Studies on the creation and destruction of coherence by quantum channels

Place: Room 203, Center for Theoretical Physics, Polish Academy of Sciences, Al. Lotników 32/46, 02-668 Warsaw, Poland

Zoom link: https://us06web.zoom.us/j/84427806931?pwd=ODBjZkNCUW94VUhCREFxbjRSeDBFdz09‍

Meeting ID: 844 2780 6931Access code: nisq‍

Abstract‍

I will talk about the studies on the creation and destruction of coherence by quantum channels. First, we will see how decoherence appears in matrix form through an example of a phase-damping channel on one qubit. This provides a qualitative perspective, serving as a good starting point. Next, we will briefly review the resource theory of coherence, explaining the basic framework and notion. To understand the ability of quantum channels to generate coherence, we begin by considering the cohering power and generalized cohering power of channels. These quantifiers have important operational meaning: the cohering power of a channel represents the minimum coherence in a state required to simulate the channel with incoherent channels. If the employed coherence quantifier is subadditive, the minimum coherence coincides with the generalized cohering power. This suggests that we can regard quantum coherence in a state plus incoherent operations as a quantum channel. It is natural to consider the reverse direction: can we identify a quantum channel as a resource of coherence? We will see a positive answer to this question by demonstrating that another type of measure, coherence generating capacity, quantifies how much maximally coherent state can be generated by a given channel and incoherent operations. The coherence-generating capacity is bounded by or equal to complete cohering power, which has a similar expression to generalized cohering power but is defined by taking into account coherence generation in the environment as well. I will present that complete cohering power and generalized cohering power are equal, which is also published in my earlier work.  In that paper, I also introduced completed decohering power defined in a similar way to study decoherence with taking into account decoherence in the environment as well too. I will show that, in some cases, entanglement between the system and environment enhances decoherence, which does not occur in the creation of coherence. Finally, I provide some ideas for future applications.

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