Spin- s $s$ Dicke States and Their Preparation

IF 4.4 Q1 OPTICS Advanced quantum technologies Pub Date : 2024-09-09 DOI:10.1002/qute.202400057

Rafael I. Nepomechie, Francesco Ravanini, David Raveh

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Abstract

The notion of $s u (2)$ spin- $s$ Dicke states is introduced, which are higher-spin generalizations of usual (spin-1/2) Dicke states. These multi-qudit states can be expressed as superpositions of $s u (2 s + 1)$ qudit Dicke states. They satisfy a recursion formula, which is used to formulate an efficient quantum circuit for their preparation, whose size scales as $s k (2 s n - k)$ , 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.