通往量子理论(或量子理论)的康庄大道,扩展摘要
A Royal Road to Quantum Theory (or Thereabouts), Extended Abstract
摘要:
从简单的假设出发,以一种非常简单的方式,得到了有限维概率模型在形式上实的Jordan代数上的表示。这提供了一个框架,在这个框架中,实的、复的和四元数的量子力学可以被平等地对待,并为其他的替代方案提供了一些(但不是太多)空间。这是基于早期的工作(arXiv:1206:2897),但这里的开发被进一步简化,并以多种方式扩展。我还讨论了组织概率模型的可能性,受这里讨论的假设,到对称monoidal类别,表明这样的类别将自动具有匕首紧凑的结构。(最近与霍华德·巴纳姆(Howard Barnum)和马修·格雷顿(Matthew Graydon)的合作(arXiv:1507.06278)展示了这类的几个类别。
英文摘要:
A representation of finite-dimensional probabilistic models in terms of formally real Jordan algebras is obtained, in a strikingly easy way, from simple assumptions. This provides a framework in which real, complex and quaternionic quantum mechanics can be treated on an equal footing, and allows some (but not too much) room for other alternatives. This is based on earlier work (arXiv:1206:2897), but the development here is further simplified, and also extended in several ways. I also discuss the possibilities for organizing probabilistic models, subject to the assumptions discussed here, into symmetric monoidal categories, showing that such a category will automatically have a dagger-compact structure. (Recent joint work with Howard Barnum and Matthew Graydon (arXiv:1507.06278) exhibits several categories of this kind.)
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