We establish an operational theory of coherence (or of superposition) in quantum systems, by focusing on the optimal rate of performance of certain tasks. Namely, we introduce the two basic concepts -"coherence distillation" and "coherence cost" in the processing quantum states under so-called incoherent operations [Baumgratz/Cramer/Plenio, Phys. Rev. Lett. 113:140401 (2014)]. We then show that in the asymptotic limit of many copies of a state, both are given by simple singleletter formulas: the distillable coherence is given by the relative entropy of coherence (in other words, we give the relative entropy of coherence its operational interpretation), and the coherence cost by the coherence of formation, which is an optimization over convex decompositions of the state. An immediate corollary is that there exists no bound coherent state in the sense that one would need to consume coherence to create the state but no coherence could be distilled from it. Further we demonstrate that the coherence theory is generically an irreversible theory by a simple criterion that completely characterizes all reversible states.PACS numbers: 03.65. Aa, 03.67.Mn Introduction.-The universality of the superposition principle is the fundamental non-classical characteristic of quantum mechanics: Given any configuration space X, its elements x label an orthogonal basis |x of a Hilbert space, and we have all superpositions x ψ x |x as the possible states of the system. In particular, we could choose a completely different orthonormal basis as an equally valid computational basis, in which to express the superpositions. However, often a basis is distinguished, be it the eigenbasis of an observable or of the system's Hamiltonian, so that conservation laws or even superselection rules apply. In such a case, the eigenstates |x are distinguished as "simple" and superpositions are "complex". Indeed, in the presence of conservation laws, structured superpositions of eigenstates can serve as so-called "reference frames", which are resources to overcome the conservation laws [1][2][3]. Based on this idea,Åberg [4] and more recently Baumgratz et al. [5] have proposed to consider any non-trivial superposition as a resource, and to create a theory in which computational basis states and their probabilistic mixtures are for free (or worthless), and operations preserving these "incoherent" states are free as well. This suggests that coherence theory can be regarded as a resource theory.Let us briefly recall the general structure of a quantum resource theory (QRT) and basic questions that be asked in a QRT through entanglement theory (ET), which is a well-known QRT. For our purposes, a QRT has three ingredients: (1) free states (separable state in ET), (2) resource states (entangled state in ET), (3) the restricted or free operations (LOCC in ET). A necessary requirement for a consistent QRT is that no resource state can be created from any free state under any free operation. The QRT is then the study of interconversion between resource states u...

A strong converse theorem for the classical capacity of a quantum channel states that the probability of correctly decoding a classical message converges exponentially fast to zero in the limit of many channel uses if the rate of communication exceeds the classical capacity of the channel. Along with a corresponding achievability statement for rates below the capacity, such a strong converse theorem enhances our understanding of the capacity as a very sharp dividing line between achievable and unachievable rates of communication. Here, we show that such a strong converse theorem holds for the classical capacity of all entanglement-breaking channels and all Hadamard channels (the complementary channels of the former). These results follow by bounding the success probability in terms of a "sandwiched" Rényi relative entropy, by showing that this quantity is subadditive for all entanglement-breaking and Hadamard channels, and by relating this quantity to the Holevo capacity. Prior results regarding strong converse theorems for particular covariant channels emerge as a special case of our results.

We demonstrate the decoy-state quantum key distribution (QKD) with one-way quantum communication in polarization space over 102 km. Further, we simplify the experimental setup and use only one detector to implement the one-way decoy-state QKD over 75 km, with the advantage to overcome the security loopholes due to the efficiency mismatch of detectors. Our experimental implementation can really offer the unconditionally secure final keys. We use 3 different intensities of 0, 0.2, and 0.6 for the light sources in our experiment. In order to eliminate the influences of polarization mode dispersion in the long-distance single-mode optical fiber, an automatic polarization compensation system is utilized to implement the active compensation.