Abstract
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.
Highlights
We know that quantum computers can be much faster at certain tasks than classical Turing machines
It is clear that quantum superposition and quantum entanglement appear in quantum computations but how do they exactly contribute to quantum speed-up? we do not have a measure of how non-classical any given quantum computation is
We present a black box with internal classical dynamics supplemented with ’hidden’ nebits whose output mimics the output of the Grover search algorithm on quantum computer
Summary
We know that quantum computers can be much faster at certain tasks than classical Turing machines. Wigner was perhaps more successful, leaving behind a potent Wigner function formalism [11], which is extensively used in quantum optics and other branches of quantum physics Both Feynman and Wigner were extremely pragmatic in their approach to negative probabilities—as long as the final stage of calculations does not contain negative probabilities, everything is perfectly all right. Before we proceed with our arguments we would like to make another remark, following Wheeler who coined a phrase “great smokey dragon” as a poetic metaphor highlighting some counterintuitive aspects of quantum mechanics It is well accepted by most physicists (if they are forced to make such a philosophical declaration) that quantum theory is an input-output black box process. Mimicking quantum mechanics with classical stochastic dynamics supplemented with nebits might provide some intuitions or at least hints of how to translate it into purely quantum algorithms
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