Symmetric construction of reference-frame-free qudits

TL;DR

This paper presents a symmetric method to construct reference-frame-free qudits of dimension N-1 using coupled spin-1/2 particles, enabling quantum communication without shared reference frames.

Contribution

It introduces a novel symmetric scheme for encoding rotationally invariant qudits from physical qubits, allowing all states and measurements without aligned reference frames.

Findings

Constructed reference-frame-free qubits and qutrits explicitly

Demonstrated rotational invariance of the encoding

Discussed potential experimental implementations

Abstract

By exploiting a symmetric scheme for coupling $N$ spin-1/2 constituents (the physical qubits) to states with total angular momentum $N/2-1$, we construct rotationally invariant logical qudits of dimension $d=N-1$. One can encode all qudit states, and realize all qudit measurements, by this construction. The rotational invariance of all relevant objects enables one to transmit quantum information without having aligned reference frames between the parties that exchange the qudits. We illustrate the method by explicit constructions of reference-frame-free qubits and qutrits and, for the qubit case, comment on possible experimental implementations.