Sustainability assessment and complementarity

Sustainability assessments bring together different perspectives that pertain to sustainability in order to produce overall assessments and a wealth of approaches and tools have been developed in the past decades. But two major problematics remain. The problem of integration concerns the surplus of possibilities for integration; different tools produce different assessments. The problem of implementation concerns the barrier between assessment and transformation; assessments do not lead to the expected changes in practice. This paper aims to analyze issues of complementarity in sustainability assessment and transformation as a key to better handling the problems of integration and implementation. Based on a generalization of Niels Bohr’s complementarity from quantum mechanics, we have identified two forms of complementarity in sustainability assessment, observer stance complementarity and value complementarity. Unlike many other problems of sustainability assessment, complementarity is of a fundamental character connected to the very conditions for observation. Therefore complementarity cannot be overcome methodologically; only handled better or worse. Science is essential to the societal goal of sustainability, but these issues of complementarity impede the constructive role of science in the transition to more sustainable structures and practices in food systems. The agencies of sustainability assessment and transformation need to be acutely aware of the importance of different perspectives and values and the complementarities that may be connected to these differences. An improved understanding of complementarity can help to better recognize and handle issues of complementarity. These deliberations have relevance not only for sustainability assessment, but more generally for transdisciplinary research on wicked problems

Quark-lepton complementarity and self-complementarity in different schemes

With the progress of increasingly precise measurements on the neutrino mixing angles, phenomenological relations such as quark-lepton complementarity (QLC) among mixing angles of quarks and leptons and self-complementarity (SC) among lepton mixing angles have been observed. Using the latest global fit results of the quark and lepton mixing angles in the standard Chau-Keung scheme, we calculate the mixing angles and CP-violating phases in the other eight different schemes. We check the dependence of these mixing angles on the CP-violating phases in different phase schemes. The dependence of QLC and SC relations on the CP phase in the other eight schemes is recognized and then analyzed, suggesting that measurements on CP-violating phases of the lepton sector are crucial to the explicit forms of QLC and SC in different schemes.Comment: 11 pages, 3 figures, version accepted for publication in PR

When are signals complements or substitutes?

The paper introduces a notion of complementarity (substitutability) of two signals which requires that in all decision problems each signal becomes more (less) valuable when the other signal becomes available. We provide a general characterization which relates complementarity and substitutability to a Blackwell-comparison of two auxiliary signals. In a special setting with a binary state space and binary, symmetric signals, we find an explicit characterization that permits an intuitive interpretation of complementarity and substitutability. We demonstrate how these conditions extend to the general case. Finally, we study implications of complementarity and substitutability for information acquisition and in a second price auction

Role of complementarity in superdense coding

The complementarity of two observables is often captured in uncertainty relations, which quantify an inevitable tradeoff in knowledge. Here we study complementarity in the context of an information processing task: we link the complementarity of two observables to their usefulness for superdense coding (SDC). In SDC, Alice sends two classical dits of information to Bob by sending a single qudit. However, we show that encoding with commuting unitaries prevents Alice from sending more than one dit per qudit, implying that complementarity is necessary for SDC to be advantagous over a classical strategy for information transmission. When Alice encodes with products of Pauli operators for the $X$ and $Z$ bases, we quantify the complementarity of these encodings in terms of the overlap of the $X$ and $Z$ basis elements. Our main result explicitly solves for the SDC capacity as a function of the complementarity, showing that the entropy of the overlap matrix gives the capacity, when the preshared state is maximally entangled. We generalise this equation to resources with symmetric noise such as a preshared Werner state. In the most general case of arbitrary noisy resources, we obtain an analogous lower bound on the SDC capacity. Our results shed light on the role of complementarity in determining the quantum advantage in SDC and also seem fundamentally interesting since they bear a striking resemblance to uncertainty relations.Comment: 12 pages, 2 figures, title changed, close to published versio

Complementarity and Identification

This paper examines the identification power of assumptions that formalize the notion of complementarity in the context of a nonparametric bounds analysis of treatment response. I extend the literature on partial identification via shape restrictions by exploiting cross-dimensional restrictions on treatment response when treatments are multidimensional; the assumption of supermodularity can strengthen bounds on average treatment effects in studies of policy complementarity. This restriction can be combined with a statistical independence assumption to derive improved bounds on treatment effect distributions, aiding in the evaluation of complex randomized controlled trials. Complementarities arising from treatment effect heterogeneity can be incorporated through supermodular instrumental variables to strengthen identification in studies with one or multiple treatments. An application examining the long-run impact of zoning on the evolution of urban spatial structure illustrates the value of the proposed identification methods.Comment: 46 page

How much complementarity?

Bohr placed complementary bases at the mathematical centre point of his view of quantum mechanics. On the technical side then my question translates into that of classifying complex Hadamard matrices. Recent work (with Barros e Sa) shows that the answer depends heavily on the prime number decomposition of the Hilbert space. By implication so does the geometry of quantum state space.Comment: 6 pages; talk at the Vaxjo conference on Foundations of Probability and Physics, 201

Complementarity and correlations

We provide an interpretation of entanglement based on classical correlations between measurement outcomes of complementary properties: states that have correlations beyond a certain threshold are entangled. The reverse is not true, however. We also show that, surprisingly, all separable nonclassical states exhibit smaller correlations for complementary observables than some strictly classical states. We use mutual information as a measure of classical correlations, but we conjecture that the first result holds also for other measures (e.g. the Pearson correlation coefficient or the sum of conditional probabilities).Comment: Published version (+1 reference