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BackgroundA sex-based evaluation of prognosis in heart failure (HF) is lacking.Methods and resultsWe analyzed the Metabolic Exercise test data combined with Cardiac and Kidney Indexes (MECKI) score registry, which includes HF with reduced ejection fraction (HFrEF) patients. A cross-validation procedure was performed to estimate weights separately for men and women of all MECKI score parameters: left ventricular ejection fraction (LVEF), hemoglobin, kidney function assessed by Modification of Diet in Renal Disease, blood sodium level, ventilation vs. carbon dioxide production slope, and peak oxygen consumption (peakVO2). The primary outcomes were the composite of all-cause mortality, urgent heart transplant, and implant of a left ventricle assist device. The difference in predictive ability between the native and sex recalibrated MECKI (S-MECKI) was calculated using a receiver operating characteristic (ROC) curve at 2 years and a calibration plot. We retrospectively analyzed 7,900 HFrEF patients included in the MECKI score registry (mean age 61 ± 13 years, 6,456 men/1,444 women, mean LVEF 33% ± 10%, mean peakVO2 56.2% ± 17.6% of predicted) with a median follow-up of 4.05 years (range 1.72–7.47). Our results revealed an unadjusted risk of events that was doubled in men compared to women (9.7 vs. 4.1) and a significant difference in weight between the sexes of most of the parameters included in the MECKI score. S-MECKI showed improved risk classification and accuracy (area under the ROC curve: 0.7893 vs. 0.7799, p = 0.02) due to prognostication improvement in the high-risk settings in both sexes (MECKI score >10 in men and >5 in women).ConclusionsS-MECKI, i.e., the recalibrated MECKI according to sex-specific differences, constitutes a further step in the prognostic assessment of patients with severe HFrEF.

Abstract Entanglement and coherence are fundamental properties of quantum systems, promising to power near-future quantum technologies, such as quantum computation, quantum communication, and quantum metrology. Yet, their quantification, rather than mere detection, generally requires reconstructing the spectrum of quantum states, i.e., experimentally challenging measurement sets that increase exponentially with the system size. Here, we demonstrate quantitative bounds to operationally useful entanglement and coherence that are universally valid, analytically computable, and experimentally friendly. Specifically, our main theoretical results are lower and upper bounds to the coherent information and the relative entropy of coherence in terms of local and global purities of quantum states. To validate our proposal, we experimentally implement two purity detection methods in an optical system: shadow estimation with random measurements and collective measurements on pairs of state copies. The experiment shows that both the coherent information and the relative entropy of coherence of pure and mixed unknown quantum states can be bounded by purity functions. Our research offers an efficient means of verifying large-scale quantum information processing.

Local quantum uncertainty and interferometric power were introduced by Girolami et al. as geometric quantifiers of quantum correlations. The aim of the present paper is to discuss their properties in a unified manner by means of the metric adjusted skew information defined by Hansen.

The characterization of quantum coherence in the context of quantum information theory and its interplay with quantum correlations is currently subject of intense study. Coherence in a Hamiltonian eigenbasis yields asymmetry, the ability of a quantum system to break a dynamical symmetry generated by the Hamiltonian. We here propose an experimental strategy to witness multipartite entanglement in many-body systems by evaluating the asymmetry with respect to an additive Hamiltonian. We test our scheme by simulating asymmetry and entanglement detection in a three-qubit Greenberger–Horne–Zeilinger (GHZ) diagonal state.

A major signature of quantum mechanics beyond classical physics is coherence, the existence of superposition states. The recently developed resource theory of quantum coherence allows the formalization of incoherent operations—those operations which cannot create coherence. We identify the set of operations which additionally do not use coherence. These are such that coherence cannot be exploited by a classical observer, who measures incoherent properties of the system, to go beyond classical dynamics. We give a physical interpretation in terms of interferometry and prove a dilation theorem, showing how these operations can always be constructed by the system interacting, in an incoherent way, with an ancilla. Such a physical justification is not known for the incoherent operations; thus, our results lead to a physically well-motivated resource theory of coherence. Next, we investigate the implications for coherence in multipartite systems. We show that quantum correlations can be defined naturally with respect to a fixed basis, providing a link between coherence and quantum discord. We demonstrate the interplay between these two quantities in the operations that we study and suggest implications for the theory of quantum discord by relating these operations to those which cannot create discord.