论文标题
凯利（Kelly
Kelly Betting with Quantum Payoff: a continuous variable approach
论文作者
论文摘要
这项研究的主要目的是介绍一个半古典模型，描述了投注方案，其中与常规方法不同，赌徒的回报被编码为量子记忆元素的内部自由度。在我们的计划中，我们假设投资资本与自由能的量子类似物（即，Allahverdyan，Balian和Nieuwenhuizen功能的自由能的量子类似物）的单一模式电磁辐射模式，该模式取决于投注，经验丰富的损失和损害的结果，这些辐射的结果是，该辐射的结果和损失的结果和损失的结果。量子记忆的随机演变类似于我们在玻色症高斯通道的理论设置中表征的随机激光动力学。就像在经典的凯利（Kelly）标准中一样，我们定义了模型的渐近加倍速度，并确定了固定赔率和获胜概率的最佳赌博策略。因此，研究模型的性能是输入资本状态的函数，假设后者属于高斯密度矩阵集（即流离失所的，挤压的热吉布斯状态），这表明赌徒的最佳选择是将所有她/他的初始资源都投入到连贯的状态振幅中。
The main purpose of this study is to introduce a semi-classical model describing betting scenarios in which, at variance with conventional approaches, the payoff of the gambler is encoded into the internal degrees of freedom of a quantum memory element. In our scheme, we assume that the invested capital is explicitly associated with the quantum analog of the free-energy (i.e. ergotropy functional by Allahverdyan, Balian, and Nieuwenhuizen) of a single mode of the electromagnetic radiation which, depending on the outcome of the betting, experiences attenuation or amplification processes which model losses and winning events. The resulting stochastic evolution of the quantum memory resembles the dynamics of random lasing which we characterize within the theoretical setting of Bosonic Gaussian channels. As in the classical Kelly Criterion for optimal betting, we define the asymptotic doubling rate of the model and identify the optimal gambling strategy for fixed odds and probabilities of winning. The performance of the model are hence studied as a function of the input capital state under the assumption that the latter belongs to the set of Gaussian density matrices (i.e. displaced, squeezed thermal Gibbs states) revealing that the best option for the gambler is to devote all her/his initial resources into coherent state amplitude.
