Dynamical resource theory of quantum coherence
Dynamical resource theory of quantum coherence
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DOI：
10.1103/physrevresearch.2.023298
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发表时间：
2019-10
影响因子：
4.2
通讯作者：
G. Saxena;E. Chitambar;G. Gour
中科院分区：
文献类型：
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作者：
G. Saxena;E. Chitambar;G. Gour
消相干在我们周围随处可见。每一个与环境相互作用的量子系统都注定要在这里破译。量子相干的保持是量子技术面临的主要挑战之一，但它作为一种资源的使用非常有前途，可以带来各种操作优势，例如在量子算法中。因此，近年来，人们致力于量化系统中存在的一致性。在本文中，我们阐述了动力学相干性的量子资源理论。我们遵循的基本物理原理是，自由动力学物体是那些不能保持或分配相干性的物体。这导致我们将经典频道确定为该理论中的自由元素。因此，即使是量子身份通道也不是免费的，因为所有的物理系统都经历了退相干，因此，保持相干性应该被视为一种资源。在我们的工作中，我们介绍了四种不同类型的自由超通道(类似于MIO、DIO、IO和SIO)，并详细讨论了其中的两种，即退相协变非相干超通道(DISC)、最大非相干超通道(MISC)。后者由不从经典通道生成非经典通道的所有超通道组成。对于MISC和DISC，我们使用基于通道散度的单调来量化动态相干性。我们证明了其中的一些单调具有精确的、近似的和自由的量子通道的相干成本。此外，我们还证明了信道的自由渐近代价等于一种新的正则化相对熵。最后，我们证明了在MISC和DISC下，两个通道之间的转换距离可以使用半定程序(SDP)来计算。
Decoherence is all around us. Every quantum system that interacts with the environment is doomed to decohere. The preservation of quantum coherence is one of the major challenges faced in quantum technologies, but its use as a resource is very promising and can lead to various operational advantages, for example in quantum algorithms. Hence, much work has been devoted in recent years to quantify the coherence present in a system. In the present paper, we formulate the quantum resource theory of dynamical coherence. The underlying physical principle we follow is that the free dynamical objects are those that cannot preserve or distribute coherence. This leads us to identify classical channels as the free elements in this theory. Consequently, even the quantum identity channel is not free as all physical systems undergo decoherence and hence, the preservation of coherence should be considered a resource. In our work, we introduce four different types of free superchannels (analogous to MIO, DIO, IO, and SIO) and discuss in detail two of them, namely, dephasing-covariant incoherent superchannels (DISC), maximally incoherent superchannels (MISC). The latter consists of all superchannels that do not generate non-classical channels from classical ones. We quantify dynamical coherence using channel-divergence-based monotones for MISC and DISC. We show that some of these monotones have operational interpretations as the exact, the approximate, and the liberal coherence cost of a quantum channel. Moreover, we prove that the liberal asymptotic cost of a channel is equal to a new type of regularized relative entropy. Finally, we show that the conversion distance between two channels under MISC and DISC can be computed using a semi-definite program (SDP).