The Essentially Entangled Component of Multipartite Mixed Quantum States, its Properties and an Efficient Algorithm for its Extraction

Abstract

We introduce with geometric means a density matrix decomposition of a multipartite quantum system of a finite dimension into two density matrices: a separable one, also known as the best separable approximation, and an essentially entangled one, which contains no product states components. We show that this convex decomposition can be achieved in practice with the help of an algorithm based on linear programming, which in the general case scales polynomially with the dimension of the multipartite system. Furthermore, we suggest methods for analyzing the multipartite entanglement content of the essentially entangled component and derive analytically an upper bound for its rank. We illustrate the algorithm at an example of a composed system of total dimension 12 undergoing loss of coherence due to classical noise and we trace the time evolution of its essentially entangled component. We suggest a "geometric" description of entanglement dynamics and show how it explains the well-known phenomena of sudden death and revival of multipartite entanglement.

References have been added. In particular, the results have been connected to the concept of the best separable approximation of a density matrix

References in corpus (8)

• Entanglement detection
• Finite-Time Disentanglement via Spontaneous Emission
• Sudden Birth Versus Sudden Death of Entanglement in Multipartite Systems
• Taming multiparticle entanglement
• Open-System Dynamics of Entanglement
• Constructing N-qubit entanglement monotones from anti-linear operators
• Entangled three-qubit states without concurrence and three-tangle
• Detecting separable states via semidefinite programs

Cited by in corpus (4)

• Building separable approximations for quantum states via neural networks
• Anomalies of weight-based coherence measure and mixed maximally coherent states
• Investigating bound entangled two-qutrit states via the best separable approximation
• Convex-roof entanglement measures of density matrices block diagonal in disjoint subspaces for the study of thermal states