Fundamental limitations to key distillation from Gaussian states with Gaussian operations
Fundamental limitations to key distillation from Gaussian states with Gaussian operations
复制标题
DOI：
10.1103/physrevresearch.5.033153
复制
发表时间：
2020-10
期刊：
影响因子：
--
通讯作者：
Ludovico Lami;L. Mišta;G. Adesso
中科院分区：
文献类型：
--
作者：
Ludovico Lami;L. Mišta;G. Adesso
通过局部高斯运算、局部经典处理和公共通信，建立了从连续可变量子高斯态中提取密钥的基本上界。对于单向通信，我们证明了密钥是由构造$E_{F,2}^{\ maththrm {\scriptscriptstyle G}}$的Renyi-$2$高斯纠缠约束的，并且不等式在纯高斯状态下是饱和的。如果允许双向公共通信，但Alice和Bob采用的协议从破坏性的局部高斯测量开始，情况也是如此。在双向通信和任意交互协议的最一般设置中，我们认为$2 E_{F,2}^{\ maththrm {\scriptscriptstyle G}}$仍然是可提取密钥的一个界，尽管我们推测$2$是多余的。最后，对于包含所有双模态的广义高斯态，我们证明了最近提出的关于$E_{F,2}}^{\ maththrm {\scriptscriptstyle G}}$与高斯本征纠缠相等的猜想，从而赋予这两个测度更可靠的运算意义。
We establish fundamental upper bounds on the amount of secret key that can be extracted from continuous variable quantum Gaussian states by using only local Gaussian operations, local classical processing, and public communication. For one-way communication, we prove that the key is bounded by the Renyi-$2$ Gaussian entanglement of formation $E_{F,2}^{\mathrm{\scriptscriptstyle G}}$, with the inequality being saturated for pure Gaussian states. The same is true if two-way public communication is allowed but Alice and Bob employ protocols that start with destructive local Gaussian measurements. In the most general setting of two-way communication and arbitrary interactive protocols, we argue that $2 E_{F,2}^{\mathrm{\scriptscriptstyle G}}$ is still a bound on the extractable key, although we conjecture that the factor of $2$ is superfluous. Finally, for a wide class of Gaussian states that includes all two-mode states, we prove a recently proposed conjecture on the equality between $E_{F,2}^{\mathrm{\scriptscriptstyle G}}$ and the Gaussian intrinsic entanglement, thus endowing both measures with a more solid operational meaning.