A set of multipartite orthogonal product states is locally irreducible, if it not possible to eliminate one or more from the by orthogonality-preserving local measurements. An effective way prove that a irreducible show only trivial measurement can be performed this set. In general, difficult such an must trivial. work, we develop two basic techniques deal with problem. Using these techniques, successfully existence unextendible bases (UPBs) are in every bipartition <mml:math...

Strong quantum nonlocality was introduced recently as a stronger manifestation of in multipartite systems through the notion local irreducibility all bipartitions. Known existing results for sets strongly nonlocal orthogonal states are limited to product states. In this paper, based on Rubik's cube, we give construction such consisting entangled $d\ensuremath{\bigotimes}d\ensuremath{\bigotimes}d$ $d\ensuremath{\ge}3$. Consequently, answer an open problem given by Halder et al. [Phys. Rev....

A set of multipartite orthogonal quantum states is strongly nonlocal if it locally irreducible for every bipartition the subsystems [S. Halder, M. Banik, S. Agrawal, and Bandyopadhyay, Phys. Rev. Lett. 122, 040403 (2019)]. Although this property has been shown in three-, four-, five-partite systems, existence sets $N$-partite systems remains unknown when $N\ensuremath{\ge}6$. In paper, we successfully show that a entangled exists ${({\mathbb{C}}^{d})}^{\ensuremath{\bigotimes}N}$ all...

It is impossible to mask an arbitrary quantum state into the correlations between two subsystems such that original information completely unknown each local system. This no-masking theorem proposed by Modi et al. [K. Modi, A. K. Pati, Sen(De), and U. Sen, Phys. Rev. Lett. 120, 230501 (2018)]. In this work, we propose concept of $k$-uniform masking in multipartite systems indicate relation error-correcting codes (QECCs) heterogeneous masking. As a consequence, show special case Singleton...

A set of orthogonal product states is strongly nonlocal if it locally irreducible in every bipartition, which shows the phenomenon strong quantum nonlocality without entanglement. Although such a has been shown to any three-, four-, and five-partite systems, existence sets multipartite systems remains unknown. In this paper, by using general decomposition <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>N</mml:mi></mml:math>-dimensional hypercubes, we present...

We introduce the class of multiply constant-weight codes to improve reliability certain physically unclonable function response, and extend classical coding methods construct from known \(q\) -ary codes. derive analogs Johnson bounds give constructions showing these be asymptotically tight up a constant factor under conditions. also examine rates demonstrate that are same as those corresponding parameters.

A set of multipartite orthogonal product states is strongly nonlocal if it locally irreducible in every bipartition, which shows the phenomenon strong quantum nonlocality without entanglement. It known that unextendible bases (UPBs) can show Thus interesting to investigate for UPBs. Most UPBs with minimum size cannot demonstrate nonlocality. In this paper, we construct a series different large sizes $d_A\otimes d_B\otimes d_C$ and d_C\otimes d_D$ $d_A, d_B, d_C, d_D\geq 3$, also these have...

Manganese-based compounds are expected to become promising candidates for lithium-ion battery anodes by virtue of their high theoretical specific capacity and low conversion potential. However, application is hindered inferior electrical conductivity drastic volume variations. In this work, a unique heterostructure composed MnO MnS spatially confined in pyrolytic carbon microspheres (MnO@MnS/C) was synthesized through an integrated solvothermal method, calcination, low-temperature...

We completely characterize the condition when a tile structure provides an unextendible product basis (UPB), and construct UPBs of different large sizes in $\mathbb{C}^m\otimes\mathbb{C}^n$ for any $n\geq m\geq 3$. This solves open problem [S. Halder et al., Phys. Rev. A 99, 062329 (2019)]. As application, we show that our size $(mn-4\lfloor\frac{m-1}{2}\rfloor)$ can be perfectly distinguished by local operations classical communications assisted with...

Splitter sets are closely related to lattice tilings, and have applications in flash memories conflict-avoiding codes. The study of k-radius sequences was motivated by some problems occurring large data transfer. It is observed that the existence splitter yields short length. In this paper, we obtain several new results contributing sequences. We give constructions perfect sets, as well nonexistence on them. As a byproduct, optimal Furthermore, provide explicit for certain values n,...

Constant-weight codes (CWCs) play an important role in coding theory. The problem of determining the sizes for optimal ternary CWCs with length <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$n$</tex></formula> , weight 4, and minimum Hamming distance 5 ( Notation="TeX">$(n,5,4)_{3}$</tex> </formula> code) has been settled all positive integers xmlns:xlink="http://www.w3.org/1999/xlink"> <tex...

Abstract Unextendible product basis is an important object in quantum information theory and features a broad spectrum of applications, ranging from nonlocality to cryptography. A generalized concept called uncompletable also attracts much attention. In this paper, we find some unextendible bases that are every bipartition, which answers 19 year-old open question proposed by DiVincenzo et al (2003 Commun. Math. Phys. 238 379–410). As consequence, connect such local hiding information,...

Perilla frutescens (L.), a traditional edible and medicinal crop, contains diverse triterpenes with multiple pharmacological properties. However, the biosynthesis of in perilla remains rarely revelation. In this study, nine putative 2,3-oxidosqualene cyclase (OSC) genes (PfOSC1-9) were screened from P. genome functionally characterized by heterologous expression. Camelliol C, triterpenol effect, was first identified as abundant seeds, camelliol C synthase (PfOSC7) utilizing yeast system....

A set of orthogonal states is the strongest nonlocal if it locally stable in every bipartition, which shows strong quantum nonlocality proposed by Halder et al. [Phys. Rev. Lett. 122, 040403 (2019)]. The existence sets with minimum size an open question. In this work, we partially solve question constructing $2\ensuremath{\bigotimes}2\ensuremath{\bigotimes}2\ensuremath{\bigotimes}2$ and $2\ensuremath{\bigotimes}{d}_{2}\ensuremath{\bigotimes}{d}_{3}$, where...

Abstract We prove quadratic upper bounds on the order of any autotopism a quasigroup or Latin square, and hence also automorphism Steiner triple system 1‐factorization complete graph. A corollary is that permutation σ chosen uniformly at random from symmetric group will almost surely not be an n , graph . Nor one component for square For groups it known automorphisms must have less than but we show quasigroups can greater The smallest such has 7034. prime possess autotopisms consist three...

We construct the first class of permutation codes that are capable correcting a burst up to s unstable deletions, for general s. Efficient decoding algorithms presented show correctness our constructions.

Multiply constant-weight codes (MCWCs) have been recently studied to improve the reliability of certain physically unclonable function response. In this paper, we give combinatorial constructions for MCWCs, which yield several new infinite families optimal MCWCs. Furthermore, demonstrate that Johnson-type upper bounds MCWCs are asymptotically tight fixed Hamming weights and distances. Finally, provide 2-D

Frameproof codes are used to preserve the security in context of coalition when fingerprinting digital data. Let M <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c,l</sub> (q) be largest cardinality a q-ary c-frameproof code length l and R =lim xmlns:xlink="http://www.w3.org/1999/xlink">q→∞</sub> (q)/q <sup xmlns:xlink="http://www.w3.org/1999/xlink">[ l/c]</sup> . It has been determined by Blackburn that =1 l≡1(mod c), =2 c=2 is even,...

Abstract The necessary conditions for the existence of a super‐simple resolvable balanced incomplete block design on v points with size k = 4 and index λ 2, are that ≥ 16 $v \equiv 4\; (\bmod\; {12})$ . These shown to be sufficient. © 2006 Wiley Periodicals, Inc. J Combin Designs 15: 341–356, 2007

A new ordering, extending the notion of universal cycles Chung et al. (1992), is proposed for blocks $k$-uniform set systems. Existence minimum coverings pairs by triples that possess such an ordering established all orders. The application to construction short 2-radius sequences given, along with some found through a computer search.

The Johnson-type upper bound on the maximum size of a code length n, distance d = 2w - 1, and constant n composition w̅ is [n/w <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> ] largest component w̅. Recently, Chee et al. proved that this can be achieved for all constant-composition codes sufficiently large lengths. Let N xmlns:xlink="http://www.w3.org/1999/xlink">ccc</sub> (w) smallest such length. determination (w̅) trivial binary...

Splitter sets have been widely studied due to their applications in flash memories, and close relations with lattice tilings conflict avoiding codes. In this paper, we give necessary sufficient conditions for the existence of nonsingular perfect splitter sets, B[-k <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> , k xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> ](p) where 0 ≤ = 4. Meanwhile, constructions are given. When do not...