Quantum hypothesis testing (QHT) has been traditionally studied from the information-theoretic perspective, wherein one is interested in the optimal decay rate of error probabilities as a function of ...the number of samples of an unknown state. In this paper, we study the sample complexity of QHT, wherein the goal is to determine the minimum number of samples needed to reach a desired error probability. By making use of the wealth of knowledge that already exists in the literature on QHT, we characterize the sample complexity of binary QHT in the symmetric and asymmetric settings, and we provide bounds on the sample complexity of multiple QHT. In more detail, we prove that the sample complexity of symmetric binary QHT depends logarithmically on the inverse error probability and inversely on the negative logarithm of the fidelity. As a counterpart of the quantum Stein's lemma, we also find that the sample complexity of asymmetric binary QHT depends logarithmically on the inverse type II error probability and inversely on the quantum relative entropy, provided that the type II error probability is sufficiently small. We then provide lower and upper bounds on the sample complexity of multiple QHT, with it remaining an intriguing open question to improve these bounds. The final part of our paper outlines and reviews how sample complexity of QHT is relevant to a broad swathe of research areas and can enhance understanding of many fundamental concepts, including quantum algorithms for simulation and search, quantum learning and classification, and foundations of quantum mechanics. As such, we view our paper as an invitation to researchers coming from different communities to study and contribute to the problem of sample complexity of QHT, and we outline a number of open directions for future research.
We develop a resource theory of symmetric distinguishability, the fundamental objects of which are elementary quantum information sources, i.e., sources that emit one of two possible quantum states ...with given prior probabilities. Such a source can be represented by a classical-quantum state of a composite system \(XA\), corresponding to an ensemble of two quantum states, with \(X\) being classical and \(A\) being quantum. We study the resource theory for two different classes of free operations: \((i)\) \({\rm{CPTP}}_A\), which consists of quantum channels acting only on \(A\), and \((ii)\) conditional doubly stochastic (CDS) maps acting on \(XA\). We introduce the notion of symmetric distinguishability of an elementary source and prove that it is a monotone under both these classes of free operations. We study the tasks of distillation and dilution of symmetric distinguishability, both in the one-shot and asymptotic regimes. We prove that in the asymptotic regime, the optimal rate of converting one elementary source to another is equal to the ratio of their quantum Chernoff divergences, under both these classes of free operations. This imparts a new operational interpretation to the quantum Chernoff divergence. We also obtain interesting operational interpretations of the Thompson metric, in the context of the dilution of symmetric distinguishability.
Fawzi and Fawzi recently defined the sharp Rényi divergence, \(D_\alpha^\#\), for \(\alpha \in (1, \infty)\), as an additional quantum Rényi divergence with nice mathematical properties and ...applications in quantum channel discrimination and quantum communication. One of their open questions was the limit \({\alpha} \to 1\) of this divergence. By finding a new expression of the sharp divergence in terms of a minimization of the geometric Rényi divergence, we show that this limit is equal to the Belavkin-Staszewski relative entropy. Analogous minimizations of arbitrary generalized divergences lead to a new family of generalized divergences that we call kringel divergences, and for which we prove various properties including the data-processing inequality.
We derive the 3D quintic NLS as the mean field limit of a Bose gas with three-body interactions. The quintic NLS is energy-critical, leading to several new difficulties in comparison with the cubic ...NLS which emerges from Bose gases with pair-interactions. Our method is based on Bogoliubov's approximation, which also provides the information on the fluctuations around the condensate in terms of a norm approximation for the N-body wave function.
Neural networks enjoy widespread success in both research and industry and, with the imminent advent of quantum technology, it is now a crucial challenge to design quantum neural networks for fully ...quantum learning tasks. Here we propose the use of quantum neurons as a building block for quantum feed-forward neural networks capable of universal quantum computation. We describe the efficient training of these networks using the fidelity as a cost function and provide both classical and efficient quantum implementations. Our method allows for fast optimisation with reduced memory requirements: the number of qudits required scales with only the width, allowing the optimisation of deep networks. We benchmark our proposal for the quantum task of learning an unknown unitary and find remarkable generalisation behaviour and a striking robustness to noisy training data.
Cartilage defects in the knee are being diagnosed with increased frequency and are treated with a variety of techniques. The aim of any cartilage repair procedure is to generate the highest tissue ...quality, which might correlate with improved clinical outcomes, return-to-sport, and long-term durability. Minced cartilage implantation (MCI) is a relatively simple and cost-effective technique to transplant autologous cartilage fragments in a single-step procedure. Minced cartilage has a strong biologic potential since autologous, activated non-dedifferentiated chondrocytes are utilized. It can be used both for small and large cartilage lesions, as well as for osteochondral lesions. As it is purely an autologous and homologous approach, it lacks a significant regulatory oversight process and can be clinically adopted without such limitations. The aim of this narrative review is to provide an overview of the current evidence supporting autologous minced cartilage implantation.
Tumor-infiltrating immune cells are highly relevant for prognosis and identification of immunotherapy targets in hepatocellular carcinoma (HCC). The recently developed CIBERSORT method allows immune ...cell profiling by deconvolution of gene expression microarray data. By applying CIBERSORT, we assessed the relative proportions of immune cells in 41 healthy human livers, 305 HCC samples and 82 HCC adjacent tissues. The obtained immune cell profiles provided enumeration and activation status of 22 immune cell subtypes. Mast cells were evaluated by immunohistochemistry in ten HCC patients. Activated mast cells, monocytes and plasma cells were decreased in HCC, while resting mast cells, total and naïve B cells, CD4
memory resting and CD8
T cells were increased when compared to healthy livers. Previously described S1, S2 and S3 molecular HCC subclasses demonstrated increased M1-polarized macrophages in the S3 subclass with good prognosis. Strong total immune cell infiltration into HCC correlated with total B cells, memory B cells, T follicular helper cells and M1 macrophages, whereas weak infiltration was linked to resting NK cells, neutrophils and resting mast cells. Immunohistochemical analysis of patient samples confirmed the reduced frequency of mast cells in human HCC tumor tissue as compared to tumor adjacent tissue. Our data demonstrate that deconvolution of gene expression data by CIBERSORT provides valuable information about immune cell composition of HCC patients.
Despite major advances in medicine, blood-borne biomarkers are urgently needed to support decision-making, including polytrauma. Here, we assessed serum-derived extracellular vesicles (EVs) as ...potential markers of decision-making in polytrauma.
Our Liquid Biopsy in Organ Damage (LiBOD) study aimed to differentiate polytrauma with organ injury from polytrauma without organ injury. We analysed of blood-borne small EVs at the individual level using a combination of immunocapture and high-resolution imaging.
To this end, we isolated, purified, and characterized small EVs according to the latest Minimal Information for Studies of Extracellular Vesicles (MISEV) guidelines from human blood collected within 24 h post-trauma and validated our results using a porcine polytrauma model.
We found that small EVs derived from monocytes CD14
and CD14
CD61
were significantly elevated in polytrauma with organ damage. To be precise, our findings revealed that CD9
CD14
and CD14
CD61
small EVs exhibited superior performance compared to CD9
CD61
small EVs in accurately indicating polytrauma with organ damage, reaching a sensitivity and a specificity of 0.81% and 0.97%, respectively. The results in humans were confirmed in an independent porcine model of polytrauma.
These findings suggest that these specific types of small EVs may serve as valuable, non-invasive, and objective biomarkers for assessing and monitoring the severity of polytrauma and associated organ damage.
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