Abstract

Phase covariant qubit dynamics describes an evolution of a two-level system under simultaneous action of pure dephasing, energy dissipation, and energy gain with time-dependent rates \(\gamma_{z}(t)\), \(\gamma_{-}(t)\), and \(\gamma_{+}(t)\), respectively. Non-negative rates correspond to completely positive divisible dynamics, which can still exhibit such peculiarities as non-monotonicity of populations for any initial state. We find a set of quantum channels attainable in the completely positive divisible phase covariant dynamics and show that this set coincides with the set of channels attainable in semigroup phase covariant dynamics. We also construct new examples of eternally indivisible dynamics with \(\gamma_{z}(t)<0\) for all \(t>0\) that is neither unital nor commutative. Using the quantum Sinkhorn theorem, we for the first time derive a restriction on the decoherence rates under which the dynamics is positive divisible, namely, \(\gamma_{\pm}(t)\geq 0\), \(\sqrt{\gamma_{+}(t)\gamma_{-}(t)}+2\gamma_{z}(t)>0\). Finally, we consider phase covariant convolution master equations and find a class of admissible memory kernels that guarantee complete positivity of the dynamical map.

中文翻译：

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相位协变量子位动力学和除数

摘要

相位协变量子位动力学描述了纯相位，能量耗散和能量增益同时作用下的两级系统的演化，时间依赖于速率\（\ gamma_ {z}（t）\），\（\ gamma _ {- }（t）\）和\（\ gamma _ {+}（t）\）。非负比率对应于完全正的可整除动力学，对于任何初始状态，它仍可能表现出诸如人口非单调性之类的特殊性。我们发现了一组在完全正整除相协变动力学中可达到的量子通道，并表明该组与在半群相协变动力学中可达到的一组通道相吻合。我们还用以下方法构造了永恒不可分割的动力学的新例子：对于所有既不是单位也不是可交换的\（t> 0 \），\（\ gamma_ {z}（t）<0 \）。利用量子Sinkhorn定理，我们首次得出了对退相干速率的限制，在该退相干速率下，动力学可以被正整除，即\（\ gamma _ {\ pm}（t）\ geq 0 \），\（\ sqrt { \ gamma _ {+}（t）\ gamma _ {-}（t）} + 2 \ gamma_ {z}（t）> 0 \）。最后，我们考虑相位协变卷积主方程，并找到一类可允许的内存核，它们保证了动力学图的完全正性。