arXiv quant-ph/04071442004-07quant-ph

具有连续和/或离散能谱的量子系统的时变操作的分解

Decomposition of time-covariant operations on quantum systems with continuous and/or discrete energy spectrum

Dominik Janzing

备注：: latex, 33 pages, domains of unbounded operators are now explicitly specified. Presentation more detailed. Implementing the shift after the dephasing is sometimes more convenient
DOI：: 10.1063/1.2142839

摘要：

每个完全正的映射G，其Hamilton时间演化是CP-映射G_σ上的积分或和，其中σ是转移到环境或从环境获取的能量。如果谱是非简并的，则每个G_σ都是一个退相通道，后面跟着一个能量移动。退相由密度算子与（正式定义的）正算子的Hadamard乘积给出。能量位移的Kraus算子是一个部分等距，它定义了R上关于非平移不变测度的平移。作为一个例子，我计算了这种分解明确的旋转不变高斯通道上的一个单一的模式。我解决的问题，在什么条件下的协变通道破坏相互正交的国家在同一轨道上的叠加。对于允许输出态在同一轨道上相互正交的信道，利用CP映射值测度（G_σ）的傅里叶变换，导出了量子容量的一个下界.

英文摘要：

Every completely positive map G that commutes which the Hamiltonian time evolution is an integral or sum over (densely defined) CP-maps G_σwhere σis the energy that is transferred to or taken from the environment. If the spectrum is non-degenerated each G_σis a dephasing channel followed by an energy shift. The dephasing is given by the Hadamard product of the density operator with a (formally defined) positive operator. The Kraus operator of the energy shift is a partial isometry which defines a translation on R with respect to a non-translation-invariant measure. As an example, I calculate this decomposition explicitly for the rotation invariant gaussian channel on a single mode. I address the question under what conditions a covariant channel destroys superpositions between mutually orthogonal states on the same orbit. For channels which allow mutually orthogonal output states on the same orbit, a lower bound on the quantum capacity is derived using the Fourier transform of the CP-map-valued measure (G_σ).

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英文摘要：

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