Strong converse exponents for a quantum channel discrimination problem and quantum-feedback-assisted communication

This paper studies the difficulty of discriminating between an arbitrary quantum channel and a "replacer" channel that discards its input and replaces it with a fixed state. We show that, in this particular setting, the most general adaptive discrimination strategies provide no asymptotic advantage over non-adaptive tensor-power strategies. This conclusion follows by proving a quantum Stein's lemma for this channel discrimination setting, showing that a constant bound on the Type I error leads to the Type II error decreasing to zero exponentially quickly at a rate determined by the maximum relative entropy registered between the channels. The strong converse part of the lemma states that any attempt to make the Type II error decay to zero at a rate faster than the channel relative entropy implies that the Type I error necessarily converges to one. We then refine this latter result by identifying the optimal strong converse exponent for this task. As a consequence of these results, we can establish a strong converse theorem for the quantum-feedback-assisted capacity of a channel, sharpening a result due to Bowen. Furthermore, our channel discrimination result demonstrates the asymptotic optimality of a non-adaptive tensor-power strategy in the setting of quantum illumination, as was used in prior work on the topic. The sandwiched Renyi relative entropy is a key tool in our analysis. Finally, by combining our results with recent results of Hayashi and Tomamichel, we find a novel operational interpretation of the mutual information of a quantum channel N as the optimal type II error exponent when discriminating between a large number of independent instances of N and an arbitrary "worst-case" replacer channel chosen from the set of all replacer channels.Comment: v3: 35 pages, 4 figures, accepted for publication in Communications in Mathematical Physic

“You’ve Got a Friend in Me”: Helping Students Help AI

ChatGPT and its family of generative tools may seem new, but the process that ChatGPT imitates is as old as Egyptian papyri: The end-user still had to adapt the form text to each person’s unique situation. Similarly, modern attorneys may use AI to adapt legal documents to their clients’ needs. But they must also learn how to spot problems in AI-generated documents — omissions, wrongful additions, inaccurate law, legalese, and poor typography. They need to instruct ChatGPT or other generative AI to continue revising until the document reflects best practices. In short, our students as future attorneys need to know how to help AI be helpful. A student who hasn’t learned how to approach drafting or redrafting a good legal document will be at AI’s mercy rather than being able to use the AI tech to create good documents. A clueless student using AI is really no better off than generations of lawyers who have blindly recycled old forms that are full of problems. Specifically, Charles and Cooney’s presentation will cover these topics: Brief history of legal forms (positive and negative) Survey results of how other disciplines are using AI A real-to-life positive approach to working with AI to generate legal documents Experience from incorporating AI into teaching Research & Writing, Advocacy, and Drafting How to arm students with knowledge about what makes a document sound, navigable, and enforceabl

The Proposed U.S.-South Korea Free Trade Agreement (KORUS FTA): Provisions and Implications

On June 30, 2007, United States Trade Representative Susan Schwab and South Korean Foreign Trade Minister Kim Hyung-chong signed the proposed U.S.-South Korean Free Trade Agreement (KORUS FTA) for their respective countries. If approved, the KORUS FTA would be the largest FTA that South Korea has signed to date and would be the second largest (next to North American Free Trade Agreement NAFTA) in which the United States participates. South Korea is the seventh-largest trading partner of the United States and the United States is South Korea’s third largest trading partner. Various studies conclude that the agreement would increase bilateral trade and investment flows. The final text of the proposed KORUS FTA covers a wide range of trade and investment issues and, therefore, could have wide economic implications for both the United States and South Korea. The KORUS FTA includes issues on which the two countries achieved early agreement, such as the elimination on tariffs on trade in most manufactured goods and the partial liberalization in services trade. The agreement also includes provisions on a number of very sensitive issues, such as autos, agriculture, and trade remedies, on which agreement was reached only during the final hours of negotiations. If the agreement is to enter into force, Congress will have to approve implementation legislation. The negotiations were conducted under the trade promotion authority (TPA), also called fast-track trade authority, that the Congress granted the President under the Bipartisan Trade Promotion Act of 2002 (P.L. 107-210). The authority allows the President to enter into trade agreements that receive expedited congressional consideration (no amendments and limited debate). The White House has not indicated when it will send the draft implementing legislation to Congress. (The TPA sets no deadline for the President to do this.) While a broad swath of the U.S. business community supports the agreement, the KORUS FTA faces opposition from some groups, including some auto and steel manufacturers and labor unions. In addition, the agricultural community and some Members of Congress have withheld support for the agreement until South Korea lifts its restrictions on imports of U.S. beef. Some U.S. supporters view passage of the KORUS FTA as important to secure new opportunities in the South Korea market. Opponents claim that the KORUS FTA does not go far enough in opening up the South Korean market and is a lost opportunity to resolve long running concerns about South Korean barriers. Other observers have suggested the outcome of the KORUS FTA could have implications for the U.S.-South Korean alliance as a whole. Differences between the White House and the Democratic leadership in the Congress over the implications of the KORUS FTA have made the timing and even the likelihood of the President’s submission and the Congress’s subsequent consideration of implementing legislation uncertain. This report will be updated as events warrant

Analyzing large-scale conservation interventions with Bayesian hierarchical models: a case study of supplementing threatened Pacific salmon.

Myriad human activities increasingly threaten the existence of many species. A variety of conservation interventions such as habitat restoration, protected areas, and captive breeding have been used to prevent extinctions. Evaluating the effectiveness of these interventions requires appropriate statistical methods, given the quantity and quality of available data. Historically, analysis of variance has been used with some form of predetermined before-after control-impact design to estimate the effects of large-scale experiments or conservation interventions. However, ad hoc retrospective study designs or the presence of random effects at multiple scales may preclude the use of these tools. We evaluated the effects of a large-scale supplementation program on the density of adult Chinook salmon Oncorhynchus tshawytscha from the Snake River basin in the northwestern United States currently listed under the U.S. Endangered Species Act. We analyzed 43 years of data from 22 populations, accounting for random effects across time and space using a form of Bayesian hierarchical time-series model common in analyses of financial markets. We found that varying degrees of supplementation over a period of 25 years increased the density of natural-origin adults, on average, by 0-8% relative to nonsupplementation years. Thirty-nine of the 43 year effects were at least two times larger in magnitude than the mean supplementation effect, suggesting common environmental variables play a more important role in driving interannual variability in adult density. Additional residual variation in density varied considerably across the region, but there was no systematic difference between supplemented and reference populations. Our results demonstrate the power of hierarchical Bayesian models to detect the diffuse effects of management interventions and to quantitatively describe the variability of intervention success. Nevertheless, our study could not address whether ecological factors (e.g., competition) were more important than genetic considerations (e.g., inbreeding depression) in determining the response to supplementation

Eggshell pigment composition covaries with phylogeny but not with life history or with nesting ecology traits of British passerines

No single hypothesis is likely to explain the diversity in eggshell coloration and patterning across birds, suggesting that eggshell appearance is most likely to have evolved to fulfill many nonexclusive functions. By controlling for nonindependent phylogenetic associations between related species, we describe this diversity using museum eggshells of 71 British breeding passerine species to examine how eggshell pigment composition and concentrations vary with phylogeny and with life-history and nesting ecology traits. Across species, concentrations of biliverdin and protoporphyrin, the two main pigments found in eggshells, were strongly and positively correlated, and both pigments strongly covaried with phylogenetic relatedness. Controlling for phylogeny, cavity-nesting species laid eggs with lower protoporphyrin concentrations in the shell, while higher biliverdin concentrations were associated with thicker eggshells for species of all nest types. Overall, these relationships between eggshell pigment concentrations and the biology of passerines are similar to those previously found in nonpasserine eggs, and imply that phylogenetic dependence must be considered across the class in further explanations of the functional significance of avian eggshell coloration

Antibacterial Properties of a Tri-Sodium Citrate Modified Glass Polyalkenoate Cement

Primary deep infection following joint replacement surgery accounts for 7% of all revisions. Glass polyalkenoate cements (GPCs) have previously been shown to exhibit antibacterial properties. The present study had two objectives. The first was to determine if addition of tri-sodium citrate (TSC) to the powder phase of an Al-free GPC (0.04 SrO-0.12 CaO-0.36 ZnO-0.48 SiO2, by mole fraction) enhanced the resultant cement\u27s antibacterial properties against three strains of bacteria that are commonly found in periprosthetic sites following total joint replacements (TJRs); namely, E. coli, B. fragilis, and S. epidermidis. Four cement sets were prepared, which contained 0 wt% TSC (control), 5 wt% TSC, 10 wt% TSC, and 15 wt% TSC. All the TSC-modified cements were found to exhibit large inhibition zones against all the bacterial strains, especially the cement containing 15 wt% TSC against E. coli. The antibacterial properties of the TSC containing GPCs are attributed to the release of Zn and Na ions from the cements and the presence of the TSC. The second objective was to investigate if, when a modified GPC is embedded in a bovine bone model, ionic transfer occurs. It was found that Zn ions migrated from the cement to the surrounding bone, particularly at the cement-bone interface. This is a desirable outcome as Zn ions are known to play a vital role in both bone metabolism and the regeneration of healthy bone. The present results point to the potential clinical benefits of using TSC-modified GPCs in TJRs. © 2009 Wiley Periodicals, Inc

Strong converse exponents for a quantum channel discrimination problem and quantum-feedback-assisted communication.

Summary: We study the difficulty of discriminating between an arbitrary quantum channel and a "replacer" channel that discards its input and replaces it with a fixed state. Background: Quantum channel discrimination is a natural extension of a basic problem in quantum hypothesis testing, that of distinguishing between the possible states of a quantum system. In an i.i.d. binary state discrimination problem, the discriminator is provided with n quantum systems in the state ρ ⊗n or σ ⊗n , and the task is to apply a binary measurement {Q n , I ⊗n − Q n } to these n systems, with 0 ≤ Q n ≤ I ⊗n . One is then concerned with two kinds of error probabilities: α n (Q n ) ≡ Tr {(I ⊗n − Q n )ρ ⊗n } , the probability of incorrectly rejecting the null hypothesis, the Type I error, and β n (Q n ) ≡ Tr {Q n σ ⊗n } , the probability of incorrectly rejecting the alternative hypothesis, the Type II error. One studies the asymptotic behaviour of α n and β n as n → ∞, expecting there to be a trade-off between minimising α n and minimising β n . In quantum channel discrimination, we have a quantum channel with input system A and output system B, and we are given that the channel is described by either the completely positive trace-1 A more detailed version of this work is available on the arXiv