Marvian Iman, Spekkens Robert W
Departments of Physics and Electrical and Computer Engineering, Duke University, Durham, North Carolina 27708, USA.
Perimeter Institute for Theoretical Physics, 31 Caroline St. N, Waterloo, Ontario, Canada N2L 2Y5.
Phys Rev Lett. 2019 Jul 12;123(2):020404. doi: 10.1103/PhysRevLett.123.020404.
Symmetries of both closed- and open-system dynamics imply many significant constraints. These generally have instantiations in both classical and quantum dynamics (Noether's theorem, for instance, applies to both sorts of dynamics). We here provide an example of such a constraint which has no counterpart for a classical system, that is, a uniquely quantum consequence of symmetric dynamics. Specifically, we demonstrate the impossibility of broadcasting asymmetry (symmetry breaking) relative to a continuous symmetry group, for bounded-size quantum systems. The no-go theorem states that if two initially uncorrelated systems interact by symmetric dynamics and asymmetry is created at one subsystem, then the asymmetry of the other subsystem must be reduced. We also find a quantitative relation describing the trade-off between the subsystems. These results cannot be understood in terms of additivity of asymmetry, because, as we show here, any faithful measure of asymmetry violates both subadditivity and superadditivity. Rather, they must be understood as a consequence of an (intrinsically quantum) information-disturbance principle. Our result also implies that if a bounded-size quantum reference frame for the symmetry group, or equivalently, a bounded-size reservoir of coherence (e.g., a clock with coherence between energy eigenstates in quantum thermodynamics) is used to implement any operation that is not symmetric, then the quantum state of the frame or reservoir is necessarily disturbed in an irreversible fashion, i.e., degraded.
封闭系统和开放系统动力学的对称性都意味着许多重要的限制。这些限制通常在经典动力学和量子动力学中都有实例（例如，诺特定理适用于这两种动力学）。我们在此提供一个这样的限制的例子，它在经典系统中没有对应物，也就是说，这是对称动力学的一个独特的量子结果。具体而言，对于有界规模的量子系统，我们证明了相对于连续对称群广播不对称性（对称性破缺）是不可能的。这个不可行定理表明，如果两个初始不相关的系统通过对称动力学相互作用，并且在一个子系统中产生了不对称性，那么另一个子系统的不对称性必然会减小。我们还发现了一个定量关系，描述了子系统之间的权衡。这些结果不能用不对称性的可加性来理解，因为正如我们在此所展示的，任何忠实的不对称性度量都违反了次可加性和超可加性。相反，它们必须被理解为（本质上是量子的）信息干扰原理的结果。我们的结果还意味着，如果使用有界规模的对称群量子参考系，或者等效地，有界规模的相干源（例如，量子热力学中具有能量本征态之间相干性的时钟）来执行任何不对称的操作，那么参考系或源的量子态必然会以不可逆的方式受到干扰，即退化。
