D-outcome measurement for a nonlocality test

For the purpose of the nonlocality test, we propose a general correlation observable of two parties by utilizing local $d$-outcome measurements with SU($d$) transformations and classical communications. Generic symmetries of the SU($d$) transformations and correlation observables are found for the test of nonlocality. It is shown that these symmetries dramatically reduce the number of numerical variables, which is important for numerical analysis of nonlocality. A linear combination of the correlation observables, which is reduced to the Clauser-Horne-Shimony-Holt (CHSH) Bell's inequality for two outcome measurements, is led to the Collins-Gisin-Linden-Massar-Popescu (CGLMP) nonlocality test for $d$-outcome measurement. As a system to be tested for its nonlocality, we investigate a continuous-variable (CV) entangled state with $d$ measurement outcomes. It allows the comparison of nonlocality based on different numbers of measurement outcomes on one physical system. In our example of the CV state, we find that a pure entangled state of any degree violates Bell's inequality for $d(\ge 2)$ measurement outcomes when the observables are of SU($d$) transformations.Comment: 16 pages, 2 figure

Response of strongly-interacting matter to magnetic field: some exact results

We derive some exact results concerning the response of strongly-interacting matter to external magnetic fields. Our results come from consideration of triangle anomalies in medium. First, we define an "axial magnetic susceptibility," then we examine its beahvior in two flavor QCD via response theory. In the chirally restored phase, this quantity is proportional to the fermion chemical potential, while in the phase of broken chiral symmetry it can be related, through triangle anomalies, to an in-medium amplitude for the neutral pion to decay to two photons. We confirm the latter result by calculation in a linear sigma model, where this amplitude is already known in the literature.Comment: 13 pages, no figures, To be submitted to Physical Review D, fixed an omitted referenc

An Analysis of the Search Spaces for Generate and Validate Patch Generation Systems

We present the first systematic analysis of the characteristics of patch search spaces for automatic patch generation systems. We analyze the search spaces of two current state-of-the-art systems, SPR and Prophet, with 16 different search space configurations. Our results are derived from an analysis of 1104 different search spaces and 768 patch generation executions. Together these experiments consumed over 9000 hours of CPU time on Amazon EC2. The analysis shows that 1) correct patches are sparse in the search spaces (typically at most one correct patch per search space per defect), 2) incorrect patches that nevertheless pass all of the test cases in the validation test suite are typically orders of magnitude more abundant, and 3) leveraging information other than the test suite is therefore critical for enabling the system to successfully isolate correct patches. We also characterize a key tradeoff in the structure of the search spaces. Larger and richer search spaces that contain correct patches for more defects can actually cause systems to find fewer, not more, correct patches. We identify two reasons for this phenomenon: 1) increased validation times because of the presence of more candidate patches and 2) more incorrect patches that pass the test suite and block the discovery of correct patches. These fundamental properties, which are all characterized for the first time in this paper, help explain why past systems often fail to generate correct patches and help identify challenges, opportunities, and productive future directions for the field

X-ray Raman compression via two-stream instability in dense plasmas

A Raman compression scheme suitable for x-rays, where the Langmuir wave is created by an intense beam rather than the pondermotive potential between the seed and pump pulses, is proposed. The required intensity of the seed and pump pulses enabling the compression could be mitigated by more than a factor of 100, compared to conventionally available other Raman compression schemes. The relevant wavelength of x-rays ranges from 1 to 10 nm