A little bit of classical magic to achieve quantum speedup

TL;DR

This paper introduces nebits, a classical bit with signed probabilities, demonstrating that classical stochastic processes augmented with nebits can match or surpass quantum search speedups without requiring negative probability interpretations.

Contribution

The paper presents nebits, a novel classical construct with signed probabilities, showing they can achieve quantum-like speedups and serve as a measure of non-classicality.

Findings

Classical dynamics with nebits can match quantum search speedup.

Nebits do not require operational interpretation of negativity.

Nebits can help discover new quantum algorithms.

Abstract

We introduce nebit, a classical bit with a signed probability distribution. We quantify its entropy using Szekely theorem on signed probability measures and show that classical stochastic dynamics supplemented with nebits 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.