Gleason-Busch theorem for sequential measurements

Gleason's theorem is a statement that, given some reasonable assumptions, the Born rule used to calculate probabilities in quantum mechanics is essentially unique [A. M. Gleason, Indiana Univ. Math. J. 6, 885 (1957)]. We show that Gleason's theorem contains within it also the structure of sequential measurements, and along with this the state update rule. We give a small set of axioms, which are physically motivated and analogous to those in Busch's proof of Gleason's theorem [P. Busch, Phys. Rev. Lett. 91, 120403 (2003)], from which the familiar Kraus operator form follows. An axiomatic approach has practical relevance as well as fundamental interest, in making clear those assumptions which underlie the security of quantum communication protocols. Interestingly, the two-time formalism is seen to arise naturally in this approach

Adaptation, Legal Resiliency, and the U.S. Army Corps of Engineers: Managing Water Supply in a Climate-Altered World

There are existing legal systems that embody planned resiliency. One of these is the multiple-use paradigm, which instructs resource managers to manage resources to maximize their multiple uses. Despite this built-in resiliency into practice. One of these agencies, the United States Army Corps of Engineers, is charged with managing water storage throughout much of the United States for multiple purposes, including human needs, agriculture, transportation, recreation, electricity generation, habitat, and the environment. This Article examines the Corps\u27 history in managing this water storage and shows that the Corps is currently ill equipped to administer its requirements with resilience. Given the expected demographic growth and climate-changed future, these problems are only going to grow worse. This Article analyzes the potential obstacles to effective, resilient management and makes suggestions about how the Corps, and ultimately other agencies, can effectively make their administrative systems more adaptive and thus better suited to meet new demands

A microfabricated sensor for thin dielectric layers

We describe a sensor for the measurement of thin dielectric layers capable of operation in a variety of environments. The sensor is obtained by microfabricating a capacitor with interleaved aluminum fingers, exposed to the dielectric to be measured. In particular, the device can measure thin layers of solid frozen from a liquid or gaseous medium. Sensitivity to single atomic layers is achievable in many configurations and, by utilizing fast, high sensitivity capacitance read out in a feedback system onto environmental parameters, coatings of few layers can be dynamically maintained. We discuss the design, read out and calibration of several versions of the device optimized in different ways. We specifically dwell on the case in which atomically thin solid xenon layers are grown and stabilized, in cryogenic conditions, from a liquid xenon bath

Two-time state formalism for quantum eavesdropping

The key piece of knowledge which quantum eavesdroppers can access is the correlation between prior and future events, i.e., the postselected results of the legitimate preparations and measurements. We present a method for optimizing eavesdropping strategies which is closely related to the two-time state formalism, the natural way to analyze such scenarios; it converts the task of optimization into an eigenvalue problem. Our framework is applied to the familiar BB84 and B92 protocols as well as to the largely unexplored three-state scheme, which has a remarkable feature: the best eavesdropping strategy does not extract any information about the sent state

Multiple-copy state discrimination of noisy qubits

Multiple-copy state discrimination is a fundamental task in quantum information processing. If there are two, pure, nonorthogonal states then both local and collective schemes are known to reach the Helstrom bound, the maximum probability of successful discrimination allowed by quantum theory. For mixed states, it is known that only collective schemes can perform optimally, so it might be expected that these schemes are more resilient to preparation noise. We calculate the probability of success for two schemes, a local scheme based on Bayesian updating and quantum data gathering, the simplest possible collective measurement, and consider imperfect preparation fidelity. We find two surprising results. First, both schemes converge upon the same many-copy limit, which is less than unity. Second, the local scheme performs better in all cases. This highlights the point that one should take into account noise when designing state discrimination schemes

Amino acid modulation of lifespan and reproduction in Drosophila

Manipulating amino acid (AA) intake in Drosophila can profoundly affect lifespan and reproduction. Remarkably, AA manipulation can uncouple the commonly observed trade-off between these traits. This finding seems to challenge the idea that this trade- off is due to competitive resource allocation, but here we argue that this view might be too simplistic. We also discuss the mechanisms of the AA response, mediated by the IIS/TOR and GCN2 pathways. Elucidating how these pathways respond to specific AA will likely yield important insights into how AA modulate the reproduction-lifespan relationship. The Drosophila model offers powerful genetic tools, combined with options for precise diet manipulation, to address these fundamental questions

Relatively Complete Counterexamples for Higher-Order Programs

In this paper, we study the problem of generating inputs to a higher-order program causing it to error. We first study the problem in the setting of PCF, a typed, core functional language and contribute the first relatively complete method for constructing counterexamples for PCF programs. The method is relatively complete in the sense of Hoare logic; completeness is reduced to the completeness of a first-order solver over the base types of PCF. In practice, this means an SMT solver can be used for the effective, automated generation of higher-order counterexamples for a large class of programs. We achieve this result by employing a novel form of symbolic execution for higher-order programs. The remarkable aspect of this symbolic execution is that even though symbolic higher-order inputs and values are considered, the path condition remains a first-order formula. Our handling of symbolic function application enables the reconstruction of higher-order counterexamples from this first-order formula. After establishing our main theoretical results, we sketch how to apply the approach to untyped, higher-order, stateful languages with first-class contracts and show how counterexample generation can be used to detect contract violations in this setting. To validate our approach, we implement a tool generating counterexamples for erroneous modules written in Racket.Comment: In Proceedings of the 36th annual ACM SIGPLAN conference on Programming Language Design and Implementation, Portland, Oregon, June 201