Construction of genuine multipartite entangled states

Abstract

Genuine multipartite entanglement is of great importance in quantum information, especially from the experimental point of view. Nevertheless, it is difficult to construct genuine multipartite entangled states systematically, because the genuine multipartite entanglement is unruly. We propose another product based on the Kronecker product in this paper. The Kronecker product is a common product in quantum information with good physical interpretation. We mainly investigate whether the proposed product of two genuine multipartite entangled states is still a genuine entangled one. We understand the entanglement of the proposed product better by characterizing the entanglement of the Kronecker product. Then we show the proposed product is a genuine multipartite entangled state in two cases. The results provide a systematical method to construct genuine multipartite entangled states of more parties.

arXiv commentrevised Lemma 7, added Appendix A

References in corpus (27)

• Quantum entanglement
• Quantum Cryptography
• Separability Criterion for Density Matrices
• The Security of Practical Quantum Key Distribution
• Separability of Mixed States: Necessary and Sufficient Conditions
• 14-qubit entanglement: creation and coherence
• Beating the channel capacity limit for linear photonic superdense coding
• Classification of mixed three-qubit states
• 10-qubit entanglement and parallel logic operations with a superconducting circuit
• 18-qubit entanglement with photon's three degrees of freedom
• Teleportation and Dense Coding with Genuine Multipartite Entanglement
• Exact and Asymptotic Measures of Multipartite Pure State Entanglement
• Taming multiparticle entanglement
• Separability criteria for genuine multiparticle entanglement
• Experimental entanglement of a six-photon symmetric Dicke state
• Device-independent witnesses of genuine multipartite entanglement
• Evidence for Bound Entangled States with Negative Partial Transpose
• Genuine 12-qubit entanglement on a superconducting quantum processor
• Partial separability and entanglement criteria for multiqubit quantum states
• Witnessing genuine multipartite entanglement with positive maps
• Tensor Rank and Stochastic Entanglement Catalysis for Multipartite Pure States
• Genuine multiparticle entanglement of permutationally invariant states
• Tensor rank is not multiplicative under the tensor product
• Rank three bipartite entangled states are distillable
• Role of correlations in the two-body-marginal problem
• Tripartite to Bipartite Entanglement Transformations and Polynomial Identity Testing
• Construction of three qubit genuine entanglement with bi-partite positive partial transposes

Cited by in corpus (5)

• Inertias of entanglement witnesses
• Construction of genuinely entangled multipartite subspaces from bipartite ones by reducing the total number of separated parties
• Tripartite genuinely entangled states from entanglement-breaking subspaces
• Hybrid of Gradient Descent And Semidefinite Programming for Certifying Multipartite Entanglement Structure
• The additivity of states uniquely determined by marginals