Absolutely maximally entangled pure states of multipartite quantum systems

Abstract

Absolutely maximally entangled (AME) pure states of a system composed of $N$ parties are distinguished by the property that for any splitting at least one partial trace is maximally mixed. Due to maximal possible correlations between any two selected subsystems these states have numerous applications in various fields of quantum information processing including multi-user teleportation, quantum error correction and secret sharing. We present an updated survey of various techniques to generate such strongly entangled states, including those going beyond the standard construction of graph and stabilizer states. Our contribution includes, in particular, analysis of the degree of entanglement of reduced states obtained by partial trace of AME projectors, states obtained by a symmetric superposition of GHZ states, an orthogonal frequency square representation of the "golden" AME state and an updated summary of the number of local unitary equivalence classes.

arXiv comment41 pages, 20 figures, extended discussion about applications

References in corpus (120)

• Quantum entanglement
• The Large N Limit of Superconformal Field Theories and Supergravity
• Mixed State Entanglement and Quantum Error Correction
• Separability Criterion for Density Matrices
• Holographic Derivation of Entanglement Entropy from AdS/CFT
• Three qubits can be entangled in two inequivalent ways
• Quantum secret sharing
• Distributed Entanglement
• Good Quantum Error-Correcting Codes Exist
• Entanglement Measures and Purification Procedures
• How to share a quantum secret
• Multiple Particle Interference and Quantum Error Correction
• Holographic quantum error-correcting codes: Toy models for the bulk/boundary correspondence
• Geometric measure of entanglement and applications to bipartite and multipartite quantum states
• Four qubits can be entangled in nine different ways
• Generalized Schmidt decomposition and classification of three-quantum-bit states
• Global entanglement in multiparticle systems
• Holographic duality from random tensor networks
• Exact and Asymptotic Measures of Multipartite Pure State Entanglement
• On the Entangling Power of Quantum Evolutions
• Everything You Always Wanted to Know About LOCC (But Were Afraid to Ask)
• The randomized measurement toolbox
• Multipartite entanglement, quantum-error-correcting codes, and entangling power of quantum evolutions
• Graphical description of the action of local Clifford transformations on graph states
• Mixed-state entanglement from local randomized measurements
• Exact Correlation Functions for Dual-Unitary Lattice Models in 1+1 Dimensions
• Absolute Maximal Entanglement and Quantum Secret Sharing
• Automated Search for new Quantum Experiments
• Quantum marginal problem and N-representability
• Quantifying entanglement resources
• How entangled can two couples get?
• Maximally multipartite entangled states
• Multipartite generalisation of the Schmidt decomposition
• Computing Local Invariants of Qubit Systems
• Absolutely Maximally Entangled states, combinatorial designs and multi-unitary matrices
• Multi-Qubit Systems: Highly Entangled States and Entanglement Distribution
• Genuinely multipartite entangled states and orthogonal arrays
• Absolutely maximally entangled states of seven qubits do not exist
• Local unitary equivalence of multipartite pure states
• Multiqubit symmetric states with high geometric entanglement
• All Maximally Entangled Four Qubits States
• One-qubit reduced states of a pure many-qubit state: polygon inequalities
• Entanglement and quantum combinatorial designs
• Bounds on absolutely maximally entangled states from shadow inequalities, and the quantum MacWilliams identity
• Exploring pure quantum states with maximally mixed reductions
• Creating ensembles of dual unitary and maximally entangling quantum evolutions
• Polynomial invariants for discrimination and classification of four-qubit entanglement
• Multipartite entanglement in heterogeneous systems
• Hyper-invariant tensor networks and holography
• Thirty-six entangled officers of Euler: Quantum solution to a classically impossible problem
• Unitary quantum gates, perfect entanglers and unistochastic maps
• Generalized Criterion of Maximally Multi-Qubit Entanglement
• Local Unitary Classification of Arbitrary Dimensional Multipartite Pure States
• Necessary and sufficient conditions for local manipulation of multipartite pure quantum states
• Exploring the Tensor Networks/AdS Correspondence
• Code properties from holographic geometries
• Calderbank-Steane-Shor Holographic Quantum Error Correcting Codes
• Quantum Codes of Maximal Distance and Highly Entangled Subspaces
• Constructing optimal quantum error correcting codes from absolute maximally entangled states
• Entangling Power of Permutations
• Bound entanglement from randomized measurements
• Relativity of pure states entanglement
• Quantum circuits for maximally entangled states
• Tensor network and ($p$-adic) AdS/CFT
• A complete hierarchy for the pure state marginal problem in quantum mechanics
• Multipartite Entanglement and Frustration
• Information-theoretic interpretation of quantum error-correcting codes
• Multipartite-entanglement monotones and polynomial invariants
• Entanglement between two subsystems, the Wigner semicircle and extreme value statistics
• Analytic Expressions for Geometric Measure of Three Qubit States
• Can local dynamics enhance entangling power?
• Analysing quantum systems with randomised measurements
• Entanglement of Subspaces and Error Correcting Codes
• Central charges of aperiodic holographic tensor network models
• Majorana dimers and holographic quantum error-correcting codes
• Constructions of k-uniform and absolutely maximally entangled states beyond maximum distance codes
• Quantum error correction codes and absolutely maximally entangled states
• Construction and local equivalence of dual-unitary operators: from dynamical maps to quantum combinatorial designs
• Phase transitions for random states and a semi-circle law for the partial transpose
• Hierarchical generalization of dual unitarity
• Stochastic Local Operations with Classical Communication of Absolutely Maximally Entangled States
• On bipartite unitary matrices generating subalgebra-preserving quantum operations
• Holographic Codes from Hyperinvariant Tensor Networks
• Absolutely maximally entangled state equivalence and the construction of infinite quantum solutions to the problem of 36 officers of Euler
• Orthogonality for Quantum Latin Isometry Squares
• Absolutely maximally entangled states, quantum maximum distance separable codes, and quantum repeaters
• Minimal Renyi-Ingarden-Urbanik entropy of multipartite quantum states
• Gaussian maximally multipartite entangled states
• Entanglement detection with trace polynomials
• Existence of Universal Entangler
• 9 $\times$ 4 = 6 $\times$ 6: Understanding the quantum solution to the Euler's problem of 36 officers
• Entangling power of multipartite unitary gates
• Fine-Structure Classification of Multiqubit Entanglement by Algebraic Geometry
• Deterministic generation of qudit photonic graph states from quantum emitters
• On some classes of bipartite unitary operators
• $k$-uniform mixed states
• Tensor rank and entanglement of pure quantum states
• Conformal Properties of Hyperinvariant Tensor Networks
• Quantum combinatorial designs and $k$-uniform states
• Modifying method of constructing quantum codes from highly entangled states
• Highly entangled multi-qubit states with simple algebraic structure
• Cut-resistant links and multipartite entanglement resistant to particle loss
• Genuinely quantum SudoQ and its cardinality
• Hyper-Invariant MERA: Approximate Holographic Error Correction Codes with Power-Law Correlations
• Geometric approach to entanglement quantification with polynomial measures
• Criterion for SLOCC Equivalence of Multipartite Quantum States
• Polynomial invariants of degree 4 for even-$n$ qubits and their applications in entanglement classification
• Tensor network decompositions for absolutely maximally entangled states
• Near-Term Spin-Qubit Architecture Design via Multipartite Maximally-Entangled States
• Construction of perfect tensors using biunimodular vectors
• Two-Unitary Complex Hadamard Matrices of Order $36$
• Bulk-boundary correspondence from hyper-invariant tensor networks
• Engineering holography with stabilizer graph codes
• Four-qubit critical states
• Finding maximal quantum resources
• Quantum convolutional channels and multiparameter families of 2-unitary matrices
• On two maximally entangled couples
• Distinguishing Graph States by the Properties of Their Marginals
• Characterizing maximally many-body entangled fermionic states by using $M$-body density matrix
• Quantum Circuits for High-Dimensional Absolutely Maximally Entangled States