发表机构
Joint Center for Quantum Information and Computer Science, NIST/University of Maryland; Joint Quantum Institute, NIST/University of Maryland; Department of Physics, University of Maryland; Centre for Quantum Technologies, National University of Singapore; Department of Computer Science and Institute for Advanced Computer Studies, University of Maryland; Department of Computer Science, National University of Singapore（马里兰大学与美国国家标准与技术研究院联合量子信息与计算中心; 马里兰大学与美国国家标准与技术研究院联合量子研究所; 马里兰大学物理系; 新加坡国立大学量子技术中心; 马里兰大学计算机科学与高级计算机研究所; 新加坡国立大学计算机系）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文结合量子金融、图论与语境性，提出基于非局域博弈的量子市场，证明排他性量子资产优于经典资产，并用独立数和Lovász theta数给出公平价格上界。
AI 中文摘要
经济学和金融学的一个核心主题是对策略性博弈和赌注、提供不确定未来现金流的投资以及其他类似资产的机构和合约进行估值。通常，这种估值涉及概率模型、随机变量以及计算复杂收益的期望值。在超越这一经典框架的基础上，出现了一种场景，其中资产是非对易算子，内在的不确定性由量子态描述。在这项工作中，我们将量子金融的这些概念与图论框架和语境性思想相结合。我们讨论了排他性量子资产，并引入了持有此类资产相对于持有经典资产可以提供优势的场景。特别是，我们考虑了一个基于非局域博弈（如CHSH博弈）的“量子市场”，并证明该设置可以作为一个具有明确定义的金融结构的市场运作。我们基于图论量（如独立数和Lovász theta数）提供了量子资产公平价格的上界。我们对非对易资产市场的洞察有助于阐明在一个充满量子技术的世界中金融体系可能呈现的面貌。
英文摘要
A central topic in economics and finance is the valuation of strategic games and bets, of investments providing uncertain future cashflows, and of other asset-like structures and contracts. Often, such valuation involves a probabilistic model, random variables, and computing expectation values of complex payoffs. Extending beyond this classical framework, a scenario emerges where assets are non-commuting operators and the inherent uncertainty is described by quantum states. In this work, we combine such notions of quantum finance with a graph-theoretic framework and ideas from contextuality. We discuss exclusive quantum assets and introduce scenarios when holding such assets can provide advantages over holding classical assets. In particular, we consider a "quantum market" based on nonlocal games such as the CHSH game and demonstrate that this setting can function as a market with well-defined financial structures. We provide upper bounds on the fair prices of the quantum assets based on graph-theoretic quantities like the independence number and the Lovász theta number. Our insights into markets of non-commuting assets help to elucidate what a financial system in a world filled with quantum technology could look like.
Comments48 pages, 5 figures, 1 table
