摘要
设H_m是维数为m的复希尔伯特空间,S(H_m?H_n)为复双体希尔伯特空间H_m?H_n上的量子态的全体,S_(sep)(H_m?H_n)为其中可分量子态构成的凸集.映射φ:S(H_m?H_n)→S(H_m?H_n)是满射,且φ(S_(sep)(H_m?H_n))=S_(sep)(H_m?H_n).若对于某个r∈R~+\1},满射φ保持量子态凸组合的Tsallis熵S~r(tρ+(1-t)σ)=S~r(tφ(ρ)+(1-t)φ(σ))对于任意的ρ、σ∈S(H_m?H_n)和任意的t∈[0,1]成立;那么在H_m、H_n上分别存在酉算子U_m、V_n,使得φ(ρ)=(U_m?V_n)ρ(U_m?V_n)~*对于任意的ρ∈S_(sep)(H_m?H_n)成立.
Let H_m be the complex Hilbert space with dimension m, S(H_m?H_n) be all the quantum states acting on complex bipartite Hilbert space H_m?H_n and S_(sep)(H_m?H_n) be the convex set of comparable quantum states.■be a surjective map and■For some r∈R~+\1}, if φ satisfies Tsallis entropy■for any ρ,σ∈S(H_m?H_n) and for any t∈[0,1], there exist unitary operators U_m, V_n acting on H_m, H_n such thatφ(ρ)=(U_m?V_n)ρ(U_m?V_n)~* for anyρ∈S_(sep)(H_m?H_n).
引文
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