Estimation of unknown qubit elementary gates and alignment of reference frames are formally the same problem. Using quantum states made out of $N$ qubits, we show that the theoretical precision limit for both problems, which behaves as $1/N^{2}$, can be asymptotically attained with a covariant protocol that exploits the quantum correlation of internal degrees of freedom instead of the more fragile entanglement between distant parties. This cuts by half the number of qubits needed to achieve the precision of the dense covariant coding protocol.
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机译：未知量子位基本门的估计和参考帧的对齐在形式上是相同的问题。使用由$ N $个量子位组成的量子状态，我们证明这两个问题的理论精度极限（表现为$ 1 / N ^ {2} $）可以通过利用内部度的量子相关性的协变协议渐近地获得自由，而不是遥远的政党之间更加脆弱的纠缠。这将实现密集协变编码协议的精度所需的量子位数量减少了一半。
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