Eisert J
Blackett Laboratory, Imperial College London, UK.
Phys Rev Lett. 2005 Jul 22;95(4):040502. doi: 10.1103/PhysRevLett.95.040502.
In this Letter, the problem of finding optimal success probabilities of linear optics quantum gates is linked to the theory of convex optimization. It is shown that by exploiting this link, upper bounds for the success probability of networks realizing single-mode gates can be derived, which hold in generality for postselected networks of arbitrary size, any number of auxiliary modes, and arbitrary photon numbers. As a corollary, the previously formulated conjecture is proven that the optimal success probability of a nonlinear sign shift without feedforward is 1/4, a gate playing the central role in the scheme of Knill-Laflamme-Milburn for quantum computation. The concept of Lagrange duality is shown to be applicable to provide rigorous proofs for such bounds, although the original problem is a difficult nonconvex problem in infinitely many objective variables. The versatility of this approach is demonstrated.
在本信函中，寻找线性光学量子门最优成功概率的问题与凸优化理论相关联。结果表明，通过利用这种关联，可以推导出实现单模门的网络成功概率的上界，这些上界普遍适用于任意大小、任意数量辅助模式和任意光子数的后选择网络。作为推论，证明了先前提出的猜想：无前馈的非线性符号移位的最优成功概率为1/4，该门在Knill-Laflamme-Milburn量子计算方案中起着核心作用。尽管原始问题是一个在无限多个目标变量中的困难非凸问题，但拉格朗日对偶概念被证明适用于为此类界限提供严格证明。展示了这种方法的通用性。
