01523nas a2200145 4500008003900000022001400039245004500053210004500098490000800143520111500151100001901266700002401285700002001309856004801329 2017 d a1364-502100aInterferometric visibility and coherence0 aInterferometric visibility and coherence0 v4733 aRecently, the basic concept of quantum coherence (or superposition) has gained a lot of renewed attention, after Baumgratz et al. (Phys. Rev. Lett. 113, 140401. (doi: 10.1103/PhysRevLett.113.140401)), following Aberg (http://arxiv.org/abs/quant-ph/0612146), have proposed a resource theoretic approach to quantify it. This has resulted in a large number of papers and preprints exploring various coherence monotones, and debating possible forms for the resource theory. Here, we take the view that the operational foundation of coherence in a state, be it quantum or otherwise wave mechanical, lies in the observation of interference effects. Our approach here is to consider an idealized multi-path interferometer, with a suitable detector, in such a way that the visibility of the interference pattern provides a quantitative expression of the amount of coherence in a given probe state. We present a general framework of deriving coherence measures from visibility, and demonstrate it by analysing several concrete visibility parameters, recovering some known coherence measures and obtaining some new ones.1 aBiswas, Tanmoy1 aDiaz, Maria, Garcia1 aWinter, Andreas uhttps://grupsderecerca.uab.cat/giq/node/84701611nas a2200157 4500008003900000022001400039245004800053210004600101490000700147520116500154100002101319700002401340700002101364700002001385856004801405 2017 d a2469-992600aResource theory of coherence: Beyon} states0 aResource theory of coherence Beyon states0 v953 aWe generalize the recently proposed resource theory of coherence (or superposition) [T. Baumgratz et al., Phys. Rev. Lett. 113, 140401 (2014); A. Winter and D. Yang, Phys. Rev. Lett. 116, 120404 ( 2016)] to the setting where not just the free (”incoherent”) resources, but also the manipulated objects, are quantum operations rather than states. In particular, we discuss an information theoretic notion of the coherence capacity of a quantum channel and prove a single-letter formula for it in the case of unitaries. Then we move to the coherence cost of simulating a channel and prove achievability results for unitaries and general channels acting on a d-dimensional system; we show that a maximally coherent state of rank d is always sufficient as a resource if incoherent operations are allowed, and one of rank d(2) for “strictly incoherent” operations. We also show lower bounds on the simulation cost of channels that allow us to conclude that there exists bound coherence in operations, i.e., maps with nonzero cost of implementing them but zero coherence capacity; this is in contrast to states, which do not exhibit bound coherence.

1 aBen Dana, Khaled1 aDiaz, Maria, Garcia1 aMejatty, Mohamed1 aWinter, Andreas uhttps://grupsderecerca.uab.cat/giq/node/848