Article
Operations Research & Management Science
Xiao-Bing Li, Suliman Al-Homidan, Qamrul Hasan Ansari, Jen-Chih Yao
Summary: This paper uses an asymptotic assumption to study the maximum of finitely many convex polynomials, showing that it is an asymptotically well-behaved function. Two examples are provided to illustrate the main result, and some known results from recent literature are reproduced as an application.
OPERATIONS RESEARCH LETTERS
(2021)
Article
Computer Science, Information Systems
Mohamed Taoufiq Damir, Alex Karrila, Laia Amoros, Oliver W. Gnilke, David Karpuk, Camilla Hollanti
Summary: The design of lattice coset codes for wiretap channels considers bounds on the eavesdropper's correct decoding probability and information leakage. Both information leakage and error probability are controlled by the average flatness factor of the eavesdropper's lattice, leading to the study of well-rounded lattices for minimizing this factor. The constructions of some well-rounded lattices are also provided in order to achieve optimal results.
IEEE TRANSACTIONS ON INFORMATION THEORY
(2021)
Article
Chemistry, Analytical
Jung Hoon Lee, Yunjoo Kim, Jong Yeol Ryu
Summary: This paper proposes a random beam-based non-orthogonal multiple access (NOMA) scheme for low latency multiple-input single-output (MISO) broadcast channels. The scheme supports multiple users by utilizing random beams, and improves system performance by optimizing user grouping and power allocation.
Article
Engineering, Electrical & Electronic
Ignacio Santamaria, Victor Elvira
Summary: In this letter, a stochastic representation for the eigenvalues of 2 x 2 complex central uncorrelated Wishart matrices with an arbitrary number of degrees of freedom is presented. The draws from the joint pdf of the eigenvalues are generated by means of a simple transformation of a chi-squared random variable and an independent beta random variable. This sampling scheme provides a simple derivation of some eigenvalue function distributions and may be useful in wireless communications and multivariate statistical analysis.
IEEE SIGNAL PROCESSING LETTERS
(2021)
Article
Engineering, Electrical & Electronic
Kuang-Hao Liu
Summary: Analyzing the QD probability of NOMA on Rician fading channels is complex due to the dependence on the angle between user channels and the complexities involved with random vectors and matrices. Approximation methods are proposed to derive a closed-form expression for the QD probability over MISO Rician channels and to evaluate the optimality of NOMA on Rician fading channels.
IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY
(2021)
Article
Engineering, Electrical & Electronic
Gabor Fodor, Sebastian Fodor, Miklos Telek
Summary: In this study, a minimum mean squared error receiver for time-varying Rayleigh fading channels in multi-user multiple input multiple output systems is proposed using a random matrix theoretical approach. The receiver minimizes symbol error and improves signal-to-interference-plus-noise ratio.
IEEE TRANSACTIONS ON COMMUNICATIONS
(2022)
Article
Mathematics, Applied
Ion Nechita, Satvik Singh
Summary: This paper introduces a graphical calculus for computing averages of tensor network diagrams with random vectors containing independent uniform complex phases or signs. The method is also applicable to the real case and can be used to study the separability condition of relevant bipartite matrices. Furthermore, the paper analyzes the twirling of linear maps between matrix algebras by independent diagonal unitary matrices, showcasing another application of the method.
LINEAR ALGEBRA AND ITS APPLICATIONS
(2021)
Article
Physics, Mathematical
Faedi Loulidi, Ion Nechita
Summary: The notion of compatibility dimension for a set of quantum measurements is introduced, with bounds provided using cloning and algebraic techniques. The case of two orthonormal bases, particularly mutually unbiased bases, is analyzed in detail.
JOURNAL OF MATHEMATICAL PHYSICS
(2021)
Article
Mathematics
Ion Nechita, Simon Schmidt, Moritz Weber
Summary: The article introduces a Sinkhorn-type algorithm for generating quantum permutation matrices that encode symmetries of graphs. It demonstrates the algorithm's application in the representation theory of the quantum permutation group and its subgroups, as well as its use in determining whether a given graph has quantum symmetries.
EXPERIMENTAL MATHEMATICS
(2023)
Article
Physics, Mathematical
Ryszard Kukulski, Ion Nechita, Tukasz Pawela, Zbigniew Puchala, Karol Zyczkowski
Summary: Various techniques for generating random quantum channels acting on d-dimensional quantum states have been investigated, including three mathematically equivalent approaches to the sampling problem. The conditions under which these techniques provide a uniform Lebesgue measure on the convex set of quantum operations are discussed, along with a comparison of their advantages and computational complexity. Additionally, mean values of several characteristics of a given quantum channel have been computed, and spectral properties of random quantum channels and their invariant states have been studied.
JOURNAL OF MATHEMATICAL PHYSICS
(2021)
Article
Quantum Science & Technology
Satvik Singh, Ion Nechita
Summary: This article examines the invariance and covariance of bipartite matrices and linear maps under the actions of diagonal unitary and orthogonal groups, presenting a variety of examples to demonstrate their diverse scenarios. It analyzes their linear algebraic structure, investigates different notions of positivity, and generalizes the concept of completely positive matrices. Additionally, explicit characterizations of covariance for linear maps are provided, along with the analysis of properties like positivity, decomposability, and complete positivity.
Article
Physics, Multidisciplinary
Maria Anastasia Jivulescu, Cecilia Lancien, Ion Nechita
Summary: This paper introduces and studies a class of entanglement criteria based on local contractions and tensor norms. The performance of these criteria is analyzed on different systems and quantum states, and previously studied criteria are viewed within this framework. By deriving systematic relations between the criteria, two conjectures are confirmed.
ANNALES HENRI POINCARE
(2022)
Article
Physics, Multidisciplinary
Satvik Singh, Ion Nechita
Summary: We prove the validity of the PPT2 conjecture for linear maps between matrix algebras that are covariant under the action of the diagonal unitary group. This conjecture applies to many important maps, such as Choi-type maps, depolarizing maps, dephasing maps, amplitude damping maps, and mixtures thereof.
ANNALES HENRI POINCARE
(2022)
Article
Physics, Mathematical
Andreas Bluhm, Ion Nechita
Summary: This article reviews the maximal noise robustness of incompatible measurements and rederives them using tensor norms. It also explores the related concepts of incompatibility witnesses.
JOURNAL OF MATHEMATICAL PHYSICS
(2022)
Article
Physics, Multidisciplinary
Satvik Singh, Ion Nechita
Summary: We study bipartite unitary operators that are invariant under the local actions of diagonal unitary and orthogonal groups. The structural properties of these operators are investigated and it is argued that the diagonal symmetry makes them suitable for analytical study. As a first application, large new families of dual unitary gates are constructed in arbitrary finite dimensions, which serve as important toy models for studying entanglement spreading in quantum circuits. The non-local nature of these invariant operators is analyzed in both discrete and continuous settings. It is found that these operators can be used to simulate any bipartite unitary gate via stochastic local operations and classical communication. Furthermore, a one-to-one connection between the set of local diagonal unitary invariant dual unitary operators with maximum entangling power and the set of complex Hadamard matrices is established. Finally, the distinguishability of unitary operators in the setting of the stated diagonal symmetry is discussed.
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
(2022)
Article
Physics, Mathematical
Andreas Bluhm, Anna Jencova, Ion Nechita
Summary: In this work, the authors investigate measurement incompatibility in general probabilistic theories (GPTs) and provide several equivalent characterizations of compatible measurements. They use these characterizations to study the amount of incompatibility present in different GPTs and find new bounds on the maximal incompatibility in more than three qubit measurements.
COMMUNICATIONS IN MATHEMATICAL PHYSICS
(2022)
Article
Physics, Multidisciplinary
Qing-Hua Zhang, Ion Nechita
Summary: We propose a new criterion for incompatibility of quantum channels based on Fisher information. The criterion is inspired by a similar one for quantum measurements. We provide analytical conditions for the incompatibility of two Schur channels and compare the newly introduced criterion with known results from asymmetric quantum cloning.
Article
Quantum Science & Technology
Teiko Heinosaari, Maria Anastasia Jivulescu, Ion Nechita
Summary: This article studies the partially ordered set of equivalence classes of quantum measurements endowed with the post-processing partial order. By mapping this set into a simpler partially ordered set using an order preserving map, the essential structure is preserved while unnecessary details are ignored. The proposed map based on Fisher information is shown to be optimal among all quadratic maps.
Article
Quantum Science & Technology
Faedi Loulidi, Ion Nechita
Summary: This article examines the relationship between the incompatibility of quantum measurements and Bell inequalities, and finds that the Clauser-Horne-Shimony-Holt inequality and its variants are the only ones that satisfy the condition.
Article
Quantum Science & Technology
Andreas Bluhm, Ion Nechita
Summary: In this study, the amount of steerability in quantum theory is characterized by connecting the maximal violation of a steering inequality to an inclusion problem of free spectrahedra. The findings provide new upper bounds on the maximal violation of steering inequalities and prove the optimality of previously obtained violations. The study also investigates the inclusion constants of matrix cube and matrix diamond and derives new bounds on the amount of incompatibility available in dichotomic quantum measurements.
Article
Computer Science, Theory & Methods
Ion Nechita, Jordi Pillet
Summary: We introduce SudoQ, a quantum version of Sudoku where entries in the grid are projections instead of integers, leading to a larger solution set. We analyze a randomized algorithm for computing solutions and present two conjectures linking quantum and classical solutions of SudoQ puzzles, supported by analytical and numerical evidence.
QUANTUM INFORMATION & COMPUTATION
(2021)
