论文标题
玻色石高斯频道中的多数阶梯
Majorization ladder in bosonic Gaussian channels
论文作者
论文摘要
我们显示了在玻色杆高斯频道中存在多数阶梯的存在，也就是说，我们证明，$ n \ text {th} $ Energy Eigenstate（Fock State）产生的通道输出将$（N \！+\！+\！1）\ text {th} $ Entern {$ Enterge eigenstate（fock state（Fock state））大大化通道输出。这反映了通道输入处的能量与在其输出处的无序关系之间的显着联系，如多数化理论所捕获的。以前在纯损失通道和量子限制放大器的特殊情况下已知该结果，在这里我们在这里实现了其对任何单模相位旋化（或 - 对比）的玻感高斯高斯通道的非平凡概括。我们证明的关键是明确构造柱状矩阵，该矩阵将其输入处的任何两个随后的Fock状态都关联到通道的输出。通过利用最近发现的关于高斯单位的多光子过渡概率的复发关系，这是可能的[M. G. Jabbour和N. J. Cerf，物理。 Rev. Research 3，043065（2021）]。然后讨论这些结果的可能的概括和含义。
We show the existence of a majorization ladder in bosonic Gaussian channels, that is, we prove that the channel output resulting from the $n\text{th}$ energy eigenstate (Fock state) majorizes the channel output resulting from the $(n\!+\!1)\text{th}$ energy eigenstate (Fock state). This reflects a remarkable link between the energy at the input of the channel and a disorder relation at its output as captured by majorization theory. This result was previously known in the special cases of a pure-loss channel and quantum-limited amplifier, and we achieve here its nontrivial generalization to any single-mode phase-covariant (or -contravariant) bosonic Gaussian channel. The key to our proof is the explicit construction of a column-stochastic matrix that relates the outputs of the channel for any two subsequent Fock states at its input. This is made possible by exploiting a recently found recurrence relation on multiphoton transition probabilities for Gaussian unitaries [M. G. Jabbour and N. J. Cerf, Phys. Rev. Research 3, 043065 (2021)]. Possible generalizations and implications of these results are then discussed.
