Tapping into Permutation Symmetry for Improved Detection of k-Symmetric Extensions.

Symmetric extensions are essential in quantum mechanics, providing a lens through which to investigate the correlations of entangled quantum systems and to address challenges like the quantum marginal problem. Though semi-definite programming (SDP) is a recognized method for handling symmetric extensions, it struggles with computational constraints, especially due to the large real parameters in generalized qudit systems. In this study, we introduce an approach that adeptly leverages permutation symmetry. By fine-tuning the SDP problem for detecting k-symmetric extensions, our method markedly diminishes the searching space dimensionality and trims the number of parameters essential for positive-definiteness tests. This leads to an algorithmic enhancement, reducing the complexity from O(d2k) to O(kd2) in the qudit k-symmetric extension scenario. Additionally, our approach streamlines the process of verifying the positive definiteness of the results. These advancements pave the way for deeper insights into quantum correlations, highlighting potential avenues for refined research and innovations in quantum information theory.

Two-Pronged Approach: Synergistic Tuning of the Surface and Carbon Core to Achieve Yellow Emission in Lignin-Based Carbon Dots.

In this study, yellow emissive lignin-based carbon dots (Y-CDs) were successfully prepared through a synergistic approach to adjust its surface and carbon core states. The lignin was initially effectively oxidized and carboxymethylated to impart abundant -COOH onto the precursor, which eventually adjusts the surface state of the CDs. Subsequently, α-naphthol was employed during the solvothermal treatment of lignin with the aim of elevating the sp2 domain content in the CDs and, thus, adjusting its carbon core state. The obtained Y-CDs possessed abundant carboxyl groups and nanoscale spherical shape with an average diameter of 5.21 nm. Meanwhile, the energy gap of Y-CDs was 2.46 eV and the optimal emission wavelength was 561 nm under the excitation wavelength of 410 nm. Synergistic adjusting carbon core and surface of the Y-CDs would alter the surface charge distribution and promote the delocalization of π electrons, and thus lead to a red shifting with the emission wavelength of 154 nm. Furthermore, a shape memory film with excellent recovery performance and fluorescent properties was designed by embedding the Y-CDs into polyvinyl alcohol (PVA) polymer. The incorporation of Y-CDs could impart the film with considerable high-value applications in the fields of intelligent sensing, biomedicine, and tissue engineering.

Enhanced Effects of Iron on Mycelial Growth, Metabolism and In Vitro Antioxidant Activity of Polysaccharides from Lentinula edodes.

The polysaccharides found in Lentinula edodes have a variety of medicinal properties, such as anti-tumor and anti-viral effects, but their content in L. edodes sporophores is very low. In this study, Fe2+ was added to the liquid fermentation medium of L. edodes to analyze its effects on mycelial growth, polysaccharide and enzyme production, gene expression, and the activities of enzymes involved in polysaccharide biosynthesis, and in vitro antioxidation of polysaccharides. The results showed that when 200 mg/L of Fe2+ was added, with 7 days of shaking at 150 rpm and 3 days of static culture, the biomass reached its highest value (0.28 mg/50 mL) 50 days after the addition of Fe2+. Besides, Fe2+ addition also enhanced intracellular polysaccharide (IPS) and exopolysaccharide (EPS) productions, the levels of which were 2.98- and 1.79-fold higher than the control. The activities of the enzymes involved in polysaccharides biosynthesis, including phosphoglucomutase (PGM), phosphoglucose isomerase (PGI), and UDPG-pyrophosphorylase (UGP) were also increased under Fe2+ addition. Maximum PGI activity reached 1525.20 U/mg 30 days after Fe2+ addition, whereas PGM and UGP activities reached 3607.05 U/mg and 3823.27 U/mg 60 days after Fe2+ addition, respectively. The Pearson correlation coefficient showed a strong correlation (p < 0.01) between IPS production and PGM and UGP activities. The corresponding coding genes of the three enzymes were also upregulated. When evaluating the in vitro antioxidant activities of polysaccharides, EPS from all Fe2+-treated cultures exhibited significantly better capacity (p < 0.05) for scavenging -OH radicals. The results of the two-way ANOVA indicated that the abilities of polysaccharides to scavenge O2− radicals were significantly (p < 0.01) affected by Fe2+ concentration and incubation time. These results indicated that the addition of iron provided a good way to achieve desirable biomass, polysaccharide production, and the in vitro antioxidation of polysaccharides from L. edodes.

Preparation of sulfur-doped carbon quantum dots from lignin as a sensor to detect Sudan I in an acidic environment.

To achieve a rapid and facile quantitative evaluation of Sudan I illegally added in ketchup, fluorescent carbon quantum dots with excellent stability in acidic environments are required as the actual pH value of ketchup is close to 4.0. In this paper, we developed a green approach to prepare sulfur-doped carbon quantum dots (SCQDs) via hydrothermal treatment of lignin, isolated from pre-hydrolysis liquor, in sulfuric acid solution. The resultant SCQDs from lignin possessed sulfur-containing groups, which exhibited excellent fluorescence with a quantum yield up to 13.5% and good stability in acidic environments with a wide pH range of 0-5.0. Therefore, the SCQDs were successfully employed as a sensor to detect Sudan I in acidic solutions with excellent selectivity and sensitivity. The linear range for Sudan I was 0-40 µM, while the limit of detection was 0.12 µM. In addition, the fluorescent indicator paper functionalized with SCQDs also showed outstanding selectivity to Sudan I. The proposed SCQD sensing system not only displayed application potential for quantitative evaluation of Sudan I dye in practical samples, but also provided a way to convert lignin-based waste into highly valued nanoscale materials.

Supervised learning in Hamiltonian reconstruction from local measurements on eigenstates.

Reconstructing a system Hamiltonian through measurements on its eigenstates is an important inverse problem in quantum physics. Recently, it was shown that generic many-body local Hamiltonians can be recovered by local measurements without knowing the values of the correlation functions. In this work, we discuss this problem in more depth for different systems and apply supervised learning method via neural networks to solve it. For low-lying eigenstates, the inverse problem is well-posed, neural networks turn out to be efficient and scalable even with a shallow network and a small data set. For middle-lying eigenstates, the problem is ill-posed, we present a modified method based on transfer learning accordingly. Neural networks can also efficiently generate appropriate initial points for numerical optimization based on the BFGS method.

Experimental quantum Hamiltonian identification from measurement time traces.

Identifying Hamiltonian of a quantum system is of vital importance for quantum information processing. In this article, we realized and benchmarked a quantum Hamiltonian identification algorithm recently proposed (Zhang and Sarovar, 2014). we realized the algorithm on a liquid nuclear magnetic resonance quantum information processor using two types of working media with different forms of Hamiltonian. Our experiment realized the quantum identification algorithm based on free induction decay signals. We also showed how to process data obtained in a practical experiment. We studied the influence of decoherence by numerical simulations. Our experiments and simulations demonstrate that the algorithm is effective and robust.

Experimental optimal single qubit purification in an NMR quantum information processor.

High quality single qubits are the building blocks in quantum information processing. But they are vulnerable to environmental noise. To overcome noise, purification techniques, which generate qubits with higher purities from qubits with lower purities, have been proposed. Purifications have attracted much interest and been widely studied. However, the full experimental demonstration of an optimal single qubit purification protocol proposed by Cirac, Ekert and Macchiavello [Phys. Rev. Lett. 82, 4344 (1999), the CEM protocol] more than one and half decades ago, still remains an experimental challenge, as it requires more complicated networks and a higher level of precision controls. In this work, we design an experiment scheme that realizes the CEM protocol with explicit symmetrization of the wave functions. The purification scheme was successfully implemented in a nuclear magnetic resonance quantum information processor. The experiment fully demonstrated the purification protocol, and showed that it is an effective way of protecting qubits against errors and decoherence.