We introduce nebit, a classical bit with a signed probability distribution. We study its properties and basic transformations that can be applied to it. Then, we introduce a simple dynamical model – a classical random walk supplemented with nebits. We show that such a model exhibits some counterintuitive non-classical properties and that it can achieve or even exceed the speedup of Grover’s quantum search algorithm. The proposed classical dynamics never reveals negativity of nebits and thus we do not need any operational interpretation of negative probabilities. We argue that nebits can be useful as a measure of non-classicality as well as a tool to find new quantum algorithms.

我们引入nebit，这是一个带符号概率分布的经典位。我们研究了它的属性和可以应用的基本转换。然后，我们介绍了一个简单的动力学模型-经典的随机游走，并附加了进位。我们证明了这种模型表现出一些违反直觉的非经典性质，并且可以达到甚至超过格罗弗的量子搜索算法的速度。拟议中的经典动力学永远不会揭示负数的消极性，因此我们不需要对负概率进行任何操作性解释。我们认为，小数点可以作为衡量非经典性的手段，也可以作为寻找新的量子算法的工具。