Qudit Dicke state preparation

TL;DR

This paper presents a method to deterministically prepare qudit Dicke states, extending the concept of Dicke states to higher dimensions, with explicit circuit decompositions implemented in cirq for qubits and qutrits.

Contribution

It introduces a circuit for deterministic preparation of arbitrary qudit Dicke states and provides explicit gate decompositions for implementation.

Findings

Circuit for qudit Dicke state preparation formulated.

Explicit gate decompositions provided for qubits and qutrits.

Implementation demonstrated in cirq.

Abstract

Qudit Dicke states are higher-dimensional analogues of an important class of highly-entangled completely symmetric quantum states known as (qubit) Dicke states. A circuit for preparing arbitrary qudit Dicke states deterministically is formulated. An explicit decomposition of the circuit in terms of elementary gates is presented, and is implemented in cirq for the qubit and qutrit cases.