查看“︁通粹纠缠度 (量子计算)”︁的源代码

在[[量子信息科学]]中，通粹纠缠度<ref>{{cite web|title=量子网络与纠缠传输|url=https://www.scholarset.com/post/detail?fid=2173|access-date=2023-10-26|archive-date=2023-10-26|archive-url=https://web.archive.org/web/20231026061759/https://www.scholarset.com/post/detail?fid=2173|dead-url=no}}</ref>是一种涉及[[量子位元|量子比特]]的状态不变量，用来度量纠缠度。<ref name="Hill1997">Scott Hill and William K. Wootters, [https://arxiv.org/abs/quant-ph/9703041 Entanglement of a Pair of Quantum Bits] {{Wayback|url=https://arxiv.org/abs/quant-ph/9703041 |date=20240227035804 }}, 1997.</ref><ref name="Wootters1998">William K. Wootters, [https://dx.doi.org/10.1103/PhysRevLett.80.2245 Entanglement of Formation of an Arbitrary State of Two Qubits] 1998.</ref><ref name="Hildebrand2007">Roland Hildebrand, [https://dx.doi.org/10.1063/1.2795840 Concurrence revisited], 2007</ref><ref name="Djocovic2009">D. Ž. Ðoković and A. Osterloh, [https://dx.doi.org/10.1063/1.3075830 On polynomial invariants of several qubits], 2009</ref>

== 定义 ==
'''通粹纠缠度'''是一种纠缠单调函数（一种测量纠缠的方法），针对两个[[量子位元|量子比特]]的混合状态定义为：    

: <math> \mathcal{C}(\rho)\equiv\max(0,\lambda_1-\lambda_2-\lambda_3-\lambda_4) </math>

其中<math>\lambda_1,...,\lambda_4</math>是如下 Hermitian 矩阵的特征值（按降序排列）

: <math>R = \sqrt{\sqrt{\rho}\tilde{\rho}\sqrt{\rho}} </math>

其中

: <math>\tilde{\rho} = (\sigma_{y}\otimes\sigma_{y})\rho^{*}(\sigma_{y}\otimes\sigma_{y})</math>

由密度矩阵的转置共轭<math>\rho^{*}</math>和[[泡利矩陣|泡利自旋矩阵]]<math>\sigma_y</math>得到。


{{Reflist|refs=<ref name="Hill1997">Scott Hill and William K. Wootters, [https://arxiv.org/abs/quant-ph/9703041 Entanglement of a Pair of Quantum Bits], 1997.</ref>
<ref name="Wootters1998">William K. Wootters, [https://dx.doi.org/10.1103/PhysRevLett.80.2245 Entanglement of Formation of an Arbitrary State of Two Qubits] 1998.</ref>
<ref name="Hildebrand2007">Roland Hildebrand, [https://dx.doi.org/10.1063/1.2795840 Concurrence revisited], 2007</ref>
<ref name="Djocovic2009">D. Ž. Ðoković and A. Osterloh, [https://dx.doi.org/10.1063/1.3075830 On polynomial invariants of several qubits], 2009</ref>}}


[[Category:量子信息科学]]
[[Category:理论计算机科学]]