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.

中文翻译：

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排列操作下的不对称激活及其与相干性的关系


Dicke 状态及其退相干状态对于排列是不变的。但是，当每个量子比特状态都附加了另一个量子比特状态时，整个状态对于排列来说并不是不变的，并且对于排列具有一定的不对称性。不对称的量可以通过群作用或互信息下可区分状态的数量来衡量。通常，整个状态的不对称量大于添加状态的不对称量。也就是说，不对称激活发生在这种情况下。本文研究了 Dicke 状态下的不对称激活量。为了渐近地解决不对称激活问题，我们通过使用超几何函数的几个公式引入了一种新型的中心极限定理。我们揭示了 Dicke 状态下的不对称量和不对称激活量比特定类型的极限中具有退相干态的不对称激活具有严格更大的阶数。