21pAN-8 On information ows in quantum measurement from the view point of the relative entropy

Alexandre Baraviera, Carlos F. Lardizabal, Artur Oscar Lopes +1 more

Kenjiro Yanagi

Fedor Herbut

The well-known two-slit interference is understood as a special relation between an observable (localization at the slits) and a state (being on both slits). The relation between an observable and a quantum state is investigated in the general case. It is assumed that the amount of coherence equals that of the incompatibility between an observable and a state. On these grounds, an argument is presented that leads to a natural quantum measure of coherence, called 'coherence or incompatibility information'. Its properties are studied in detail, making use of 'the mixing property of relative entropy' derived in this paper. A precise relation between the measure of coherence of an observable and that of its coarsening is obtained and discussed from the intuitive point of view. Convexity of the measure is proved, and thus the fact that it is an information entity is established. A few more detailed properties of the coherence information are derived with a view to investigating the final-state entanglement in general repeatable measurement, and, more importantly, general bipartite entanglement in follow-ups of this study.

Masashi Ban

Abstract. The well-known two-slit interference is understood as a special relation between observable (localization at the slits) and state (being on both slits). Relation between an observable and a quantum state is investigated in the general case. It is assumed that the amount of coherence equals that of incompatibility between observable and state. On ground of this, an argument is presented that leads to a natural quantum measure of coherence, called ”coherence or incompatibility information”. Its properties are studied in detail making use of ’the mixing property of relative entropy ’ derived in this article. A precise relation between the measure of coherence of an observable and that of its coarsening is obtained and discussed from the intuitive point of view. Convexity of the measure is proved, and thus the fact that it is an information entity is established. A few more detailed properties of coherence information are derived with a view to investigate final-state entanglement in general repeatable measurement, and, more importantly, general bipartite entanglement in follow ups of this study.

James Fullwood

We construct a 2-categorical extension of the relative entropy functor of Baez and Fritz, and show that our construction is functorial with respect to vertical morphisms. Moreover, we show such a ‘2-relative entropy’ satisfies natural 2-categorial analogues of convex linearity, vanishing under optimal hypotheses, and lower semicontinuity. While relative entropy is a relative measure of information between probability distributions, we view our construction as a relative measure of information between channels.