Properties of multi-partite dark states

TL;DR

This paper explores the properties and existence of dark and semi-dark states in multi-qudit systems, revealing their relationships, rarity, and potential use in constructing decoherence-free qudits.

Contribution

It defines dark and semi-dark states for multi-qudit systems, establishes their equivalence in two-level systems, and demonstrates their potential for creating decoherence-free qudits.

Findings

Semi-dark states are equivalent to singlet states of the rotation group.

Dark states are rare but exist in many multi-qudit systems.

Dark states can be used to construct decoherence-free qudits.

Abstract

We investigate and define dark and semi-dark states for multiple qudit systems. For two-level systems, semi-dark and dark states are equivalent. We show that the semi-dark states are equivalent to the singlet states of the rotation group. They exist for many multiple qudit systems, whereas dark states are quite rare. We then show that when a dark state is collapsed onto another dark state of fewer parties, the resulting state is again dark. Furthermore, one can use two orthogonal multi-qudit dark states to construct a decoherence-free qudit.