Perfect Strategies for Non-Local Games

We describe the main classes of non-signalling bipartite correlations in terms of states on operator system tensor products. This leads to the introduction of another new class of games, called reflexive games, which are characterised as the hardest non-local games that can be won using a given set of strategies. We provide a characterisation of their perfect strategies in terms of operator system quotients. We introduce a new class of non-local games, called imitation games, in which the players display linked behaviour, and which contain as subclasses the classes of variable assignment games, binary constraint system games, synchronous games, many games based on graphs, and unique games. We associate a C*-algebra C∗(G) to any imitation game G, and show that the existence of perfect quantum commuting (resp. quantum, local) strategies of G can be characterised in terms of properties of this C*-algebra. We single out a subclass of imitation games, which we call mirror games, and provide a characterisation of their quantum commuting strategies that has an algebraic flavour, showing in addition that their approximately quantum perfect strategies arise from amenable traces on the encoding C*-algebra

Dynamics of Metal Centers Monitored by Nuclear Inelastic Scattering

Nuclear inelastic scattering of synchrotron radiation has been used now since 10 years as a tool for vibrational spectroscopy. This method has turned out especially useful in case of large molecules that contain a M\"ossbauer active metal center. Recent applications to iron-sulfur proteins, to iron(II) spin crossover complexes and to tin-DNA complexes are discussed. Special emphasis is given to the combination of nuclear inelastic scattering and density functional calculations

Typical local measurements in generalised probabilistic theories: emergence of quantum bipartite correlations

What singles out quantum mechanics as the fundamental theory of Nature? Here we study local measurements in generalised probabilistic theories (GPTs) and investigate how observational limitations affect the production of correlations. We find that if only a subset of typical local measurements can be made then all the bipartite correlations produced in a GPT can be simulated to a high degree of accuracy by quantum mechanics. Our result makes use of a generalisation of Dvoretzky's theorem for GPTs. The tripartite correlations can go beyond those exhibited by quantum mechanics, however.Comment: 5 pages, 1 figure v2: more details in the proof of the main resul

Theoretical framework for quantum networks

We present a framework to treat quantum networks and all possible transformations thereof, including as special cases all possible manipulations of quantum states, measurements, and channels, such as, e.g., cloning, discrimination, estimation, and tomography. Our framework is based on the concepts of quantum comb-which describes all transformations achievable by a given quantum network-and link product-the operation of connecting two quantum networks. Quantum networks are treated both from a constructive point of view-based on connections of elementary circuits-and from an axiomatic one-based on a hierarchy of admissible quantum maps. In the axiomatic context a fundamental property is shown, which we call universality of quantum memory channels: any admissible transformation of quantum networks can be realized by a suitable sequence of memory channels. The open problem whether this property fails for some nonquantum theory, e.g., for no-signaling boxes, is posed.Comment: 23 pages, revtex

Dynamics and thermalization of the nuclear spin bath in the single-molecule magnet Mn12-ac: test for the theory of spin tunneling

The description of the tunneling of a macroscopic variable in the presence of a bath of localized spins is a subject of great fundamental and practical interest, and is relevant for many solid-state qubit designs. Instead of focusing on the the "central spin" (as is most often done), here we present a detailed study of the dynamics of the nuclear spin bath in the Mn12-ac single-molecule magnet, probed by NMR experiments down to very low temperatures (T = 20 mK). We find that the longitudinal relaxation rate of the 55Mn nuclei in Mn12-ac becomes roughly T-independent below T = 0.8 K, and can be strongly suppressed with a longitudinal magnetic field. This is consistent with the nuclear relaxation being caused by quantum tunneling of the molecular spin, and we attribute the tunneling fluctuations to the minority of fast-relaxing molecules present in the sample. The transverse nuclear relaxation is also T-independent for T < 0.8 K, and can be explained qualitatively and quantitatively by the dipolar coupling between like nuclei in neighboring molecules. We also show that the isotopic substitution of 1H by 2H leads to a slower nuclear longitudinal relaxation, consistent with the decreased tunneling probability of the molecular spin. Finally, we demonstrate that, even at the lowest temperatures, the nuclear spins remain in thermal equilibrium with the lattice phonons, and we investigate the timescale for their thermal equilibration. After a review of the theory of macroscopic spin tunneling in the presence of a spin bath, we argue that most of our experimental results are consistent with that theory, but the thermalization of the nuclear spins is not.Comment: 24 pages, 18 figures. Experimental study of the spin bath dynamics in quantum nanomagnets, plus an extensive review and application of the theor

Minimum error discrimination of Pauli channels

We solve the problem of discriminating with minimum error probability two given Pauli channels. We show that, differently from the case of discrimination between unitary transformations, the use of entanglement with an ancillary system can strictly improve the discrimination, and any maximally entangled state allows to achieve the optimal discrimination. We also provide a simple necessary and sufficient condition in terms of the structure of the channels for which the ultimate minimum error probability can be achieved without entanglement assistance. When such a condition is satisfied, the optimal input state is simply an eigenstate of one of the Pauli matrices.Comment: 8 pages, no figure

Probabilistic theories with purification

We investigate general probabilistic theories in which every mixed state has a purification, unique up to reversible channels on the purifying system. We show that the purification principle is equivalent to the existence of a reversible realization of every physical process, namely that every physical process can be regarded as arising from a reversible interaction of the system with an environment, which is eventually discarded. From the purification principle we also construct an isomorphism between transformations and bipartite states that possesses all structural properties of the Choi-Jamiolkowski isomorphism in quantum mechanics. Such an isomorphism allows one to prove most of the basic features of quantum mechanics, like e.g. existence of pure bipartite states giving perfect correlations in independent experiments, no information without disturbance, no joint discrimination of all pure states, no cloning, teleportation, no programming, no bit commitment, complementarity between correctable channels and deletion channels, characterization of entanglement-breaking channels as measure-and-prepare channels, and others, without resorting to the mathematical framework of Hilbert spaces.Comment: Differing from the journal version, this version includes a table of contents and makes extensive use of boldface type to highlight the contents of the main theorems. It includes a self-contained introduction to the framework of general probabilistic theories and a discussion about the role of causality and local discriminabilit

Precision Subsampling System for Mars Surface Missions

The ability to analyze heterogeneous rock samples at fine spatial scales would represent a powerful addition to our planetary in situ analytical toolbox. This is particularly true for Mars, where the signatures of past environments and, potentially, habitability are preserved in chemical and morphological variations across sedimentary layers and among mineral pr.ases in a given rock specimen. On Earth, microbial life often associates with surfaces at the interface of chemical nutrients, and ultimately retains sub-millimeter to millimeter-scale layer confinement in fossilization. On Mars, and possibly other bodies, trace chemical markers (elemental, organic/molecular, isotopic, chiral, etc.) and fine-scale morphological markers (e.g., micro-fossils) may he too subtle, degraded, or ambiguous to be detected, using miniaturized instrumentation, without some concentration or isolation. This is because (i) instrument sensitivity may not be high enough to detect trace markers in bulk averages; and (ii) instrument s~lectiviry may not be sufficient to distinguish such markers from interfering/counteracting signals from the bulk. Moreover from a fundamental chemostratigraphic perspective there would be a great benefit to assessing specific chemical and stable isotopic gradients, over millimeter-to-centimeter scales and beyond, with higher precision than currently possible in situ. We have developed a precision subsampling system (PSS) that addresses this need while remaining relatively flexible to a variety of instruments that may take advantage of the capability on future missions. The PSS is relevant to a number of possible lander/rover missions, especially Mars Sample Return. Our specific PSS prototype is undergoing testing under Mars ambient conditions, on a variety of natural analog rocks and rock drill cores, using a set of complementary flight-compatible measurement techniques. The system is available for testing with other contact instruments that may benefit from precision sampling