$q$-analog qudit Dicke states

• URL: http://arxiv.org/abs/2308.08392v2
• Date: Mon, 22 Jan 2024 13:24:23 GMT
• Title: $q$-analog qudit Dicke states
• Authors: David Raveh and Rafael I. Nepomechie
• Abstract summary: We show that $q$-deformed qudit Dicke states can be compactly expressed as a weighted sum over permutations. We also discuss the preparation of these states on a quantum computer, and show that introducing a $q$-dependence does not change the circuit gate count.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Dicke states are completely symmetric states of multiple qubits (2-level systems), and qudit Dicke states are their $d$-level generalization. We define here $q$-deformed qudit Dicke states using the quantum algebra $su_q(d)$. We show that these states can be compactly expressed as a weighted sum over permutations with $q$-factors involving the so-called inversion number, an important permutation statistic in Combinatorics. We use this result to compute the bipartite entanglement entropy of these states. We also discuss the preparation of these states on a quantum computer, and show that introducing a $q$-dependence does not change the circuit gate count.

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