近日，新加坡科技与设计大学的Dario Poletti及其研究团队取得一项新进展。经过不懈努力，他们对纠缠能力和幺正量子博弈进行研究。相关研究成果已于2024年8月8日在国际知名学术期刊《物理评论A》上发表。
该研究团队考虑一类由两名竞争玩家轮流对同一个多体量子寄存器进行操作的博弈。每位玩家都可以对该寄存器执行幺正操作，并且每当其中一位玩家对寄存器进行操作后，都会测量其能量。
玩家A的目标是最大化能量，而玩家B的目标是最小化能量。如果两位玩家都能对寄存器的相同部分进行纠缠，那么这类零和博弈具有明显的后发优势。然而，研究表明，如果第一位玩家能够纠缠的量子比特数多于第二位玩家（研究人员称之为具有量子优势），那么后发优势可能会显著降低。
研究人员研究了玩家A与玩家B在不同类型的量子优势下，以及寄存器不同大小的情况下的博弈，特别是那些绝对最大纠缠态无法实现的情况。在这种情况下，他们还研究了使用随机幺正操作的有效性。最后，他们考虑了寄存器的混合初始制备情况，在这种情况下，具有量子优势的玩家可以依靠源自量子电池云母理论的策略。
附：英文原文
Title: Entangling capabilities and unitary quantum games
Author: Rebecca Erbanni, Antonios Varvitsiotis, Dario Poletti
Issue&Volume: 2024/08/08
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.
DOI: 10.1103/PhysRevA.110.022413
Source: https://journals.aps.org/pra/abstract/10.1103/PhysRevA.110.022413
来源：科学网 小柯机器人