The ultimate precision in quantum sensing could be achieved using optimal quantum probe states. However, current quantum sensing protocols do not use probe states optimally. Indeed, the calculation of optimal probe states remains an outstanding challenge. Here, we present an algorithm that efficiently calculates a probe state for correlated and uncorrelated measurement strategies. The algorithm involves a conic program, which minimizes a linear objective function subject to conic constraints on a operator-valued variable. Our algorithm outputs a probe state that is a simple function of the optimal variable. We prove that our algorithm finds the optimal probe state for channel estimation problems, even in the multiparameter setting. For many noiseless quantum sensing problems, we prove the optimality of maximally entangled probe states. We also analyze the performance of 3D-field sensing using various probe states. Our work opens the door for a plethora of applications in quantum metrology.

量子传感的终极精度可以使用最佳量子探针状态来实现。然而，当前的量子传感协议并没有以最佳方式使用探针状态。事实上，最佳探针状态的计算仍然是一个突出的挑战。在这里，我们提出了一种算法，可以有效地计算相关和不相关测量策略的探针状态。该算法涉及一个圆锥程序，该方案将受运算符值变量的圆锥约束约束的线性目标函数最小化。我们的算法输出一个探测状态，该状态是最优变量的简单函数。我们证明，即使在多参数设置中，我们的算法也能找到通道估计问题的最佳探针状态。对于许多无噪声量子传感问题，我们证明了最大纠缠探针状态的最优性。我们还分析了使用各种探针状态的 3D 场传感的性能。我们的工作为量子计量学中的大量应用打开了大门。