Quantum entanglement is essential to the development of quantum computation, communications, and technology. The controlled SWAP test, widely used for state comparison, can be adapted to an efficient and useful test for entanglement of a pure state. Here we show that the test can evidence the presence of entanglement (and further, genuine n-qubit entanglement), can distinguish entanglement classes, and that the concurrence of a two-qubit state is related to the test’s output probabilities. We also propose a multipartite measure of entanglement that acts similarly for n-qubit states. The average number of copies of the test state required to detect entanglement decreases for larger systems, to four on average for many (n ≳ 8) qubits for maximally entangled states. For non-maximally entangled states, the number of copies required to detect entanglement increases with decreasing entanglement. Furthermore, the results are robust to second order when typical small errors are introduced to the state under investigation.

量子纠缠对于量子计算、通信和技术的发展至关重要。受控 SWAP 测试广泛用于状态比较，可以适用于纯状态纠缠的有效和有用的测试。在这里，我们表明该测试可以证明纠缠的存在（以及真正的n-量子位纠缠），可以区分纠缠类别，并且两个量子位状态的并发性与测试的输出概率有关。我们还提出了一种多部分纠缠度量，它对n- qubit 状态的作用类似。对于较大的系统，检测纠缠所需的测试状态的平均副本数会减少，对于许多 ( n≳ 8) 最大纠缠态的量子位。对于非最大纠缠状态，检测纠缠所需的副本数随着纠缠的减少而增加。此外，当典型的小错误被引入被调查的状态时，结果对于二阶是稳健的。