Infinitesimal reference frames suffice to determine the asymmetry properties of a quantum system
Infinitesimal reference frames suffice to determine the asymmetry properties of a quantum system
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DOI：
10.1088/1367-2630/ac688b
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发表时间：
2021-07
影响因子：
3.3
通讯作者：
Rhea Alexander;Si Gvirtz-Chen;D. Jennings
中科院分区：
文献类型：
--
作者：
Rhea Alexander;Si Gvirtz-Chen;D. Jennings
对称性原理是物理学中的基本原理，虽然它们在拉格朗日力学中得到了很好的理解，但它们对量子通道的影响仍有一系列悬而未决的问题。不对称理论源于关于纠缠和量子参照系的信息论工作，它允许我们量化量子系统对对称群坐标的编码程度。最近，根据相对于无限多个量子参考系的关联，发现了一套完整的不对称性的熵条件。然而，这些条件在实践中很难使用，它们的物理含义也不清楚。在目前的理论工作中，我们证明了这组条件具有广泛的冗余性，并且可以限制在内部具有最大混合状态的状态空间中形成任何闭合曲面的参照系。这反过来意味着，不对称性可以简化为在最大混合状态下评估的单一的熵条件。与直觉相反，这表明我们不需要宏观的、经典的参照系来确定量子系统的不对称性质，而是无限小的参照系就足够了。在此分析的基础上，我们提供了简单、封闭的条件来估计使给定的量子态在与任何给定的对称群协变的信道下可访问所需的最小去极化。
Symmetry principles are fundamental in physics, and while they are well understood within Lagrangian mechanics, their impact on quantum channels has a range of open questions. The theory of asymmetry grew out of information-theoretic work on entanglement and quantum reference frames, and allows us to quantify the degree to which a quantum system encodes coordinates of a symmetry group. Recently, a complete set of entropic conditions was found for asymmetry in terms of correlations relative to infinitely many quantum reference frames. However, these conditions are difficult to use in practice and their physical implications unclear. In the present theoretical work, we show that this set of conditions has extensive redundancy, and one can restrict to reference frames forming any closed surface in the state space that has the maximally mixed state in its interior. This in turn implies that asymmetry can be reduced to just a single entropic condition evaluated at the maximally mixed state. Contrary to intuition, this shows that we do not need macroscopic, classical reference frames to determine the asymmetry properties of a quantum system, but instead infinitesimally small frames suffice. Building on this analysis, we provide simple, closed conditions to estimate the minimal depolarization needed to make a given quantum state accessible under channels covariant with any given symmetry group.