Multimode Gaussian optimizers for the Wehrl entropy and quantum Gaussian channels
Multimode Gaussian optimizers for the Wehrl entropy and quantum Gaussian channels
复制标题
用于 Wehrl 熵和量子高斯通道的多模高斯优化器
DOI：
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发表时间：
2017
期刊：
影响因子：
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通讯作者：
V. Giovannetti
中科院分区：
文献类型：
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作者：
G. Palma;Dario Trevisan;V. Giovannetti
我们在多模场景中证明了韦尔和冯诺依曼熵之间的基本关系，指出具有给定冯诺依曼熵的所有量子态中的最小韦尔熵是通过热高斯态实现的。我们还证明，热高斯输入状态在某些乘积基础和给定熵的情况下，最小化了所有输入状态对角线中多模量子高斯衰减器、放大器和相位逆变通道的输出冯诺依曼熵。这一结果构成了证明通用输入状态相同属性的重要一步，这仍然是一个开放的猜想。该猜想对于确定使用高斯量子限制衰减器的三重权衡编码和广播通信的最大通信速率是必要的。最后，我们证明了 n 个相同几何输入概率分布的张量积最小化了具有给定熵的所有输入概率分布中 n 模式细化的输出香农熵。
We prove in the multimode scenario a fundamental relation between the Wehrl and the von Neumann entropy, stating that the minimum Wehrl entropy among all the quantum states with a given von Neumann entropy is achieved by thermal Gaussian states. We also prove that thermal Gaussian input states minimize the output von Neumann entropy of multimode quantum Gaussian attenuators, amplifiers and phase-contravariant channels among all the input states diagonal in some product basis and with a given entropy. This result constitutes a major step towards the proof of the same property for generic input states, which is still an open conjecture. This conjecture is necessary to determine the maximum communication rates for the triple trade-off coding and broadcast communication with the Gaussian quantum-limited attenuator. Finally, we prove that the tensor product of n identical geometric input probability distributions minimizes the output Shannon entropy of the n-mode thinning among all the input probability distributions with a given entropy.