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.

41 pages, 20 figures, extended discussion about applications

References in corpus (36)

• The randomized measurement toolbox
• Multipartite entanglement, quantum-error-correcting codes, and entangling power of quantum evolutions
• Maximally multipartite entangled states
• Multi-Qubit Systems: Highly Entangled States and Entanglement Distribution
• Genuinely multipartite entangled states and orthogonal arrays
• Multiqubit symmetric states with high geometric entanglement
• All Maximally Entangled Four Qubits States
• Exploring pure quantum states with maximally mixed reductions
• Polynomial invariants for discrimination and classification of four-qubit entanglement
• Necessary and sufficient conditions for local manipulation of multipartite pure quantum states
• Entangling Power of Permutations
• Analytic Expressions for Geometric Measure of Three Qubit States
• Analysing quantum systems with randomised measurements
• Construction and local equivalence of dual-unitary operators: from dynamical maps to quantum combinatorial designs
• Hierarchical generalization of dual unitarity
• 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
• Existence of Universal Entangler
• Entanglement detection with trace polynomials
• 9 $\times$ 4 = 6 $\times$ 6: Understanding the quantum solution to the Euler's problem of 36 officers
• Deterministic generation of qudit photonic graph states from quantum emitters
• Quantum combinatorial designs and $k$-uniform states
• Criterion for SLOCC Equivalence of Multipartite Quantum States
• Tensor network decompositions for absolutely maximally entangled states
• Near-Term Spin-Qubit Architecture Design via Multipartite Maximally-Entangled States
• Two-Unitary Complex Hadamard Matrices of Order $36$
• Construction of perfect tensors using biunimodular vectors
• 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
• Distinguishing Graph States by the Properties of Their Marginals
• On two maximally entangled couples
• Characterizing maximally many-body entangled fermionic states by using $M$-body density matrix
• Quantum Circuits for High-Dimensional Absolutely Maximally Entangled States