Lostaglio Matteo, Müller Markus P
ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, Castelldefels (Barcelona) 08860, Spain.
Institute for Quantum Optics and Quantum Information, Austrian Academy of Sciences, Boltzmanngasse 3, A-1090 Vienna, Austria.
Phys Rev Lett. 2019 Jul 12;123(2):020403. doi: 10.1103/PhysRevLett.123.020403.
In the presence of conservation laws, superpositions of eigenstates of the corresponding conserved quantities cannot be generated by quantum dynamics. Thus, any such coherence represents a potentially valuable resource of asymmetry, which can be used, for example, to enhance the precision of quantum metrology or to enable state transitions in quantum thermodynamics. Here we ask if such superpositions, already present in a reference system, can be broadcast to other systems, thereby distributing asymmetry indefinitely at the expense of creating correlations. We prove a no-go theorem showing that this is forbidden by quantum mechanics in every finite-dimensional system. In doing so, we also answer some open questions in the quantum information literature concerning the sharing of timing information of a clock and the possibility of catalysis in quantum thermodynamics. We also prove that even weaker forms of broadcasting, of which Åberg's "catalytic coherence" is a particular example, can only occur in the presence of infinite-dimensional reference systems. Our results set fundamental limits on the creation and manipulation of quantum coherence and shed light on the possibilities and limitations of quantum reference frames to act catalytically without being degraded.
在守恒定律存在的情况下，相应守恒量的本征态叠加不能由量子动力学产生。因此，任何这样的相干性都代表了一种潜在的有价值的不对称资源，例如可用于提高量子计量的精度或实现量子热力学中的态跃迁。在这里，我们要问的是，已经存在于参考系统中的这种叠加是否可以广播到其他系统，从而以创建相关性为代价无限期地分配不对称性。我们证明了一个不可行定理，表明在每个有限维系统中，这都被量子力学所禁止。在此过程中，我们还回答了量子信息文献中一些关于时钟定时信息共享以及量子热力学中催化可能性的开放性问题。我们还证明，即使是更弱形式的广播（其中阿贝格的“催化相干性”就是一个特殊例子），也只能在存在无限维参考系统的情况下发生。我们的结果为量子相干性的创建和操纵设定了基本限制，并阐明了量子参考系在不退化的情况下进行催化作用的可能性和局限性。
