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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.

Leaf shape is a vital agronomic trait that affects plant and canopy architecture, yield, and other production attributes of upland cotton. Compared with normal leaves, lobed leaves have potential advantages in improving canopy structure and increasing cotton yield. A chromosomal introgression segment from Gossypium barbadense L. conferring sub-okra leaf shape to Gossypium hirsutum L. was identified on chromosome D01. To determine the effects of this transferred sub-okra leaf shape on the leaf anatomical characteristics, photosynthesis-related traits, and yield of short-season cotton, we performed a field experiment with three sets of near-isogenic lines carrying okra, sub-okra, and normal leaf shape in Lu54 (L54) and Shizao 2 (SZ2) backgrounds. Compared with normal leaves, sub-okra leaves exhibited reduced leaf thickness and smaller leaf mass per area; moreover, the deeper lobes of sub-okra leaves improved the plant canopy structure by decreasing leaf area index by 11.24%–22.84%. Similarly, the intercepted PAR rate of lines with sub-okra leaf shape was also reduced. The chlorophyll content of sub-okra leaves was lower than that of okra and normal leaf shapes; however, the net photosynthetic rate of sub-okra leaves was 8.17%–29.81% higher than that of other leaf shapes at most growth stages. Although the biomass of lines with sub-okra leaf shape was less than that of lines with normal leaves, the average first harvest yield and total yield of lines with the sub-okra leaf shape increased by 6.36% and 5.72%, respectively, compared with those with normal leaves. Thus, improvements in the canopy structure and photosynthetic and physiological characteristics contributed to optimizing the light environment, thereby increasing the yield of lines with sub-okra leaf shape. Our results suggest that the sub-okra leaf trait from G. barbadense L. may have practical applications for cultivating short-season varieties with high photosynthetic efficiency, and improving yield, which will be advantageous for short-season varieties.

Adenosine kinase (ADK) is a key enzyme widely distributed in plants, playing an important role in maintaining cellular energy homeostasis and regulating plant growth, development, and responses to environmental stresses. However, research on ADK genes in cotton (Gossypium hirsutum), an economically significant crop, has been limited. This study identified 92 ADK genes from four cotton species (G. arboreum, G. raimondii, G. hirsutum, and G. barbadense) using HMMER and Local BLASTP methods and classified them into six groups. Chromosomal localization revealed a random distribution of ADK genes in G. hirsutum, with 13 genes located on the At subgenome and 14 genes on the Dt subgenome. Gene structure analysis showed consistency in exon–intron organization within subgroups, while conserved motif analysis identified subgroup-specific motifs, indicating functional diversity. Synteny and collinearity mapping analysis revealed that the primary expansion mechanisms of the ADK gene family in cotton are polyploidy and segmental duplication. Cis-regulatory elements in GhADK promoters were classified into light response, hormone response, developmental regulation, and stress response. We also analyzed the expression patterns of GhADK genes under a low temperature (4 °C) and drought conditions. Most GhADK genes responded to cold stress with different expression patterns, indicating their roles in rapid response and long-term cold adaptation. Under drought stress, expression patterns varied, with some genes showing sustained high expression levels. The qRT-PCR validation of transcriptomic data confirmed the stress-induced expression patterns of selected GhADK genes. Functional analysis through the VIGS silencing of GhADK25 demonstrated its importance in cold and drought stress responses, with silencing resulting in poor growth under stress, highlighting its significance in stress tolerance. This study provides a basis for further understanding the evolutionary relationships and functions of the cotton ADK gene family.

Abstract To achieve scalable quantum information processing, great efforts have been devoted to the creation of large-scale entangled states in various physical systems. Ultracold atom in optical lattice is considered as one of the promising platforms due to its feasible initialization and parallel manipulation. In this work, we propose an efficient scheme to generate and characterize global entanglement in the optical lattice. With only two-layer quantum circuits, the generation utilizes two-qubit entangling gates based on the superexchange interaction in double wells. The parallelism of these operations enables the generation to be fast and scalable. To verify the entanglement of this non-stabilizer state, we mainly design three complementary detection protocols which are less resource-consuming compared to the full tomography. In particular, one just needs two homogenous local measurement settings to identify the entanglement property. Our entanglement generation and verification protocols provide the foundation for the further quantum information processing in optical lattice.

Measurement-device-independent QKD schemes suffer from a trade-off between ease of implementation (avoiding the need for global phase locking) and high rates (quadratic improvement in rate). Here, the authors propose a protocol which offers both simple implementation and strong performances.

Quantum measurements can produce unpredictable randomness arising from the uncertainty principle. When measuring a state with von Neumann measurements, the intrinsic randomness can be quantified by the quantum coherence of the state on the measurement basis. Unlike projection measurements, there are additional and possibly hidden degrees of freedom in an apparatus for generic measurements. We propose an adversary scenario to characterize the intrinsic randomness of general measurements with arbitrary input states. Interestingly, we discover that certain measurements, including symmetric and information-complete ones, generate nonzero randomness for all states, which suggests a new approach for designing source-independent random number generators without state characterization. Furthermore, our results reveal that intrinsic randomness can quantify coherence under general measurements, which generalizes the result in the standard resource theory of state coherence.

Abstract Quantum key distribution (QKD) enables secure key exchanges between two remote users. The ultimate goal of secure communication is to establish a global quantum network. The existing field tests suggest that quantum networks are feasible. To achieve a practical quantum network, we need to overcome several challenges including realizing versatile topologies for large scales, simple network maintenance, extendable configuration and robustness to node failures. To this end, we present a field operation of a quantum metropolitan-area network with 46 nodes and show that all these challenges can be overcome with cutting-edge quantum technologies. In particular, we realize different topological structures and continuously run the network for 31 months, by employing standard equipment for network maintenance with an extendable configuration. We realize QKD pairing and key management with a sophisticated key control centre. In this implementation, the final keys have been used for secure communication such as real-time voice telephone, text messaging and file transmission with one-time pad encryption, which can support 11 pairs of users to make audio calls simultaneously. Combined with intercity quantum backbone and ground–satellite links, our metropolitan implementation paves the way toward a global quantum network.

Salinity is a major abiotic stress that restricts cotton growth and affects fiber yield and quality. Although studies on salt tolerance have achieved great progress in cotton since the completion of cotton genome sequencing, knowledge about how cotton copes with salt stress is still scant. S-adenosylmethionine (SAM) plays important roles in many organelles with the help of the SAM transporter, and it is also a synthetic precursor for substances such as ethylene (ET), polyamines (PAs), betaine, and lignin, which often accumulate in plants in response to stresses. This review focused on the biosynthesis and signal transduction pathways of ET and PAs. The current progress of ET and PAs in regulating plant growth and development under salt stress has been summarized. Moreover, we verified the function of a cotton SAM transporter and suggested that it can regulate salt stress response in cotton. At last, an improved regulatory pathway of ET and PAs under salt stress in cotton is proposed for the breeding of salt-tolerant varieties.

Abstract Background The overall genetic distribution and divergence of cloned genes among bread wheat varieties that have occurred during the breeding process over the past few decades in Ningxia Province, China, are poorly understood. Here, we report the genetic diversities of 44 important genes related to grain yield, quality, adaptation and resistance in 121 Ningxia and 86 introduced wheat cultivars and advanced lines. Results The population structure indicated characteristics of genetic components of Ningxia wheat, including landraces of particular genetic resources, introduced varieties with rich genetic diversities and modern cultivars in different periods. Analysis of allele frequencies showed that the dwarfing alleles Rht-B1b at Rht-B1 and Rht-D1b at Rht-D1, 1BL/1RS translocation, Hap-1 at GW2-6B and Hap-H at Sus2-2B are very frequently present in modern Ningxia cultivars and in introduced varieties from other regions but absent in landraces. This indicates that the introduced wheat germplasm with numerous beneficial genes is vital for broadening the genetic diversity of Ningxia wheat varieties. Large population differentiation between modern cultivars and landraces has occurred in adaptation genes. Founder parents carry excellent allele combinations of important genes, with a higher number of favorable alleles than modern cultivars. Gene flow analysis showed that six founder parents have greatly contributed to breeding improvement in Ningxia Province, particularly Zhou 8425B, for yield-related genes. Conclusions Varieties introduced from other regions with rich genetic diversity and landraces with well-adapted genetic resources have been applied to improve modern cultivars. Founder parents, particularly Zhou 8425B, for yield-related genes have contributed greatly to wheat breeding improvement in Ningxia Province. These findings will greatly benefit bread wheat breeding in Ningxia Province as well as other areas with similar ecological environments.

Abstract Background Cotton (Gossypium spp.) fiber yield is one of the key target traits, and improved fiber yield has always been thought of as an important objective in the breeding programs and production. Although some studies had been reported for the understanding of genetic bases for cotton yield-related traits, the detected quantitative trait loci (QTL) for the traits is still very limited. To uncover the whole-genome QTL controlling three yield-related traits in upland cotton (Gossypium hirsutum L.), phenotypic traits were investigated under four planting environments and 9244 single-nucleotide polymorphism linkage disequilibrium block (SNPLDB) markers were developed in an association panel consisting of 315 accessions. Results A total of 53, 70 and 68 significant SNPLDB loci associated with boll number (BN), boll weight (BW) and lint percentage (LP), were respectively detected through a restricted two-stage multi-locus multi-allele genome-wide association study (RTM-GWAS) procedure in multiple environments. The haplotype/allele effects of the significant SNPLDB loci were estimated and the QTL-allele matrices were organized for offering the abbreviated genetic composition of the population. Among the significant SNPLDB loci, six of them were simultaneously identified in two or more single planting environments and were thought of as the stable SNPLDB loci. Additionally, a total of 115 genes were annotated in the nearby regions of the six stable SNPLDB loci, and 16 common potential candidate genes controlling target traits of them were predicted by two RNA-seq data. One of 16 genes (GH_D06G2161) was mainly expressed in the early ovule-development stages, and the stable SNPLDB locus (LDB_19_62926589) was mapped in its promoter region. Conclusion This study identified the QTL alleles and candidate genes that could provide important insights into the genetic basis of yield-related traits in upland cotton and might facilitate breeding cotton varieties with high yield.

Ubiquitination is a post-translational regulatory mechanism that controls a variety of biological processes in plants. The E3 ligases confer specificity by recognizing target proteins for ubiquitination. Here, we identified SEVEN IN ABSENTIA (SINA) ubiquitin ligases, which belong to the RING-type E3 ligase family, in upland cotton (Gossypium hirsutum). Twenty-four GhSINAs were characterized, and the expression levels of GhSINA7, GhSINA8, and GhSINA9 were upregulated at 24 h after inoculation with Verticillium dahliae. In vitro ubiquitination assays indicated that the three GhSINAs possessed E3 ubiquitin ligase activities. Transient expression in Nicotiana benthamiana leaves showed that they localized to the nucleus. And yeast two-hybrid (Y2H) screening revealed that they could interact with each other. The ectopic overexpression of GhSINA7, GhSINA8, and GhSINA9 independently in Arabidopsis thaliana resulted in increased tolerance to V. dahliae, while individual knockdowns of GhSINA7, GhSINA8, and GhSINA9 compromised cotton resistance to the pathogen. Thus, GhSINA7, GhSINA8, and GhSINA9 act as positive regulators of defense responses against V. dahliae in cotton plants.

Quantum information science provides powerful technologies beyond the scope of classical physics. In practice, accurate control of quantum operations is a challenging task with current quantum devices. The implementation of high fidelity and multi-qubit quantum operations consumes massive resources and requires complicated hardware design to fight against noise. An approach to alleviating this problem is to replace quantum operations with classical processing. Despite the common practice of this approach, rigorous criteria to determine whether a given quantum operation is replaceable classically are still missing. In this work, we define the classically replaceable operations in four general scenarios. In each scenario, we provide their necessary and sufficient criteria and point out the corresponding classical processing. For a practically favorable case of unitary classically replaceable operations, we show that the replaced classical processing is deterministic. Beyond that, we regard the irreplaceability of quantum operations by classical processing as a quantum resource and relate it to the performance of a channel in a non-local game, as manifested in a robustness measure.

The SWEET (sugars will eventually be exported transporter) proteins, a family of sugar transporters, mediate sugar diffusion across cell membranes. Pathogenic fungi can acquire sugars from plant cells to satisfy their nutritional demands for growth and infection by exploiting plant SWEET sugar transporters. However, the mechanism underlying the sugar allocation in cotton plants infected by Verticillium dahliae, the causative agent of Verticillium wilt, remains unclear. In this study, observations of the colonization of cotton roots by V. dahliae revealed that a large number of conidia had germinated at 48-hour post-inoculation (hpi) and massive hyphae had appeared at 96 hpi. The glucose content in the infected roots was significantly increased at 48 hpi. On the basis of an evolutionary analysis, an association analysis, and qRT-PCR assays, GhSWEET42 was found to be closely associated with V. dahliae infection in cotton. Furthermore, GhSWEET42 was shown to encode a glucose transporter localized to the plasma membrane. The overexpression of GhSWEET42 in Arabidopsis thaliana plants led to increased glucose content, and compromised their resistance to V. dahliae. In contrast, knockdown of GhSWEET42 expression in cotton plants by virus-induced gene silencing (VIGS) led to a decrease in glucose content, and enhanced their resistance to V. dahliae. Together, these results suggest that GhSWEET42 plays a key role in V. dahliae infection in cotton through glucose translocation, and that manipulation of GhSWEET42 expression to control the glucose level at the infected site is a useful method for inhibiting V. dahliae infection.

Privacy amplification is the key step to guarantee the security of quantum communication. The existing security proofs require the accumulation of a large number of raw key bits for privacy amplification. This is similar to block ciphers in classical cryptography that would delay the final key generation since an entire block must be accumulated ahead of privacy amplification. Moreover, any leftover errors after information reconciliation would corrupt the entire block. By modifying the security proof based on quantum error correction, we develop a stream privacy-amplification scheme, which resembles the classical stream cipher. This scheme can output the final key in a stream way, prevent error from spreading, and hence can put privacy amplification ahead of information reconciliation. The stream scheme can also help to enhance the security of trusted-relay quantum networks and improve the practicality of randomness extraction for quantum random number generators.

Histone demethylases containing JumonjiC (JmjC) domains regulate gene transcription and chromatin structure by changing the methylation status of lysine residues and play an important role in plant growth and development. In this study, a total of 332 JmjC family genes were identified from 21 different plant species. The evolutionary analysis results showed that the JmjC gene was detected in each species, that is, the gene has already appeared in algae. The phylogenetic analysis showed that the KDM3/JHDM2 subfamily genes may have appeared when plants transitioned from water to land, but were lost in lycophytes (Selaginella moellendorffii). During the evolutionary process, some subfamily genes may have been lost in individual species. According to the analysis of the conserved domains, all of the plant JmjC genes contained a typical JmjC domain, which was highly conserved during plant evolution. The analysis of cis-acting elements showed that the promoter region of the JmjC gene was rich in phytohormones and biotic and abiotic stress-related elements. The transcriptome data analysis and protein interaction analyses showed that JmjC genes play an important role in plant growth and development. The results clarified the evolutionary history of JmjC family genes in plants and lay the foundation for the analysis of the biological functions of JmjC family genes.

Histone modification is an important epigenetic modification that controls gene transcriptional regulation in eukaryotes. Histone methylation is accomplished by histone methyltransferase and can occur on two amino acid residues, arginine and lysine. JumonjiC (JmjC) domain-containing histone demethylase regulates gene transcription and chromatin structure by changing the methylation state of the lysine residue site and plays an important role in plant growth and development. In this study, we carried out genome-wide identification and comprehensive analysis of JmjC genes in the allotetraploid cotton species Gossypium hirsutum. In total, 50 JmjC genes were identified and in G. hirsutum, and 25 JmjC genes were identified in its two diploid progenitors, G. arboreum and G. raimondii, respectively. Phylogenetic analysis divided these JmjC genes into five subfamilies. A collinearity analysis of the two subgenomes of G. hirsutum and the genomes of G. arboreum and G. raimondii uncovered a one-to-one relationship between homologous genes of the JmjC gene family. Most homologs in the JmjC gene family between A and D subgenomes of G. hirsutum have similar exon-intron structures, which indicated that JmjC family genes were conserved after the polyploidization. All G. hirsutumJmjC genes were found to have a typical JmjC domain, and some genes also possess other special domains important for their function. Analysis of promoter regions revealed that cis-acting elements, such as those related to hormone and abiotic stress response, were enriched in G. hirsutum JmjC genes. According to a reverse transcription-quantitative polymerase chain reaction (RT-qPCR) analysis, most G. hirsutumJmjC genes had high abundance expression at developmental stages of fibers, suggesting that they might participate in cotton fiber development. In addition, some G. hirsutumJmjC genes were found to have different degrees of response to cold or osmotic stress, thus indicating their potential role in these types of abiotic stress response. Our results provide useful information for understanding the evolutionary history and biological function of JmjC genes in cotton.

Soil salinization, which is primarily due to excessive Na+ levels, is a major abiotic stress adversely affecting plant growth and development. The Na+/H+ antiporter (NHX) is a transmembrane protein mediating the transport of Na+ or K+ and H+ across the membrane to modulate the ionic balance of plants in response to salt stress. Research regarding NHXs has mainly focused on the vacuolar-type NHX family members. However, the biological functions of the endosomal-type NHXs remain relatively uncharacterized. In this study, 22 NHX family members were identified in Gossypium hirsutum. A phylogenetic analysis divided the GhNHX genes into two categories, with 18 and 4 in the vacuolar and endosomal groups, respectively. The chromosomal distribution of the NHX genes revealed the significant impact of genome-wide duplication during the polyploidization process on the number of GhNHX genes. Analyses of gene structures and conserved motifs indicated that GhNHX genes in the same phylogenetic cluster are conserved. Additionally, the salt-induced expression patterns confirmed that the expression levels of most of the GhNHX genes are affected by salinity. Specifically, in the endosomal group, GhNHX4A expression was substantially up-regulated by salt stress. A yeast functional complementation test proved that GhNHX4A can partially restore the salt tolerance of the salt-sensitive yeast mutant AXT3. Silencing GhNHX4A expression decreased the resistance of cotton to salt stress because of an increase in the accumulation of Na+ in stems and a decrease in the accumulation of K+ in roots. The results of this study may provide the basis for an in-depth characterization of the regulatory functions of NHX genes related to cotton salt tolerance, especially the endosomal-type GhNHX4A. Furthermore, the presented data may be useful for selecting appropriate candidate genes for the breeding of new salt-tolerant cotton varieties.

Maximally bipartite entangled state |Ψ^{+}〉, also known as the Einstein-Podolsky-Rosen pair, is the unit resource of entanglement and the key for quantum information processing. An important problem is that how many maximally bipartite entangled states could be distilled from a multipartite entangled state shared among a quantum network. Here, we focus on the distillation of |Ψ^{+}〉 from a single copy of the three-qubit W state. An interesting phenomenon in this case is that the random entanglement distillation between two unspecified parties can yield a strictly higher distillation rate (the average number of |Ψ^{+}〉 distilled from each W state) than the case between two specified parties. In this work, we develop a distillation protocol by introducing weak measurements that do not destroy the global entanglement. We find that the distillation rate can be significantly enhanced with only a few rounds by performing an extra distillation procedure between two specified parties at the final step. Experimentally, we prepare a three-photon W state in the polarization degree of freedom, and employ the path degree of freedom of each photon as probe qubits to realize the weak measurement. As a proof-of-principle demonstration, we show that the distillation rate is enhanced from 2/3, which is the theoretical limit of any distillation scheme between two specified parties, to 0.751±0.030 between two unspecified parties with only one distillation round.

Sucrose transporters (SUTs) play key roles in allocating the translocation of assimilates from source to sink tissues. Although the characteristics and biological roles of SUTs have been intensively investigated in higher plants, this gene family has not been functionally characterized in cotton. In this study, we performed a comprehensive analysis of SUT genes in the tetraploid cotton Gossypium hirsutum. A total of 18 G. hirsutum SUT genes were identified and classified into three groups based on their evolutionary relationships. Up to eight SUT genes in G. hirsutum were placed in the dicot-specific SUT1 group, while four and six SUT genes were, respectively, clustered into SUT4 and SUT2 groups together with members from both dicot and monocot species. The G. hirsutum SUT genes within the same group displayed similar exon/intron characteristics, and homologous genes in G. hirsutum At and Dt subgenomes, G. arboreum, and G. raimondii exhibited one-to-one relationships. Additionally, the duplicated genes in the diploid and polyploid cotton species have evolved through purifying selection, suggesting the strong conservation of SUT loci in these species. Expression analysis in different tissues indicated that SUT genes might play significant roles in cotton fiber elongation. Moreover, analyses of cis-acting regulatory elements in promoter regions and expression profiling under different abiotic stress and exogenous phytohormone treatments implied that SUT genes, especially GhSUT6A/D, might participate in plant responses to diverse abiotic stresses and phytohormones. Our findings provide valuable information for future studies on the evolution and function of SUT genes in cotton.

Aceraceae is a large forest tree family that comprises many economically and ecologically important species. However, because interspecific and/or intraspecific morphological variations result from frequent interspecific hybridization and introgression, it is challenging for non-taxonomists to accurately recognize and identify the tree species in Aceraceae based on a traditional approach. DNA barcoding is a powerful tool that has been proposed to accurately distinguish between species. In this study, we assessed the effectiveness of three core standard markers (matK, rbcL and ITS) plus the chloroplast locus trnS-trnG as Aceraceae barcodes. A total of 231 sequences representing 85 species in this forest family were collected. Of these four barcode markers, the discrimination power was highest for the ITS (I) region (50%) and was progressively reduced in the other three chloroplast barcodes matK (M), trnS-trnG (T) and rbcL (R); the discrimination efficiency of the ITS marker was also greater than any two-locus combination of chloroplast barcodes. However, the combinations of ITS plus single or combined chloroplast barcodes could improve species resolution significantly; T+I (90.5% resolution) and R+M+T+I (90.5% resolution) differentiated the highest portion of species in Aceraceae. Our current results show that the nuclear ITS fragment represents a more promising DNA barcode marker than the maternally inherited chloroplast barcodes. The most efficient and economical method to identify tree species in Aceraceae among single or combined DNA barcodes is the combination of T+I (90.5% resolution).

Cotton is one of the most important economic crops worldwide. As the global demands rising, cotton yield improvement is the most important goal of cotton breeding. Hybrids have great potential for increasing yield, however, the genetic mechanism of hybrids is still not clear. To investigate the genetic basis of cotton hybrids, we resequenced 9053 and sGK9708 with 62.13x coverage depth, the parents of the elite hybrid cotton CCRI63 that has obvious heterosis in lint percentage (LP) and boll weight (BW). Based on the cotton reference genome (TM-1), 1,287,661 single nucleotide polymorphisms (SNPs) and 152,479 insertions/deletions (InDels) were identified in 9053, and 1,482,784 SNPs and 152,985 InDels in sGK9708. Among them, 8649 SNPs and 629 InDels in the gene coding regions showed polymorphism between parents. Moreover, these variations involved 5092 genes, and 3835 of these genes were divided into 10 clusters based on the gene expression profiles. The genes in Cluster 3 and 7 were specifically expressed in the ovule and fiber development stage, suggesting that they might relate to LP and BW. We further co-localized the polymorphic SNPs and InDels with the reported quantitative trait loci (QTLs) of LP and BW, and identified 68 genes containing the polymorphic SNPs or InDels within these QTL intervals and as being related to fiber development. This suggested that the outstanding traits of CCRI63 such as LP and BW might be generated by accumulating the favorable variations from the parents. The results generated herein provide a genetic basis for cotton hybrids and genetic markers for marker-assisted selection breeding of cotton.

Quantum key distribution allows remote parties to generate information-theoretic secure keys. The bottleneck throttling its real-life applications lies in the limited communication distance and key generation speed, due to the fact that the information carrier can be easily lost in the channel. For all the current implementations, the key rate is bounded by the channel transmission probability η. Rather surprisingly, by matching the phases of two coherent states and encoding the key information into the common phase, this linear key-rate constraint can be overcome—the secure key rate scales with the square root of the transmission probability O(sqrt[η]), as proposed in twin-field quantum key distribution [M. Lucamarini et al. Overcoming the Rate–Distance Limit of Quantum Key Distribution without Quantum Repeaters, Nature (London) 557, 400 (2018)NATUAS0028-083610.1038/s41586-018-0066-6]. To achieve this, we develop an optical-mode-based security proof that is different from the conventional qubit-based security proofs. Furthermore, the proposed scheme is measurement device independent; i.e., it is immune to all possible detection attacks. The simulation result shows that the key rate can even exceed the transmission probability η between two communication parties. In addition, we apply phase postcompensation to devise a practical version of the scheme without phase locking, which makes the proposed scheme feasible with the current technology. This means that quantum key distribution can enjoy both sides of the world—practicality and security.

Creating large-scale entanglement lies at the heart of many quantum information processing protocols and the investigation of fundamental physics. For multipartite quantum systems, it is crucial to identify not only the presence of entanglement but also its detailed structure. This is because in a generic experimental situation with sufficiently many subsystems involved, the production of so-called genuine multipartite entanglement remains a formidable challenge. Consequently, focusing exclusively on the identification of this strongest type of entanglement may result in an all or nothing situation where some inherently quantum aspects of the resource are overlooked. On the contrary, even if the system is not genuinely multipartite entangled, there may still be many-body entanglement present in the system. An identification of the entanglement structure may thus provide us with a hint about where imperfections in the setup may occur, as well as where we can identify groups of subsystems that can still exhibit strong quantum-information-processing capabilities. However, there is no known efficient methods to identify the underlying entanglement structure. Here, we propose two complementary families of witnesses for the identification of such structures. They are based, respectively, on the detection of entanglement intactness and entanglement depth, each applicable to an arbitrary number of subsystems and whose evaluation requires only the implementation of solely two local measurements. Our method is also robust against noises and other imperfections, as reflected by our experimental implementation of these tools to verify the entanglement structure of five different eight-photon entangled states. In particular, we demonstrate how their entanglement structure can be precisely and systematically inferred from the experimental measurement of these witnesses. In achieving this goal, we also illustrate how the same set of data can be classically postprocessed to learn the most about the measured system.

The SWEET (sugars will eventually be exported transporters) proteins are sugar efflux transporters containing the MtN3_saliva domain, which affects plant development as well as responses to biotic and abiotic stresses. These proteins have not been functionally characterized in the tetraploid cotton, Gossypium hirsutum, which is a widely cultivated cotton species. In this study, we comprehensively analyzed the cotton SWEET gene family. A total of 55 putative G. hirsutum SWEET genes were identified. The GhSWEET genes were classified into four clades based on a phylogenetic analysis and on the examination of gene structural features. Moreover, chromosomal localization and an analysis of homologous genes in Gossypium arboreum, Gossypium raimondii, and G. hirsutum suggested that a whole-genome duplication, several tandem duplications, and a polyploidy event contributed to the expansion of the cotton SWEET gene family, especially in Clade III and IV. Analyses of cis-acting regulatory elements in the promoter regions, expression profiles, and artificial selection revealed that the GhSWEET genes were likely involved in cotton developmental processes and responses to diverse stresses. These findings may clarify the evolution of G. hirsutum SWEET gene family and may provide a foundation for future functional studies of SWEET proteins regarding cotton development and responses to abiotic stresses.

The security of quantum key distribution (QKD) relies on the Heisenberg uncertainty principle, with which legitimate users are able to estimate information leakage by monitoring the disturbance of the transmitted quantum signals. Normally, the disturbance is reflected as bit flip errors in the sifted key; thus, privacy amplification, which removes any leaked information from the key, generally depends on the bit error rate. Recently, a round-robin differential-phase-shift QKD protocol for which privacy amplification does not rely on the bit error rate (Sasaki et al 2014 Nature 509 475) was proposed. The amount of leaked information can be bounded by the sender during the state-preparation stage and hence, is independent of the behavior of the unreliable quantum channel. In our work, we apply the tagging technique to the protocol and present a tight bound on the key rate and employ a decoy-state method. The effects of background noise and misalignment are taken into account under practical conditions. Our simulation results show that the protocol can tolerate channel error rates close to 50% within a typical experiment setting. That is, there is a negligible restriction on the error rate in practice.

Coherence, the superposition of orthogonal quantum states, is indispensable in various quantum processes. Inspired by the polynomial invariant for classifying and quantifying entanglement, we first define polynomial coherence measure and systematically investigate its properties. Except for the qubit case, we show that there is no polynomial coherence measure satisfying the criterion that its value takes zero if and only if for incoherent states. Then, we release this strict criterion and obtain a necessary condition for polynomial coherence measure. Furthermore, we give a typical example of polynomial coherence measure for pure states and extend it to mixed states via a convex-roof construction. Analytical formula of our convex-roof polynomial coherence measure is obtained for symmetric states which are invariant under arbitrary basis permutation. Consequently, for general mixed states, we give a lower bound of our coherence measure.

Quantum cryptography holds the promise to establish an information-theoretically secure global network. All field tests of metropolitan-scale quantum networks to date are based on trusted relays. The security critically relies on the accountability of the trusted relays, which will break down if the relay is dishonest or compromised. Here, we construct a measurement-device-independent quantum key distribution (MDIQKD) network in a star topology over a 200-square-kilometer metropolitan area, which is secure against untrustful relays and against all detection attacks. In the field test, our system continuously runs through one week with a secure key rate 10 times larger than previous results. Our results demonstrate that the MDIQKD network, combining the best of both worlds—security and practicality, constitutes an appealing solution to secure metropolitan communications.

Quantum random number generators can provide genuine randomness by appealing to the fundamental principles of quantum mechanics. In general, a physical generator contains two parts—a randomness source and its readout. The source is essential to the quality of the resulting random numbers; hence, it needs to be carefully calibrated and modeled to achieve information-theoretical provable randomness. However, in practice, the source is a complicated physical system, such as a light source or an atomic ensemble, and any deviations in the real-life implementation from the theoretical model may affect the randomness of the output. To close this gap, we propose a source-independent scheme for quantum random number generation in which output randomness can be certified, even when the source is uncharacterized and untrusted. In our randomness analysis, we make no assumptions about the dimension of the source. For instance, multiphoton emissions are allowed in optical implementations. Our analysis takes into account the finite-key effect with the composable security definition. In the limit of large data size, the length of the input random seed is exponentially small compared to that of the output random bit. In addition, by modifying a quantum key distribution system, we experimentally demonstrate our scheme and achieve a randomness generation rate of over 5×10^{3} bit/s.

Quantum random number generators (QRNGs) output genuine random numbers based upon the uncertainty principle. A QRNG contains two parts in general—a randomness source and a readout detector. How to remove detector imperfections has been one of the most important questions in practical randomness generation. We propose a simple solution, measurement-device-independent QRNG, which not only removes all detector side channels but is robust against losses. In contrast to previous fully device-independent QRNGs, our scheme does not require high detector efficiency or nonlocality tests. Simulations show that our protocol can be implemented efficiently with a practical coherent state laser and other standard optical components. The security analysis of our QRNG consists mainly of two parts: measurement tomography and randomness quantification, where several new techniques are developed to characterize the randomness associated with a positive-operator valued measure.

Coherent state photon sources are widely used in quantum information processing. In many applications, such as quantum key distribution (QKD), a coherent state functions as a mixture of Fock states by assuming that its phase is continuously randomized. In practice, such a crucial assumption is often not satisfied, and therefore the security of existing QKD experiments is not guaranteed. To bridge this gap, we provide a rigorous security proof of QKD with discrete-phase-randomized coherent state sources. Our results show that the performance of the discrete-phase randomization case is close to its continuous counterpart with only a small number (say, 10) of discrete phases. Compared to the conventional continuous phase randomization case, where an infinite amount of random bits are required, our result shows that only a small amount (say, 4 bits) of randomness is needed.

A protocol with the potential of beating the existing distance records for conventional quantum key distribution (QKD) systems is proposed. It borrows ideas from quantum repeaters by using memories in the middle of the link, and that of measurement-device-independent QKD, which only requires optical source equipment at the userʼs end. For certain memories with short access times, our scheme allows a higher repetition rate than that of quantum repeaters with single-mode memories, thereby requiring lower coherence times. By accounting for various sources of nonideality, such as memory decoherence, dark counts, misalignment errors, and background noise, as well as timing issues with memories, we develop a mathematical framework within which we can compare QKD systems with and without memories. In particular, we show that with the state-of-the-art technology for quantum memories, it is potentially possible to devise memory-assisted QKD systems that, at certain distances of practical interest, outperform current QKD implementations.

Zero-knowledge proof (ZKP) is a fundamental cryptographic primitive that allows a prover to convince a verifier of the validity of a statement without leaking any further information. As an efficient variant of ZKP, noninteractive zero-knowledge proof (NIZKP) adopting the Fiat-Shamir heuristic is essential to a wide spectrum of applications, such as federated learning, blockchain, and social networks. However, the heuristic is typically built upon the random oracle model that makes ideal assumptions about hash functions, which does not hold in reality and thus undermines the security of the protocol. Here, we present a quantum solution to the problem. Instead of resorting to a random oracle model, we implement a quantum randomness service. This service generates random numbers certified by the loophole-free Bell test and delivers them with postquantum cryptography (PQC) authentication. By employing this service, we conceive and implement NIZKP of the three-coloring problem. By bridging together three prominent research themes, quantum nonlocality, PQC, and ZKP, we anticipate this work to inspire more innovative applications that combine quantum information science and the cryptography field. [ABSTRACT FROM AUTHOR]