The complexity of a quantum system and the accuracy of its description

TL;DR

This paper explores a fundamental relation linking quantum system complexity with the accuracy of its description, introducing a new measure based on the maximum number of qubits describable, with implications for understanding quantum dynamics and measurement.

Contribution

It establishes a novel relation similar to uncertainty principles that connects quantum state complexity with description accuracy, and proposes an experimental method to determine this relation using Grover search.

Findings

Relation between quantum complexity and description accuracy derived

Maximum number of qubits describable experimentally determined

Implications for quantum measurement and decoherence discussed

Abstract

The complexity of the quantum state of a multiparticle system and the maximum possible accuracy of its quantum description are connected by a relation similar to the coordinate-momentum uncertainty relation. The coefficient in this relation is equal to the maximum number of qubits whose dynamics can be adequately described by quantum theory, and therefore it can be determined experimentally through Grover search algorithm. Such a restriction of the Copenhagen formalism is relevant for complex systems; it gives a natural description of unitary dynamics together with decoherence and measurement, but also implies the existence of a minimum non-zero amplitude size, as well as a restriction on the equality of bases in the state space. The quantization of the amplitude allows us to formally introduce a certain kind of determinism into quantum evolution, which is important for complex systems.