$q$-analog qudit Dicke states

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 $s{u}_q(d)$. 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.

arXiv comment19 pages + supplementary material; v2: minor changes, version accepted by J Phys A as part of the special issue "Fields, Gravity, Strings and Beyond: In Memory of Stanley Deser"

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Cited by in corpus (9)

• Deterministic Bethe state preparation
• Efficient preparation of Dicke states
• Spin-s Dicke states and their preparation
• Dicke states as matrix product states
• Symmetric quantum states: a review of recent progress
• Deformations of the symmetric subspace of qubit chains
• Quantum group deformation of the Kittel--Shore model
• A $q$-version of the relation between the hypercube, the Krawtchouk chain and Dicke states
• Preface to Fields, Gravity, Strings and Beyond: In Memory of Stanley Deser