Quantum Randomness and Nondeterminism

TL;DR

This paper explores the concept of quantum randomness and nondeterminism, examining their theoretical implications and introducing new complexity measures for quantum states and decision problems.

Contribution

It introduces the notion of total quantum nondeterminism, potentially extending classical nondeterminism to quantum decision problems.

Findings

Quantum randomness does not increase computational power.

Different definitions of quantum state complexity are proposed.

Total quantum nondeterminism is introduced as a new concept.

Abstract

Does the notion of a quantum randomized or nondeterministic algorithm make sense, and if so, does quantum randomness or nondeterminism add power? Although reasonable quantum random sources do not add computational power, the discussion of quantum randomness naturally leads to several definitions of the complexity of quantum states. Unlike classical string complexity, both deterministic and nondeterministic quantum state complexities are interesting. A notion of \emph{total quantum nondeterminism} is introduced for decision problems. This notion may be a proper extension of classical nondeterminism.