Asymmetry activation and its relation to coherence under permutation operation

TL;DR

This paper studies how attaching additional qubits to Dicke states induces asymmetry under permutation, revealing that asymmetry activation occurs and can be analyzed using a new central limit theorem involving hypergeometric functions.

Contribution

It introduces a novel analysis of asymmetry activation in Dicke states using a new central limit theorem with hypergeometric functions.

Findings

Asymmetry activation is larger for Dicke states than for decohered states.

The asymmetry and activation scale with a larger order in the limit.

A new central limit theorem is developed for asymptotic analysis.

Abstract

A Dicke state and its decohered state are invariant for permutation. However, when another qubits state to each of them is attached, the whole state is not invariant for permutation, and has a certain asymmetry for permutation. The amount of asymmetry can be measured by the number of distinguishable states under the group action or the mutual information. Generally, the amount of asymmetry of the whole state is larger than the amount of asymmetry of the added state. That is, the asymmetry activation happens in this case. This paper investigates the amount of the asymmetry activation under Dicke states. To address the asymmetry activation asymptotically, we introduce a new type of central limit theorem by using several formulas on hypergeometric functions. We reveal that the amounts of the asymmetry and the asymmetry activation with a Dicke state have a strictly larger order than those with the decohered state in a specific type of the limit.