基于半定规划的量子状态最优无错区分

Optimum Unambiguous Discrimination of Quantum States Based on Semidefinite Programming

对于一般的量子状态最优无错区分问题,很难得到最优量子测量的解析形式。因此,有必要寻求有效实用的数值方法。基于半定规划理论,证明了无错状态区分的最优量子测量的设计问题可以转化为标准的半定规划问题,以及能直接应用半定规划的最优性条件,从而更简明地推导了一组无错状态区分的最优性条件;通过求解标准的半定规划问题,可在多项式时间内直接得到最优量子测量的数值解以及成功区分状态的最大概率值。实例仿真表明,方法易于计算机实现,能有效地设计出无错状态区分的最优量子测量算子。

For the general problem of optimum unambiguous discrimination of quantum states, it is very hard to get the explicit analytical form for optimum detection operators. Therefore, it is necessary to find an efficient numerical method for designing optimum detection operators. According to the theory of semidefinite programming, it is demonstrated that the design of the optimal quantum measurement can be formulated as a standard semidefinite programming problem, and the optimality conditions for semidefinite programming can be used to perspicuously derive a set of optimality conditions for optimum detection operators. By means of the standard semidefinite programming, the maximum value of the success probability of detection and the optimum detection operators can be obtained directly in polynomial time. It is exemplified that this method is simple to be implemented and can be used to design optimum detection operators for quantum - state discrimination efficiently.