How entangled can two couples get?

Abstract

We describe a pure state of four qubits whose single-qubit density matrices are all maximally mixed and whose average entanglement as a system of two pairs of qubits appears to be maximal.

9 pages. Note added about the robustness of the entanglement in the four-qubit state described in the paper. Version to be published in Phys. Lett. A

References in corpus (2)

• Three qubits can be entangled in two inequivalent ways
• Multipartite generalisation of the Schmidt decomposition

Cited by in corpus (123)

• Monogamy of entanglement and other correlations
• A generative modeling approach for benchmarking and training shallow quantum circuits
• Perfect Teleportation, Quantum state sharing and Superdense Coding through a Genuinely Entangled Five-qubit State
• Absolute Maximal Entanglement and Quantum Secret Sharing
• Training of Quantum Circuits on a Hybrid Quantum Computer
• Bell's theorem with and without inequalities for the three-qubit Greenberger-Horne-Zeilinger and W states
• Maximally multipartite entangled states
• Three-qubit pure-state canonical forms
• 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
• All Maximally Entangled Four Qubits States
• Quantum marginal problem and representations of the symmetric group
• 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
• Local unitary equivalence and entanglement of multipartite pure states
• From dual-unitary to quantum Bernoulli circuits: Role of the entangling power in constructing a quantum ergodic hierarchy
• Creating ensembles of dual unitary and maximally entangling quantum evolutions
• Entropic proofs of Singleton bounds for quantum error-correcting codes
• Robustness of Highly Entangled Multi-Qubit States Under Decoherence
• Nonlocality and entanglement in qubit systems
• Thirty-six entangled officers of Euler: Quantum solution to a classically impossible problem
• Entangling Power of Permutations
• Generalized concurrence measure for faithful quantification of multiparticle pure state entanglement using Lagrange's identity and wedge product
• On maximal entanglement between two pairs in four-qubit pure states
• Quantum circuits for maximally entangled states
• Three-party entanglement from positronium
• Generalized entanglement as a framework for complex quantum systems: Purity vs delocalization measures
• Multiqubit symmetric states with maximally mixed one-qubit reductions
• Multipartite Entanglement and Frustration
• $k$-Uniform states and quantum information masking
• Quantum Codes from Neural Networks
• Parametrization and distillability of three-qubit entanglement
• Entanglement of three-qubit random pure states
• Classical Statistical Mechanics Approach to Multipartite Entanglement
• Can local dynamics enhance entangling power?
• Majorana dimers and holographic quantum error-correcting codes
• Quantum error correction codes and absolutely maximally entangled states
• Entanglement measures of bipartite quantum gates and their thermalization under arbitrary interaction strength
• Digital Discovery of 100 diverse Quantum Experiments with PyTheus
• Operational approach to Bell inequalities: applications to qutrits
• Entanglement in highly symmetric multipartite quantum states
• Statistical mechanics of multipartite entanglement
• A genuine maximally seven-qubit entangled state
• Certainty relations, mutual entanglement and non-displacable manifolds
• A hybrid quantum-classical conditional generative adversarial network algorithm for human-centered paradigm in cloud
• Stochastic Local Operations with Classical Communication of Absolutely Maximally Entangled States
• Absolutely maximally entangled state equivalence and the construction of infinite quantum solutions to the problem of 36 officers of Euler
• Tripartite information of highly entangled states
• Absolutely maximally entangled states, quantum maximum distance separable codes, and quantum repeaters
• Planar Maximally Entangled States
• Gaussian maximally multipartite entangled states
• Minimal Renyi-Ingarden-Urbanik entropy of multipartite quantum states
• Characterizing ground and thermal states of few-body Hamiltonians
• Entanglement properties of multipartite informationally complete quantum measurements
• Entangling power of multipartite unitary gates
• 9 $\times$ 4 = 6 $\times$ 6: Understanding the quantum solution to the Euler's problem of 36 officers
• Locally Maximally Entangled States of Multipart Quantum Systems
• $k$-uniform mixed states
• Theoretical and computational aspects of entanglement
• Multiparty quantum states stabilized by the diagonal subgroup of the local unitary group
• Highly entangled multi-qubit states with simple algebraic structure
• Cut-resistant links and multipartite entanglement resistant to particle loss
• Quantum combinatorial designs and $k$-uniform states
• On the one-particle reduced density matrices of a pure three-qutrit quantum state
• Accurate calculation of the geometric measure of entanglement for multipartite quantum states
• Classification of nonproduct states with maximum stabilizer dimension
• Unitary Invariants and Classification of Four-Qubit States via Negativity Fonts
• Maximum stabilizer dimension for nonproduct states
• Local unitary classes of states invariant under permutation subgroups
• Bell-type inequality and quantum nonlocality in four-qubit systems
• Constructions of $k$-uniform states from mixed orthogonal arrays
• Strong subadditivity inequality for quantum entropies and four-particle entanglement
• Local Hamiltonians for Maximally Multipartite Entangled States
• The criterion for maximally entangled four-qubit state
• Near-Term Spin-Qubit Architecture Design via Multipartite Maximally-Entangled States
• Mermin Polynomials for Entanglement Evaluation in Grover's algorithm and Quantum Fourier Transform
• Entanglement classification and \emph{non-k}-separability certification via Greenberger-Horne-Zeilinger-class fidelity
• A Criterion to identify maximally entangled nine-qubit state
• Symmetric construction of reference-frame-free qudits
• Two-Unitary Complex Hadamard Matrices of Order $36$
• Construction of perfect tensors using biunimodular vectors
• On the Existence of Absolutely Maximally Entangled States of Minimal Support
• Some Entanglement Features of Highly Entangled Multiqubit States
• Quantum $k$-uniform states from quantum orthogonal arrays
• Negativity Fonts, multiqubit invariants and Four qubit Maximally Entangled States
• Quantum circuits of CNOT gates
• Mixture of entangled pure states with maximally mixed one-qudit reduced density matrices
• Geometric genuine multipartite entanglement for four-qubit systems
• A note on the Bloch representation of absolutely maximally entangled states
• Localizing genuine multiparty entanglement in noisy stabilizer states
• All possible permutational symmetries of a quantum system
• Maximally correlated multipartite quantum states
• Spectral norm of a symmetric tensor and its computation
• Existence of maximally correlated states
• Four-qubit critical states
• Cosine series quantum sampling method with applications in signal and image processing
• No invariant perfect qubit codes
• Finding maximal quantum resources
• A large-N approximated field theory for multipartite entanglement
• Uncertainty relations between quantum Fisher information and entanglement monotones
• Entanglement frustration in multimode Gaussian states
• Separable ellipsoids around multipartite states
• Quantifying High-Order Interdependencies in Entangled Quantum States
• Monogamous property of generalized W states in three-qubit systems in terms of relative entropy of entanglement
• Quantum Circuits for High-Dimensional Absolutely Maximally Entangled States
• Constructing quantum circuits for maximally entangled multi-qubit states using the genetic algorithm
• Maximal Entanglement: Applications in Quantum Information and Particle Physics
• Quantum Sequence States
• Bell inequalities with overlapping measurements
• Entanglement of Assistance as a measure of multiparty entanglement
• Entangling capabilities and unitary quantum games
• On two maximally entangled couples
• Multipartite entanglement and few-body Hamiltonians
• On orthogonal tensors and best rank-one approximation ratio
• Absolutely maximally entangled pure states of multipartite quantum systems
• Quantum Advantage in Identifying the Parity of Permutations with Certainty
• Multiqubit monogamy relations beyond shadow inequalities
• Entanglement structure for finite system under dual-unitary dynamics
• Planar two-region multi-partite maximally entangled states