Tensor Networks for Entanglement Evolution
arXiv:1204.3599
Abstract
The intuitiveness of the tensor network graphical language is becoming well known through its use in numerical simulations using methods from tensor network algorithms. Recent times have also seen rapid progress in developing equations of motion to predict the time evolution of quantum entanglement [Nature Physics, 4(\textbf{4}):99, 2008]. Here we cast these recent results into a tensor network framework and in doing so, construct a theory which exposes the topological equivalence of the evolution of a family of entanglement monotones in arbitrary dimensions. This unification was accomplished by tailoring a form of channel state duality through the interpretation of graphical tensor network rewrite rules. The introduction of tensor network methods to the theory of entanglement evolution opens the door to apply methods from the rapidly evolving area known as tensor network states.
11 eps figure files, revtex4-1
References in corpus (10)
- Matrix Product States, Projected Entangled Pair States, and variational renormalization group methods for quantum spin systems
- Non-Markovian effects on the dynamics of entanglement
- A Factorization Law for Entanglement Decay
- Non-Markovian reduced dynamics and entanglement evolution of two coupled spins in a quantum spin environment
- Evolution equation of entanglement for general bipartite systems
- Open-system dynamics of graph-state entanglement
- Dynamical simulations of classical stochastic systems using matrix product states
- Evolution and Symmetry of Multipartite Entanglement
- Categorical Quantum Circuits
- Algebraically contractible topological tensor network states