Quantum State Concentration and Classification of Multipartite Entanglement

Abstract

Entanglement is a unique nature of quantum theory and has tremendous potential for application. Nevertheless, the complexity of quantum entanglement grows exponentially with an increase in the number of entangled particles. Here we introduce a quantum state concentration scheme which decomposes the multipartite entangled state into a set of bipartite and tripartite entangled states. It is shown that the complexity of the entanglement induced by the large number of particles is transformed into the high dimensions of bipartite and tripartite entangled states for pure quantum systems. The results not only simplify the tedious work of verifying the (in)equivalence of multipartite entangled states, but also are instructive to the quantum many-body problem involving multipartite entanglement.

arXiv comment16 pages, 1 figure; published in Phys. Rev. A

References in corpus (18)

• Quantum entanglement
• Three qubits can be entangled in two inequivalent ways
• Entanglement detection
• Measurement-based quantum computation
• On the role of entanglement in quantum computational speed-up
• Classical simulation of quantum many-body systems with a tree tensor network
• Renormalization group transformations on quantum states
• Operational Families of Entanglement Classes for Symmetric $N$-Qubit States
• Efficient Tree Tensor Network States (TTNS) for Quantum Chemistry: Generalizations of the Density Matrix Renormalization Group Algorithm
• Local unitary equivalence of multipartite pure states
• Multipartite entanglement in quantum algorithms
• Classification of multipartite entanglement in all dimensions
• Local unitary equivalence and entanglement of multipartite pure states
• Local Unitary Classification of Arbitrary Dimensional Multipartite Pure States
• Classification of general n-qubit states under stochastic local operations and classical communication in terms of the rank of coefficient matrix
• Classification of Arbitrary Multipartite Entangled States under Local Unitary Equivalence
• Entanglement Classification of Four-partite States under the SLOCC
• Classification of the Entangled states L\times N\times N

Cited by in corpus (4)

• Entanglement swapping and swapped entanglement
• Isomorphism problems for tensors, groups, and cubic forms: completeness and reductions
• Separability criteria based on the correlation tensor moments for arbitrary dimensional states
• Classification of three-qubit genuine entangled states using concurrence fill