{"title":"Entangling capabilities and unitary quantum games","authors":"Rebecca Erbanni, Antonios Varvitsiotis, Dario Poletti","doi":"10.1103/physreva.110.022413","DOIUrl":null,"url":null,"abstract":"We consider a class of games between two competing players that take turns acting on the same many-body quantum register. Each player can perform unitary operations on the register, and after each one of them acts on the register the energy is measured. Player A aims to maximize the energy while player B to minimize it. This class of zero-sum games has a clear second mover advantage if both players can entangle the same portion of the register. We show, however, that if the first player can entangle a larger number of qubits than the second player (which we refer to as having quantum edge), then the second mover advantage can be significantly reduced. We study the game for different types of quantum edge of player A versus player B and for different sizes of the register, in particular, scenarios in which absolutely maximally entangled states cannot be achieved. In this case, we also study the effectiveness of using random unitaries. Last, we consider mixed initial preparations of the register, in which case the player with a quantum edge can rely on strategies stemming from the theory of ergotropy of quantum batteries.","PeriodicalId":20146,"journal":{"name":"Physical Review A","volume":null,"pages":null},"PeriodicalIF":2.9000,"publicationDate":"2024-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Physical Review A","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1103/physreva.110.022413","RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"Physics and Astronomy","Score":null,"Total":0}
引用次数: 0
Abstract
We consider a class of games between two competing players that take turns acting on the same many-body quantum register. Each player can perform unitary operations on the register, and after each one of them acts on the register the energy is measured. Player A aims to maximize the energy while player B to minimize it. This class of zero-sum games has a clear second mover advantage if both players can entangle the same portion of the register. We show, however, that if the first player can entangle a larger number of qubits than the second player (which we refer to as having quantum edge), then the second mover advantage can be significantly reduced. We study the game for different types of quantum edge of player A versus player B and for different sizes of the register, in particular, scenarios in which absolutely maximally entangled states cannot be achieved. In this case, we also study the effectiveness of using random unitaries. Last, we consider mixed initial preparations of the register, in which case the player with a quantum edge can rely on strategies stemming from the theory of ergotropy of quantum batteries.
我们考虑的是两个竞争者轮流作用于同一个多体量子寄存器的一类游戏。每个玩家都可以对寄存器进行单元操作,在每个玩家对寄存器进行操作后,都要测量能量。玩家 A 的目标是最大化能量,而玩家 B 则是最小化能量。如果双方都能纠缠寄存器的相同部分,那么这类零和博弈具有明显的后发优势。不过,我们的研究表明,如果第一名玩家能比第二名玩家纠缠更多的量子比特(我们称之为量子优势),那么第二名玩家的优势就会大大降低。我们研究了棋手 A 与棋手 B 不同类型的量子优势和不同大小的寄存器的博弈,特别是无法实现绝对最大纠缠状态的情况。在这种情况下,我们还研究了使用随机单元的有效性。最后,我们考虑了注册表的混合初始准备情况,在这种情况下,拥有量子边的棋手可以依赖量子电池各向异性理论的策略。
期刊介绍:
Physical Review A (PRA) publishes important developments in the rapidly evolving areas of atomic, molecular, and optical (AMO) physics, quantum information, and related fundamental concepts.
PRA covers atomic, molecular, and optical physics, foundations of quantum mechanics, and quantum information, including:
-Fundamental concepts
-Quantum information
-Atomic and molecular structure and dynamics; high-precision measurement
-Atomic and molecular collisions and interactions
-Atomic and molecular processes in external fields, including interactions with strong fields and short pulses
-Matter waves and collective properties of cold atoms and molecules
-Quantum optics, physics of lasers, nonlinear optics, and classical optics