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We look into multipartite quantum states on which quantum cryptographic protocols including quantum key distribution and quantum secret sharing can be perfectly performed, and define the quantum cryptographic resource distillable rate as the asymptotic rate at which such multipartite state can be distilled from a given multipartite state. Investigating several relations between entanglement and the rate, we show that there exists a multipartite bound entangled state whose quantum cryptographic resource distillable rate is strictly positive, that is, there exists a multipartite entangled state which is not distillable, but can be useful for quantum cryptography such as quantum key distribution and quantum secret sharing., 9 pages, 2 figures

We present a new quantum-memory-assisted entropic uncertainty relation for multipartite systems which shows the uncertainty principle of quantum mechanics. Notably, our results recover some well-known entropic uncertainty relations for two arbitrary incompatible observables that demonstrate the uncertainties about the results of two measurements. This uncertainty relation might play a critical role in the foundations of quantum theory.

The Seidel energy of a simple graph G is the sum of the absolute values of the eigenvalues of the Seidel matrix of G. In this paper we study the Seidel eigenvalues of complete multipartite graphs and find the exact value of the Seidel energy of the complete multipartite graphs.

We calculate spin correlation functions using IBM quantum processors, accessed online. We demonstrate the rotational invariance of the singlet state, interesting properties of the triplet states, and surprising features of a state of three entangled qubits. This exercise is ideal for remote learning and generates data with real quantum mechanical systems that are impractical to investigate in the local laboratory. Students learn a wide variety of skills, including calculation of multipartite spin correlation functions, design and analysis of quantum circuits, and remote measurement with real quantum processors.

The human face is complex and multipartite, and characterization of its genetic architecture remains challenging. Using a multivariate genome-wide association study meta-analysis of 8,246 European individuals, we identified 203 genome-wide-significant signals (120 also study-wide significant) associated with normal-range facial variation. Follow-up analyses indicate that the regions surrounding these signals are enriched for enhancer activity in cranial neural crest cells and craniofacial tissues, several regions harbor multiple signals with associations to different facial phenotypes, and there is evidence for potential coordinated actions of variants. In summary, our analyses provide insights into the understanding of how complex morphological traits are shaped by both individual and coordinated genetic actions. ispartof: Nature Genetics vol:53 issue:1 ispartof: location:United States status: Published online

Multipartite viruses have a segmented genome, with each segment encapsidated separately. In all multipartite virus species for which the question has been addressed, the distinct segments reproducibly accumulate at a specific and host-dependent relative frequency, defined as the ‘genome formula’. Here, we test the hypothesis that the multipartite genome organization facilitates the regulation of gene expression via changes of the genome formula and thus via gene copy number variations. In a first experiment, the faba bean necrotic stunt virus (FBNSV), whose genome is composed of eight DNA segments each encoding a single gene, was inoculated into faba bean or alfalfa host plants, and the relative concentrations of the DNA segments and their corresponding messenger RNAs (mRNAs) were monitored. In each of the two host species, our analysis consistently showed that the genome formula variations modulate gene expression, the concentration of each genome segment linearly and positively correlating to that of its cognate mRNA but not of the others. In a second experiment, twenty parallel FBNSV lines were transferred from faba bean to alfalfa plants. Upon host switching, the transcription rate of some genome segments changes, but the genome formula is modified in a way that compensates for these changes and maintains a similar ratio between the various viral mRNAs. Interestingly, a deep-sequencing analysis of these twenty FBNSV lineages demonstrated that the host-related genome formula shift operates independently of DNA-segment sequence mutation. Together, our results indicate that nanoviruses are plastic genetic systems, able to transiently adjust gene expression at the population level in changing environments, by modulating the copy number but not the sequence of each of their genes.

One of the fundamental traits of quantum entanglement is the restricted shareability among multipartite quantum systems, namely monogamy of entanglement, while it is well known that monogamy inequalities are always satisfied by entanglement measures with convexity. Here we present a measure of entanglement, logarithmic convex-roof extended negativity (LCREN) satisfying important characteristics of an entanglement measure, and investigate the monogamy relation for logarithmic negativity and LCREN both without convexity. We show exactly that the α th power of logarithmic negativity, and a newly defined good measure of entanglement, LCREN, obey a class of general monogamy inequalities in multiqubit systems, 2 ⊗ 2 ⊗ 3 systems and 2 ⊗ 2 ⊗ 2 n systems for α ≥ 4 ln 2 . We provide a class of general polygamy inequalities of multiqubit systems in terms of logarithmic convex-roof extended negativity of assistance (LCRENoA) for 0 ≤ β ≤ 2 . Given that the logarithmic negativity and LCREN are not convex, these results are surprising. Using the power of the logarithmic negativity and LCREN, we further establish a class of tight monogamy inequalities of multiqubit systems, 2 ⊗ 2 ⊗ 3 systems and 2 ⊗ 2 ⊗ 2 n systems in terms of the α th power of logarithmic negativity and LCREN for α ≥ 4 ln 2 . We also show that the β th power of LCRENoA obeys a class of tight polygamy inequalities of multiqubit systems for 0 ≤ β ≤ 2 .

Unlike single-network hydrogel whose thermodynamic equilibrium of all phases is governed by one single rule, double-network (DN) hydrogel is incorporated of two coexisting phases, which are separated from each other due to the differences in their mechanoresponsive responses. However, the resonance differences and multipartite dynamics of coexisting phases in these DN hydrogels have not been fully understood. This paper reports a new methodology to use a rheological model in combination of Arrhenius principle and Kirkwood approximation, to characterize the differences in mechanoresponsive resonances and viscoelastic behaviors of coexisting phases in the DN hydrogel. Their multipartite dynamics has been identified to originate from mechanical stretching, mechanochemical coupling and chemical kinetics of the ductile network, original brittle network and self-healed brittle network, respectively. Furthermore, molecular dynamics simulation and finite-element analysis have been conducted to verify the proposed model and explore the toughening mechanism, which is determined not only by the mechanochemical coupling, but also by the self-healing kinetics. Finally, effectiveness of proposed model has been well verified using the experimental results of DN hydrogels reported in literature.

Bipartite and multipartite entangled states are basic ingredients for constructing quantum networks and their accurate verification is crucial to the functioning of the networks, especially for untrusted networks. Here we propose a simple approach for verifying the Bell state in an untrusted quantum network in which one party is not honest. Only local projective measurements are required for the honest party. It turns out each verification protocol is tied to a probability distribution on the Bloch sphere and its performance has an intuitive geometric meaning. This geometric picture enables us to construct the optimal and simplest verification protocols, which are also very useful to detecting entanglement in the untrusted network. Moreover, we show that our verification protocols can achieve almost the same sample efficiencies as protocols tailored to standard quantum state verification. Furthermore, we establish an intimate connection between the verification of Greenberger-Horne-Zeilinger states and the verification of the Bell state. By virtue of this connection we construct the optimal protocol for verifying Greenberger-Horne-Zeilinger states and for detecting genuine multipartite entanglement., 8+21 pages, 4+2 figures, and 1 table; published in npj Quantum Information

In this paper, we define D-magic labelings for oriented graphs where D is a distance set. In particular, we label the vertices of the graph with distinct integers {1,2,…,|V(G)|} in such a way that the sum of all the vertex labels that are a distance in D away from a given vertex is the same across all vertices. We give some results related to the magic constant, construct a few infinite families of D-magic graphs, and examine trees, cycles, and multipartite graphs. This definition grew out of the definition of D-magic (undirected) graphs. This paper explores some of the symmetries we see between the undirected and directed version of D-magic labelings.

Detecting multipartite quantum coherence usually requires quantum state reconstruction, which is quite inefficient for large-scale quantum systems. Along this line of research, several efficient procedures have been proposed to detect multipartite quantum coherence without quantum state reconstruction, among which the spectrum-estimation-based method is suitable for various coherence measures. Here, we first generalize the spectrum-estimation-based method for the geometric measure of coherence. Then, we investigate the tightness of the estimated lower bound of various coherence measures, including the geometric measure of coherence, $l_1$-norm of coherence, the robustness of coherence, and some convex roof quantifiers of coherence multiqubit GHZ states and linear cluster states. Finally, we demonstrate the spectrum-estimation-based method as well as the other two efficient methods by using the same experimental data [Ding et al. Phys. Rev. Research 3, 023228 (2021)]. We observe that the spectrum-estimation-based method outperforms other methods in various coherence measures, which significantly enhances the accuracy of estimation., 7 pages, 1 figure

Quantum steering, a type of quantum correlation with unique asymmetry, has important applications in asymmetric quantum information tasks. We consider a new quantum steering scenario in which one half of a two-qubit Werner state is sequentially measured by multiple Alices and the other half by multiple Bobs. We find that the maximum number of Alices who can share steering with a single Bob increases from 2 to 5 when the number of measurement settings $N$ increases from 2 to 16. Furthermore, we find a counterintuitive phenomenon that for a fixed $N$, at most 2 Alices can share steering with 2 Bobs, while 4 or more Alices are allowed to share steering with a single Bob. We further analyze the robustness of the steering sharing by calculating the required purity of the initial Werner state, the lower bound of which varies from 0.503(1) to 0.979(5). Finally, we show that our both-sides sequential steering sharing scheme can be applied to control the steering ability, even the steering direction, if an initial asymmetric state or asymmetric measurement is adopted. Our work gives insights into the diversity of steering sharing and can be extended to study the problems such as genuine multipartite quantum steering when the sequential unsharp measurement is applied., 15 pages, 4 figures, 1 table

Monogamy and polygamy relations characterize the distributions of entanglement in multipartite systems. We investigate the monogamy and polygamy relations with respect to any partitions for a superposition of the generalized $W$-class state and vacuum in terms of the Tsallis-$q$ entanglement and the R\'enyi-$\alpha$ entanglement. By using the Hamming weight of the binary vectors related to the partitions of the subsystems, new classes of monogamy and polygamy inequalities are derived, which are shown to be tighter than the existing ones. Detailed examples are presented to illustrate the finer characterization of entanglement distributions., Comment: 17 pages, 4 figures

We introduce a generalized concept of quantum teleportation in the framework of quantum measurement and reversing operation. Our framework makes it possible to find an optimal protocol for quantum teleportation enabling a faithful transfer of unknown quantum states with maximum success probability up to the fundamental limit of the no-cloning theorem. Moreover, an optimized protocol in this generalized approach allows us to overcome noise in quantum channel beyond the reach of existing teleportation protocols without requiring extra qubit resources. Our proposed framework is applicable to multipartite quantum communications and primitive functionalities in scalable quantum architectures., Comment: 17 pages, 6 figures

We generalize the constructions for the multipartite reflected entropy in order to construct spacetimes capable of representing multipartite entanglement wedge cross sections of differing party number as Ryu-Takayanagi surfaces on a single replicated geometry. We devise a general algorithm for such constructions for arbitrary party number and demonstrate how such methods can be used to derive novel inequalities constraining mulipartite entanglement wedge cross sections., Comment: 23 pages, 9 figures

We introduce a simple sufficient criterion, which allows one to tell whether a subspace of a bipartite or multipartite Hilbert space is entangled. The main ingredient of our criterion is a bound on the minimal entanglement of a subspace in terms of entanglement of vectors spanning that subspace expressed for geometrical measures of entanglement. The criterion is applicable to both completely and genuinely entangled subspaces. We explore its usefulness in several important scenarios. Further, an entanglement criterion for mixed states following directly from the condition is stated. As an auxiliary result we provide a formula for the generalized geometric measure of entanglement of the $d$--level Dicke states., title slightly changed, appendix B fixed; journal ref. added

We study the discrimination of a pair of orthogonal quantum states in the many-copy setting. This is not a problem when arbitrary quantum measurements are allowed, as then the states can be distinguished perfectly even with one copy. However, it becomes highly nontrivial when we consider states of a multipartite system and locality constraints are imposed. We hence focus on the restricted families of measurements such as local operation and classical communication (LOCC), separable operations (SEP), and the positive-partial-transpose operations (PPT) in this paper. We first study asymptotic discrimination of an arbitrary multipartite entangled pure state against its orthogonal complement using LOCC/SEP/PPT measurements. We prove that the incurred optimal average error probability always decays exponentially in the number of copies, by proving upper and lower bounds on the exponent. In the special case of discriminating a maximally entangled state against its orthogonal complement, we determine the explicit expression for the optimal average error probability and the optimal trade-off between the type-I and type-II errors, thus establishing the associated Chernoff, Stein, Hoeffding, and the strong converse exponents. Our technique is based on the idea of using PPT operations to approximate LOCC. Then, we show an infinite separation between SEP and PPT operations by providing a pair of states constructed from an unextendible product basis (UPB): they can be distinguished perfectly by PPT measurements, while the optimal error probability using SEP measurements admits an exponential lower bound. On the technical side, we prove this result by providing a quantitative version of the well-known statement that the tensor product of UPBs is UPB., Comments are welcome

For any given integer $r\geqslant 3$, let $k=k(n)$ be an integer with $r\leqslant k\leqslant n$. A hypergraph is $r$-uniform if each edge is a set of $r$ vertices, and is said to be linear if two edges intersect in at most one vertex. Let $A_1,\ldots,A_k$ be a given $k$-partition of $[n]$ with $|A_i|=n_i\geqslant 1$. An $r$-uniform hypergraph $H$ is called {\it $k$-partite} if each edge $e$ satisfies $|e\cap A_i|\leqslant 1$ for $1\leqslant i\leqslant k$. In this paper, the number of linear $k$-partite $r$-uniform hypergraphs on $n\to\infty$ vertices is determined asymptotically when the number of edges is $m(n)=o(n^{\frac{4}{3}})$. For $k=n$, it is the number of linear $r$-uniform hypergraphs on vertex set $[n]$ with $m=o(n^{ \frac{4}{3}})$ edges., accepted by Graphs and Combinatorics. arXiv admin note: text overlap with arXiv:2007.12490

Notwithstanding the initial claims of general conservation, mitochondrial genomes are a largely heterogeneous set of organellar chromosomes which displays a bewildering diversity in terms of structure, architecture, gene content, and functionality. The mitochondrial genome is typically described as a single chromosome, yet many examples of multipartite genomes have been found (for example, among sponges and diplonemeans), the mitochondrial genome is typically depicted as circular, yet many linear genomes are known (for example, among jellyfish, alveolates, and apicomplexans), the chromosome is normally said to be “small”, yet there is a huge variation between the smallest and the largest known genomes (found, for example, in ctenophores and vascular plants, respectively), even the gene content is highly unconserved, ranging from the 13 oxidative phosphorylation-related enzymatic subunits encoded by animal mitochondria to the wider set of mitochondrial genes found in jakobids. In the present paper, we compile and describe a large database of 27,873 mitochondrial genomes currently available in GenBank, encompassing the whole eukaryotic domain. We discuss the major features of mitochondrial molecular diversity, with special reference to nucleotide composition and compositional biases, moreover, the database is made publicly available for future analyses on the MoZoo Lab GitHub page.

We discuss two methods that, through a combination of cyclically gluing copies of a given $n$-party boundary state in AdS/CFT and a canonical purification, creates a bulk geometry that contains a boundary homologous minimal surface with area equal to 2 or 4 times the $n$-party entanglement wedge cross-section, depending on the parity of the party number and choice of method. The areas of the minimal surfaces are each dual to entanglement entropies that we define to be candidates for the $n$-party reflected entropy. In the context of AdS$_3$/CFT$_2$, we provide a boundary interpretation of our construction as a multiboundary wormhole, and conjecture that this interpretation generalizes to higher dimensions., 20 pages, 7 figures; added references, one figure, and expanded discussion on black holes and the boundary state

Quantum entanglement is one of important resources for quantum communication. Entanglement criteria help us detect entangled states. One of important criteria is the local uncertainty relation (LUR) entanglement criteria, which is studied extensively. However, all existent LUR criteria are dependent on the chosen observables. In the paper, applying the uncertainty principle, we improve the LUR criteria to obtain entanglement criteria for multipartite Gaussian states, which are independent on observalbes.

With respect to specific cycle-related problems, edge-colored graphs can be considered as a generalization of directed graphs. We show that properly edge-colored theta graphs play a key role in characterizing the difference between edge-colored complete graphs and multipartite tournaments. We also establish sufficient conditions for an edge-colored complete graph to contain a small and a large properly edge-colored theta graph, respectively.

Based on the theoretical basis of quantum computation, entanglement has been further explored as one of the key resources. An outstanding problem in quantum computation is the detecting of entanglement, but no closed-form algorithm exists. According to an advanced matrix rearrangement approach for detecting multipartite quantum states, we give some examples to verify the effectiveness and practicability of this new criterion. Meanwhile, this paper shows how techniques from the quantum neural network can be utilized to detect entanglement. Two models, known as the discrete-variable and the continuous-variable quantum neural network, are applied to solve the separability problem. We demonstrate the utility that such a discrete-variable quantum neural network can be trained to detect the entanglement with great exactness. And the complexity of network and computation is greatly reduced. Besides, the continuous-variable quantum neural network is applied for detecting two-qumode Gaussian state. Compared with the results of the traditional neural network, this deep quantum neural network demonstrates its capability and adaptability as well.

Quantum coherence and quantum correlations lie in the center of quantum information science, since they both are considered as fundamental reasons for significant features of quantum mechanics different from classical mechanics. We present a group of complementary relations for quantum coherence and quantum correlations; specifically, we focus on thermal discord and conditional information in scenarios of multiple measurements. We show that the summation of quantum coherence quantified in different bases has a lower bound, resulting from entropic uncertainty relations with multiple measurements. Similar results are also obtained for thermal discord and for post-measurement conditional information with multiple measurements in a multipartite system. These results indicate the general applications of the uncertainty principle to various concepts of quantum information., Comment: 7 pages

Orthobunyaviruses are arboviruses (Arthropod Borne Virus) and possess multipartite genomes made up of three negative RNAs corresponding to the small (S), medium (M) and large (L) segments. Reassortment and recombination are evolutionary driving forces of such segmented viruses and lead to the emergence of new strains and species. Retrospective studies based on phylogenetical analysis are able to evaluate these mechanisms at the end of the selection process but fail to address the dynamics of emergence. This issue was addressed using two Orthobunyaviruses infecting ruminants and belonging to the Simbu serogroup: the Sathuperi virus (SATV) and the Shamonda virus (SHAV). Both viruses were associated with abortion, stillbirth and congenital malformations occurring after transplacental transmission and were suspected to spread together in different ruminant and insect populations. This study showed that different viruses related to SHAV and SATV are spreading simultaneously in ruminants and equids of the Sub-Saharan region. Their reassortment and recombination potential was evaluated in mammalian and in insect contexts. A method was set up to determine the genomic background of any clonal progeny viruses isolated after in vitro coinfections assays. All the reassortment combinations were generated in both contexts while no recombinant virus was isolated. Progeny virus populations revealed a high level of reassortment in mammalian cells and a much lower level in insect cells. In vitro selection pressure that mimicked the host switching (insect-mammal) revealed that the best adapted reassortant virus was connected with an advantageous replicative fitness and with the presence of a specific segment.

Nonlocality without entanglement(NLWE) is a nonlocal phenomenon that occurs in quantum state discrimination of multipartite separable states. In the discrimination of orthogonal separable states, the term NLWE is used when the quantum states cannot be discriminated perfectly by local operations and classical communication. In this case, the occurrence of NLWE is independent of nonzero prior probabilities of quantum states being prepared. Recently, it has been found that the occurrence of NLWE can depend on nonzero prior probabilities in minimum-error discrimination of nonorthogonal separable states. Here, we show that even in optimal unambiguous discrimination, the occurrence of NLWE can depend on nonzero prior probabilities. We further show that NLWE can occur regardless of nonzero prior probabilities, even if only one state can be locally discriminated without error. Our results provide new insights into classifying sets of multipartite quantum states in terms of quantum state discrimination., 10 pages, 1 figure, published version

We analyze decoherence and objectivization processes in spin-spin models for arbitrary spins. We first derive the most general analytic form of the decoherence factor in the measurement limit, where the interaction Hamiltonian dominates the rest. We then analyze thermal environments and derive exact, analytic formulas for both the decoherence factor and the state fidelity of post-interaction environment states. This allows to analyze the objectivization process of the state of the central spin during the interaction. We do so using, so called, Spectrum Broadcast Structures (SBS), which are specific multipartite quantum states encoding a certain operation notion of objectivity. We analyze analytically (for short times) and numerically how higher spin influences the efficiency of decoherence and objectivization processes. As expected, the higher the spin of the environment, the more efficient decoherence and objectivization become. This work is a generalization of previous studies, limited to spin-$1/2$ systems only, and we hope will be useful in future objectivity experiments., 8 pages, 1 figure

We generalize several topological indices and introduce the general degree distance of a connected graph $G$. For $a, b \in \mathbb{R}$, the general degree distance $DD_{a,b} (G) = \sum_{ v \in V(G)} [deg_{G}(v)]^a S^b_{G} (v)$, where $V(G)$ is the vertex set of $G$, $deg_G (v)$ is the degree of a vertex $v$, $S^b_{G} (v) = \sum_{ w \in V(G) \setminus \{ v \} } [d_{G} (v,w) ]^{b}$ and $d_{G} (v,w)$ is the distance between $v$ and $w$ in $G$. We present some sharp bounds on the general degree distance for multipartite graphs and trees of given order, graphs of given order and chromatic number, graphs of given order and vertex connectivity, and graphs of given order and number of pendant vertices.