Discrete phase space and minimum-uncertainty states

TL;DR

This paper explores the representation of multi-qubit quantum states using discrete phase space and introduces the concept of rotationally invariant states as minimum-uncertainty states within this framework.

Contribution

It establishes a formal connection between rotational invariance and minimum uncertainty in discrete phase space for qubit systems.

Findings

Rotationally invariant states are well-defined in discrete phase space.

Such states are characterized as minimum-uncertainty states.

The framework applies to any collection of qubits.

Abstract

The quantum state of a system of qubits can be represented by a Wigner function on a discrete phase space, each axis of the phase space taking values in a finite field. Within this framework, we show that one can make sense of the notion of a "rotationally invariant state" of any collection of qubits, and that any such state is, in a well defined sense, a state of minimum uncertainty.