Rank of a tensor and quantum entanglement
From MaRDI portal
Publication:6593278
DOI10.1080/03081087.2023.2211717zbMATH Open1547.14073MaRDI QIDQ6593278
Shmuel Friedland, Wojciech T. Bruzda, Karol Życzkowski
Publication date: 26 August 2024
Published in: Linear and Multilinear Algebra (Search for Journal in Brave)
Numerical optimization and variational techniques (65K10) Combinatorial optimization (90C27) Multilinear algebra, tensor calculus (15A69) Quantum coherence, entanglement, quantum correlations (81P40) Secant varieties, tensor rank, varieties of sums of powers (14N07)
Cites Work
- Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?
- Über homogene Polynome in ($L^{2}$)
- Combinatorial optimization. Theory and algorithms.
- Subtracting a best rank-1 approximation may increase tensor rank
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Some examples of forms of high rank
- Canonical polyadic decomposition of third-order tensors: relaxed uniqueness conditions and algebraic algorithm
- A variational approach of the rank function
- Quantum cryptography: public key distribution and coin tossing
- Refined methods for the identifiability of tensors
- Sufficient conditions for Strassen's additivity conjecture
- Computing symmetric rank for symmetric tensors
- On the rank of a binary form
- On the generic and typical ranks of 3-tensors
- The complexity of tensor rank
- On the maximal multiplicative complexity of a family of bilinear forms
- An enhanced line search scheme for complex-valued tensor decompositions. Application in DS-CDMA
- On the ranks and border ranks of symmetric tensors
- Generic and typical ranks of multi-way arrays
- Rank and optimal computation of generic tensors
- Typical tensorial rank
- Bounds on the ranks of some 3-tensors
- Three-way arrays: rank and uniqueness of trilinear decompositions, with application to arithmetic complexity and statistics
- Quantum information theory
- Decomposition of quantics in sums of powers of linear forms
- The expression of a tensor or a polyadic as a sum of products.
- Multiple invariants and generalized rank of a \(p\)-way matrix or tensor.
- Das Dämpfungsproblem in der Wellenmechanik.
- Wahrscheinlichkeitstheoretischer Aufbau der Quantenmechanik.
- Sulla rappresentazione delle coppie di forme ternarie mediante somme di potenze di forme lineari.
- Algebraische Reduction der Scharen bilinearer Formen.
- Sur une extension d'un théor`eme de Clebsch relatif aux courbes du quatrième degré.
- Relativity of pure states entanglement.
- Identifiability beyond Kruskal's bound for symmetric tensors of degree 4
- The tensor rank of tensor product of two three-qubit W states is eight
- Tensor rank is not multiplicative under the tensor product
- On the locus of points of high rank
- Ranks of tensors, secant varieties of Segre varieties and fat points
- Kruskal's uniqueness inequality is sharp
- Sets computing the symmetric tensor rank
- Secant varieties of Segre-Veronese varieties
- Counterexamples to Strassen's direct sum conjecture
- A concise proof of Kruskal's theorem on tensor decomposition
- A note on the gap between rank and border rank
- Identifiability for a class of symmetric tensors
- On the Alexander-Hirschowitz theorem
- On maximum, typical and generic ranks
- The non-singular cubic surfaces. A new method of investigation with special reference to questions of reality.
- Probability relations between separated systems.
- Discussion of probability relations between separated systems.
- On the complexity of finding tensor ranks
- Multipartite generalization of the Schmidt decomposition
- Remarks on the Symmetric Rank of Symmetric Tensors
- A Proof that the Maximal Rank for Plane Quartics is Seven
- The Computational Complexity of Duality
- Comon's Conjecture, Rank Decomposition, and Symmetric Rank Decomposition of Symmetric Tensors
- On the Uniqueness of the Canonical Polyadic Decomposition of Third-Order Tensors---Part I: Basic Results and Uniqueness of One Factor Matrix
- On the Uniqueness of the Canonical Polyadic Decomposition of Third-Order Tensors---Part II: Uniqueness of the Overall Decomposition
- Generalized Schmidt decomposability and its relation to projective norms in multipartite entanglement
- The Quantum Computer Puzzle
- On generic identifiability of symmetric tensors of subgeneric rank
- Some Numerical Results on the Rank of Generic Three-Way Arrays over $\mathbb{R}$
- Quantum entanglement
- Secant varieties of ℙ¹×⋯×ℙ¹ (𝕟-times) are NOT defective for 𝕟≥5
- ORBITOPES
- Tripartite Entanglement Transformations and Tensor Rank
- Tensor rank is NP-complete
- Generic Uniqueness Conditions for the Canonical Polyadic Decomposition and INDSCAL
- Induction for secant varieties of Segre varieties
- On the Validity of the Direct Sum Conjecture
- Optimal Evaluation of Pairs of Bilinear Forms
- Approximate Solutions for the Bilinear Form Computational Problem
- Partial and Total Matrix Multiplication
- Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer
- A Multilinear Singular Value Decomposition
- On the Best Rank-1 and Rank-(R1 ,R2 ,. . .,RN) Approximation of Higher-Order Tensors
- A Counterexample to Comon's Conjecture
- Nuclear norm of higher-order tensors
- Most boson quantum states are almost maximally entangled
- Sharp Effective Nullstellensatz
- Highly entangled tensors
- Spectral norm of a symmetric tensor and its computation
- On Strassen's Rank Additivity for Small Three-way Tensors
- An Algorithm For Generic and Low-Rank Specific Identifiability of Complex Tensors
- Geometry of Quantum States
- Symmetric Tensors and Symmetric Tensor Rank
- Effective Criteria for Specific Identifiability of Tensors and Forms
- Quantum states with Einstein-Podolsky-Rosen correlations admitting a hidden-variable model
- On Orthogonal Tensors and Best Rank-One Approximation Ratio
- Most Tensor Problems Are NP-Hard
- Optimal evaluation of pairs of bilinear forms
- Matrices
Related Items (1)
This page was built for publication: Rank of a tensor and quantum entanglement