Spin-s Dicke states and their preparation

Abstract

We introduce the notion of $su(2)$ spin-$s$ Dicke states, which are higher-spin generalizations of usual (spin-1/2) Dicke states. These multi-qudit states can be expressed as superpositions of $su(2s+1)$ qudit Dicke states. They satisfy a recursion formula, which we use to formulate an efficient quantum circuit for their preparation, whose size scales as $sk(2sn-k)$, where $n$ is the number of qudits and $k$ is the number of times the total spin-lowering operator is applied to the highest-weight state. The algorithm is deterministic and does not require ancillary qudits.

23 pages + supplementary material (cirq code), v2: added references and important new formulas (1.7) and (A.13), version accepted in Advanced Quantum Technologies

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Cited by in corpus (7)

• Deterministic Bethe state preparation
• Efficient preparation of Dicke states
• Dicke states as matrix product states
• Symmetric quantum states: a review of recent progress
• Multipartite Entanglement and Quantum Sensing in a Spin-5/2 Heisenberg Molecular Iron(III) Triangle
• Simple ways of preparing qudit Dicke states
• Spin-$s$ $U(1)$-eigenstate preparation