热纠缠态表象的建立及其在密度矩阵中的应用

Construction of Thermal Entanglement Representation and Its Application in Density Matrix

量子系统与热库之间存在量子纠缠,类比于双光子之间的纠缠,可以建立热纠缠态表象,从而便于计算和分析量子系统的热演化规律。首先根据热场动力学理论,引入虚希尔伯特空间后,使原有的希尔伯特空间扩大为2个。然后,在极高温状态下,推导出热真空态的显式形式,即|0(β)〉=(1-e-^(βω))^(1/2)exp(e^(βω/2)a^(+)a^(+))|0,0〉。接着,将平移算符作用于热真空态,得到热纠缠态表象的具体形式,即|η〉=(-1/2|η|^(2)+ηa^(+)-η^(*)a^(+)+a^(+)a^(+))|0,0〉。研究结果表明,在热纠缠态表象中可以直接得到任意量子态在热环境中的演化情况。取平移热态为实例,理论计算结果说明,低温条件下,平移热态演变为无热噪声的相干态。

There is quantum entanglement between quantum system and thermal reservoir.Analogous to entanglement between two photons,the appearance of thermal entangled states can be established.This method is convenient for calculating and analyzing the thermal evolution of quantum systems.Original Hilbert space is expanded to two Hilbert space according to the theory of thermal field dynamics and the virtual Hilbert space.Then,the explicit form of the thermal vacuum state is derived in the extremely high temperature state,i.e.,|0β>=(1-e^(-βω))^(1/2)exp(e^(-βω/2)a^(+)a^(+)|0,0>.To obtain the specific form of the thermal entangled state representation,translation operator is applied to the thermal vacuum state,i.e.,|η〉=(-1/2|η|^(2)+ηa^(+)-η^(*)a^(+)+a^(+)a^(+))|0,0.These results show that the evolution of any quantum state in thermal environment can be directly obtained in thermal entangled state representation.Taking translational thermal state as an example,the theoretical calculation results show that translational thermal state evolves into coherent state without thermal noise under low temperature conditions.