From Low-Distortion Norm Embeddings to Explicit Uncertainty Relations and Efficient Information Locking

The existence of quantum uncertainty relations is the essential reason that some classically impossible cryptographic primitives become possible when quantum communication is allowed. One direct operational manifestation of these uncertainty relations is a purely quantum effect referred to as information locking. A locking scheme can be viewed as a cryptographic protocol in which a uniformly random n-bit message is encoded in a quantum system using a classical key of size much smaller than n. Without the key, no measurement of this quantum state can extract more than a negligible amount of information about the message, in which case the message is said to be "locked". Furthermore, knowing the key, it is possible to recover, that is "unlock", the message. In this paper, we make the following contributions by exploiting a connection between uncertainty relations and low-distortion embeddings of L2 into L1. We introduce the notion of metric uncertainty relations and connect it to low-distortion embeddings of L2 into L1. A metric uncertainty relation also implies an entropic uncertainty relation. We prove that random bases satisfy uncertainty relations with a stronger definition and better parameters than previously known. Our proof is also considerably simpler than earlier proofs. We apply this result to show the existence of locking schemes with key size independent of the message length. We give efficient constructions of metric uncertainty relations. The bases defining these metric uncertainty relations are computable by quantum circuits of almost linear size. This leads to the first explicit construction of a strong information locking scheme. Moreover, we present a locking scheme that is close to being implementable with current technology. We apply our metric uncertainty relations to exhibit communication protocols that perform quantum equality testing.Comment: 60 pages, 5 figures. v4: published versio

Equilibrium states and invariant measures for random dynamical systems

Random dynamical systems with countably many maps which admit countable Markov partitions on complete metric spaces such that the resulting Markov systems are uniformly continuous and contractive are considered. A non-degeneracy and a consistency conditions for such systems, which admit some proper Markov partitions of connected spaces, are introduced, and further sufficient conditions for them are provided. It is shown that every uniformly continuous Markov system associated with a continuous random dynamical system is consistent if it has a dominating Markov chain. A necessary and sufficient condition for the existence of an invariant Borel probability measure for such a non-degenerate system with a dominating Markov chain and a finite (16) is given. The condition is also sufficient if the non-degeneracy is weakened with the consistency condition. A further sufficient condition for the existence of an invariant measure for such a consistent system which involves only the properties of the dominating Markov chain is provided. In particular, it implies that every such a consistent system with a finite Markov partition and a finite (16) has an invariant Borel probability measure. A bijective map between these measures and equilibrium states associated with such a system is established in the non-degenerate case. Some properties of the map and the measures are given.Comment: The article is published in DCDS-A, but without the 3rd paragraph on page 4 (the complete removal of the paragraph became the condition for the publication in the DCDS-A after the reviewer ran out of the citation suggestions collected in the paragraph

Quantum Iterated Function Systems

Iterated functions system (IFS) is defined by specifying a set of functions in a classical phase space, which act randomly on an initial point. In an analogous way, we define a quantum iterated functions system (QIFS), where functions act randomly with prescribed probabilities in the Hilbert space. In a more general setting a QIFS consists of completely positive maps acting in the space of density operators. We present exemplary classical IFSs, the invariant measure of which exhibits fractal structure, and study properties of the corresponding QIFSs and their invariant states.Comment: 12 pages, 1 figure include

Effects of alirocumab on types of myocardial infarction: insights from the ODYSSEY OUTCOMES trial

AIMS: The third Universal Definition of Myocardial Infarction (MI) Task Force classified MIs into five types: Type 1, spontaneous; Type 2, related to oxygen supply/demand imbalance; Type 3, fatal without ascertainment of cardiac biomarkers; Type 4, related to percutaneous coronary intervention; and Type 5, related to coronary artery bypass surgery. Low-density lipoprotein cholesterol (LDL-C) reduction with statins and proprotein convertase subtilisin-kexin Type 9 (PCSK9) inhibitors reduces risk of MI, but less is known about effects on types of MI. ODYSSEY OUTCOMES compared the PCSK9 inhibitor alirocumab with placebo in 18 924 patients with recent acute coronary syndrome (ACS) and elevated LDL-C (>/=1.8 mmol/L) despite intensive statin therapy. In a pre-specified analysis, we assessed the effects of alirocumab on types of MI. METHODS AND RESULTS: Median follow-up was 2.8 years. Myocardial infarction types were prospectively adjudicated and classified. Of 1860 total MIs, 1223 (65.8%) were adjudicated as Type 1, 386 (20.8%) as Type 2, and 244 (13.1%) as Type 4. Few events were Type 3 (n = 2) or Type 5 (n = 5). Alirocumab reduced first MIs [hazard ratio (HR) 0.85, 95% confidence interval (CI) 0.77-0.95; P = 0.003], with reductions in both Type 1 (HR 0.87, 95% CI 0.77-0.99; P = 0.032) and Type 2 (0.77, 0.61-0.97; P = 0.025), but not Type 4 MI. CONCLUSION: After ACS, alirocumab added to intensive statin therapy favourably impacted on Type 1 and 2 MIs. The data indicate for the first time that a lipid-lowering therapy can attenuate the risk of Type 2 MI. Low-density lipoprotein cholesterol reduction below levels achievable with statins is an effective preventive strategy for both MI types

A Novel, “Double-Clamp” Binding Mode for Human Heme Oxygenase-1 Inhibition

The development of heme oxygenase (HO) inhibitors is critical in dissecting and understanding the HO system and for potential therapeutic applications. We have established a program to design and optimize HO inhibitors using structure-activity relationships in conjunction with X-ray crystallographic analyses. One of our previous complex crystal structures revealed a putative secondary hydrophobic binding pocket which could be exploited for a new design strategy by introducing a functional group that would fit into this potential site. To test this hypothesis and gain further insights into the structural basis of inhibitor binding, we have synthesized and characterized 1-(1H-imidazol-1-yl)-4,4-diphenyl-2-butanone (QC-308). Using a carbon monoxide (CO) formation assay on rat spleen microsomes, the compound was found to be ∼15 times more potent (IC50 = 0.27±0.07 µM) than its monophenyl analogue, which is already a potent compound in its own right (QC-65; IC50 = 4.0±1.8 µM). The crystal structure of hHO-1 with QC-308 revealed that the second phenyl group in the western region of the compound is indeed accommodated by a definitive secondary proximal hydrophobic pocket. Thus, the two phenyl moieties are each stabilized by distinct hydrophobic pockets. This “double-clamp” binding offers additional inhibitor stabilization and provides a new route for improvement of human heme oxygenase inhibitors

Cost-Effectiveness of Alirocumab in Patients With Acute Coronary Syndromes: The ODYSSEY OUTCOMES Trial.

BACKGROUND: Cholesterol reduction with proprotein convertase subtilisin-kexin type 9 inhibitors reduces ischemic events; however, the cost-effectiveness in statin-treated patients with recent acute coronary syndrome remains uncertain. OBJECTIVES: This study sought to determine whether further cholesterol reduction with alirocumab would be cost-effective in patients with a recent acute coronary syndrome on optimal statin therapy. METHODS: A cost-effectiveness model leveraging patient-level data from ODYSSEY OUTCOMES (Evaluation of Cardiovascular Outcomes After an Acute Coronary Syndrome During Treatment With Alirocumab) was developed to estimate costs and outcomes over a lifetime horizon. Patients (n = 18,924) had a recent acute coronary syndrome and were on high-intensity or maximum-tolerated statin therapy, with a baseline low-density lipoprotein cholesterol (LDL-C) level ?70 mg/dl, non-high-density lipoprotein cholesterol ?100 mg/dl, or apolipoprotein B ?80 mg/l. Alirocumab 75 mg or placebo was administered subcutaneously every 2 weeks. Alirocumab was blindly titrated to 150 mg if LDL-C remained ?50 mg/dl or switched to placebo if 2 consecutive LDL-C levels were <15 mg/dl. Incremental cost per quality-adjusted life-year (QALY) was determined with the addition of alirocumab versus placebo and, based on clinical efficacy findings from the trial, was stratified by baseline LDL-C levels ?100 mg/dl and <100 mg/dl. RESULTS: Across the overall population recruited to the ODYSSEY OUTCOMES trial, using an annual treatment cost of US$5,850, the mean overall incremental cost-effectiveness ratio was US$92,200 per QALY (base case). The cost was US$41,800 per QALY in patients with baseline LDL-C ?100 mg/dl, whereas in those with LDL-C <100 mg/dl the cost per QALY was US$299,400. Among patients with LDL-C ?100 mg/dl, incremental cost-effectiveness ratios remained below US$100,000 per QALY across a wide variety of sensitivity analyses. CONCLUSIONS: In patients with a recent acute coronary syndrome on optimal statin therapy, alirocumab improves cardiovascular outcomes at costs considered intermediate value, with good value in patients with baseline LDL-C ?100 mg/dl but less economic value with LDL-C <100 mg/dl. (Evaluation of Cardiovascular Outcomes After an Acute Coronary Syndrome During Treatment With Alirocumab [ODYSSEY OUTCOMES]; NCT01663402)

Stable Lithium Argon compounds under high pressure

High pressure can fundamentally alter the bonding patterns of chemical elements. Its effects include stimulating elements thought to be “inactive” to form unexpectedly stable compounds with unusual chemical and physical properties. Here, using an unbiased structure search method based on CALYPSO methodology and density functional total energy calculations, the phase stabilities and crystal structures of Li−Ar compounds are systematically investigated at high pressure up to 300 GPa. Two unexpected Li(m)Ar(n) compounds (LiAr and Li(3)Ar) are predicted to be stable above 112 GPa and 119 GPa, respectively. A detailed analysis of the electronic structure of LiAr and Li(3)Ar shows that Ar in these compounds attracts electrons and thus behaves as an oxidizing agent. This is markedly different from the hitherto established chemical reactivity of Ar. Moreover, we predict that the P4/mmm phase of Li(3)Ar has a superconducting transition temperature of 17.6 K at 120 GPa