基于Rényi-α熵的参数化纠缠度量

Parameterized entanglement measures based on Rényi-αentropy

与各种非参数化纠缠度量相比,参数化纠缠度量显示了其优越性.并发纠缠被广泛用于描述量子实验中的纠缠.作为一种纠缠度量,它与特定Rényi-α熵有关.本文提出了一种基于Rényi-α熵的参数化两体纠缠度量,命名为α-对数并发纠缠.与现有的参数化度量不同,首先定义了纯态的度量,然后推广到混合态.进一步验证了α-对数并发纠缠满足纠缠度量3个条件.展示了对纯态的度量是容易计算的,然而对于混合态,解析计算只适用于特殊的双量子位态或特殊的高维混合态.因此,本文致力于建立一般两体态α-对数并发纠缠的一个下界.令人惊讶的是,这个下界是这个混合态的正部分转置判据和重排判据的函数.这表明了3种纠缠度量之间的联系.有趣的是,下界依赖于与具体态相关的熵参数.这样我们可以选择适当的参数α,使得Gα(ρ)≫0用于特定态ρ的实验纠缠检测.此外,计算了isotropic态的α-对数并发纠缠的表达式,并给出了d=2时isotropic态的解析表达式.最后,讨论了α-对数并发纠缠的的单配性.建立了两个量子比特系统中并发纠缠和α-对数并发纠缠之间的函数关系,然后得到了该函数的一些有用性质,并结合Coffman-Kundu-Wootters(CKW)不等式,建立了关于α-对数并发纠缠的单配性不等式.最终证明了单配性不等式对于α-对数并发纠缠是成立的.

Parameterized entanglement measures have demonstrated their superiority compared with kinds of unparameterized entanglement measures.Entanglement concurrence has been widely used to describe entanglement in quantum experiments.As an entanglement measure it is related to specific quantum Rényi-αentropy.In the work,we propose a parameterized bipartite entanglement measure based on the general Rényi-αentropy,which is namedα-logarithmic concurrence.This measure,different from existing parameterized measures,is defined first for pure states,then extended to the mixed states.Furthermore,we verify three necessary conditions forα-logarithmic concurrence to satisfy the entanglement measures.We show that this measure is easy to calculate for pure states.However,for mixed states,analytical calculations are only suitable for special two-qubit states or special higher-dimensional mixed states.Therefore,we devote our efforts to developing the analytical lower bound of the-logarithmic concurrence for general bipartite states.Surprisingly,this lower bound is a function on positive partial transposition criterion and realignment criterion of this mixed state.This shows the connection among the three entanglement measures.The interesting feature is that the lower bound depends on the entropy parameter associated with the detailed state.This allows us to choose appropriate parameterαsuch that Gα(ρ)≫0 for experimental entanglement detection of specific stateρ.Moreover,we calculate expressions of theα-logarithmic concurrence for isotropic states,and give a the analytic expressions for isotropic states with d=2.Finally,the monogamy of theα-logarithmic concurrence is also discussed.We set up a mathematical formulation for the monogamous property in terms ofα-logarithmic concurrence.Here we set up the functional relation between concurrence andα-logarithmic concurrence in two qubit systems.Then we obtain some useful properties of this function,and by combining the Coffman–Kundu–Wootters(CKW)inequality,we establish the monogamy inequality aboutα-logarithmic concurrence.We finally prove that the monogamy inequality holds true forα-logarithmic concurrence.