催化变换下量子资源的改变与分布

Quantum resource changes and distributions during catalytic transformations

在自然界中,物理系统往往从无序程度较低的状态演化到无序程度较高的状态,这种现象可以用熵增来识别.但是,在量子资源理论中物理系统的资源改变是无序的:自由操作下物理系统的资源不增,而联合的酉操作下物理系统的资源不减.利用量子资源完全冻结技术和催化变换方法,本文证明,在作用于物理系统和催化系统的联合自由操作下物理系统的资源保持不减,即催化的联合自由操作下量子态之间的变换完全可以由物理系统的资源改变进行刻画.利用量子资源度量的单调性、可加性与连续性,研究联合自由操作下系统态的量子资源改变与系统间量子关联的关系,得到系统态量子资源不减的必要条件是催化变换后系统的量子态与催化态是关联的.最后利用催化态在联合自由操作下的不变性,研究同一个催化态用于辅助变换多个子系统时多体系统间的关联,建立催化变换后子系统间的多体关联与催化态的重用次数之间的关系.

One physical system always evolves from a state of low disorder to another of high disorder.This phenomenon can be identified by increased entropy.As we know,quantum resource theories provide a mathematical framework for examining diverse quantum resources in states,with the primary problem being whether quantum states can be transformed into each other by free operations.Unlike natural transformations,free operations in quantum resource theories never increase the resource measure of a primary system.Generally,the standard approach to this central problem is to study approximate transformations and apply catalysts to broaden the set of possible state transformations.By combining approximate transformations and catalytic transformations,we show that the quantum correlation between the primary system and the catalytic system after approximate catalytic transformations determines quantum resource changes in the primary system as well as the distribution of quantum correlations among different primary systems.We first find and establish that the resource measure of the primary system does not decrease under global free operations on the primary system and the corresponding catalytic system using the universal freezing technology and the catalytic transformation methods.A resource measure is monotonic under free operations,additive on tensor products,and continuous.Using these features,we then access relations between variations in the resource measure of the primary system under global free operations and quantum correlations between the primary and catalytic systems.Therefore,quantum correlations exist between the primary and catalytic systems after catalytic transformations,which are essential for nondecreasing resource measures of the primary system.Finally,we establish relationships among different primary systems after repeatedly applying the same catalyst.The correlation is closely associated with the reuse times of the same catalyst.