受控幺正门的纠缠能力量化
Quantifying Entangling Power of Controlled Unitary Gates
AI总结：
本文提出可计算量ζ量化受控幺正门的纠缠能力，推导其通用上界并关联其他量子熵量，经对比验证该量可达到对应维度下纠缠能力的已知最优值。
AI中文摘要：
在量子通信和量子计算中，应用受控幺正门生成量子比特间的纠缠是常规任务。现有预测给定门可生成纠缠量的工具，要么需要对纠缠线路进行模拟，要么需要对给定受控幺正门的输入分布进行平均。本文引入可计算量ζ，其不仅能判定受控幺正门是否生成纠缠，还能在无需构造输出态的情况下量化任意特定输入对应的纠缠。针对两量子比特受控幺正门，本文确定了与该拟测量极值对应的物理条件；通过广义受控幺正架构将控制寄存器和目标寄存器的维度扩展至任意大小，推导了ζ的通用上界并确定其饱和条件；随后建立了该量与纯度、归一化线性熵、冯·诺依曼熵等已知量的函数关系；最后将本文结果与前人研究对比，表明对于控制寄存器和目标寄存器的某些特定维度，本文提出的量达到了受控幺正门纠缠能力的已知最优值。
英文摘要：
Applying controlled unitary gates to generate entanglement between qubits is a routine task in both quantum communication and computation. The existing tools for predicting how much entanglement a given gate can generate require either simulation of the entangling circuit or averaging over a distribution of inputs for a given controlled unitary gate. Here, we introduce a computable quantity $ζ$ that not only determines whether a controlled unitary gate generates entanglement, but also quantifies the entanglement for any specific input without requiring the construction of the output state. For two-qubit controlled unitary gates, we establish the physical conditions corresponding to the extremum values of the proposed quantity. Extending the dimension of control and target registers to arbitrary size through a generalized controlled unitary architecture, we derive a universal upper bound on $ζ$ and identify the conditions for its saturation. Later we establish functional relation between the quantity and other known quantities, such as purity, normalized linear entropy, and von Neumann entropy. Finally, we compare our results with previous research work and show that the quantity proposed in this work achieves the previously known optimal values of entangling power of controlled unitary gates for some specific dimensions of target and control registers.
