way communication complexity of the Boolean Hidden Matching Problem [BJK04]. Since there is a quantum one-way communication complexity protocol of O(\log n) qubits for this problem, we obtain an exponential separation of quantum and classical one-way communication complexity for partial functions. A similar result was independently obtained by Gavinsky, Kempe, de Wolf [GKdW06]. Our lower bound is obtained by Fourier analysis, using the Fourier coefficients inequality of Kahn Kalai and Linial [KKL88].

Two theorems of Jhon Bell and Communication Complexity

John Bell taught us that quantum mechanics can not be reproduced by non-contextual and local Hidden variable theory. The impossibility of replacing quantum mechanics by non-contextual Hidden Variable Theory can be turned to a impossible coloring pseudo-telepathy game to be played by two distant players. The game can not be won without communication in the classical world. But if the players share entangled state (quantum correlation) the game can be won deterministically using no communication. This again shows that though quantum correlation can not be used for communication, two parties can …