Related papers: Matrix Product States and Projected Entangled Pair…
We review different descriptions of many--body quantum systems in terms of tensor product states. We introduce several families of such states in terms of known renormalization procedures, and show that they naturally arise in that context.…
Tensor networks are generated by a set of small rank tensors and define many-body quantum states in a succinct form. The corresponding map is not one-to-one: different sets of tensors may generate the very same state. A fundamental question…
This is a partly non-technical introduction to selected topics on tensor network methods, based on several lectures and introductory seminars given on the subject. It should be a good place for newcomers to get familiarized with some of the…
One of the most striking features of quantum phases that exhibit topological order is the presence of long range entanglement that cannot be detected by any local order parameter. The formalism of projected entangled-pair states is a…
Quantum tensor network states and more particularly projected entangled-pair states provide a natural framework for representing ground states of gapped, topologically ordered systems. The defining feature of these representations is that…
We show that general string-net condensed states have a natural representation in terms of tensor product states (TPS) . These TPS's are built from local tensors. They can describe both states with short-range entanglement (such as the…
Matrix Product States can be defined as the family of quantum states that can be sequentially generated in a one-dimensional system. We introduce a new family of states which extends this definition to two dimensions. Like in Matrix Product…
The study of tensor network theory is an important field and promises a wide range of experimental and quantum information theoretical applications. Matrix product state is the most well-known example of tensor network states, which…
These are lecture notes from the 44th IFF Spring School "Quantum Information Processing" in Juelich, discussing applications of entanglement theory in condensed matter. The focus of the notes is on tensor network states, in particular…
This article reviews recent developments in the theoretical understanding and the numerical implementation of variational renormalization group methods using matrix product states and projected entangled pair states.
Mathematical foundation of the novel concept of quantum tensor product by Zanardi et al is rigorously established. The concept of relative quantum entanglement is naturally introduced and its meaning is made clear both mathematically and…
We give an introduction to the theory of multi-partite entanglement. We begin by describing the "coordinate system" of the field: Are we dealing with pure or mixed states, with single or multiple copies, what notion of "locality" is being…
The relation between entanglement entropy and the computational difficulty of classically simulating Quantum Mechanics is briefly reviewed. Matrix product states are proven to provide an efficient representation of one-dimensional quantum…
Particle systems admit a variety of tensor product structures (TPSs) depending on the complete system of commuting observables chosen for the analysis. Different notions of entanglement are associated with these different TPSs. Global…
This paper reveals the intrinsic structure of Matrix Product States (MPS) by establishing their deep connection to entangled hidden Markov models (EHMMs). It is demonstrated that a significant class of MPS can be derived as the outcomes of…
We analyze entanglement in the family of translationally-invariant matrix product states (MPS). We give a criterion to determine when two states can be transformed into each other by SLOCC transformations, a central question in entanglement…
Tensor network states provide successful descriptions of strongly correlated quantum systems with applications ranging from condensed matter physics to cosmology. Any family of tensor network states possesses an underlying entanglement…
We introduce the concept of concatenated tensor networks to efficiently describe quantum states. We show that the corresponding concatenated tensor network states can efficiently describe time evolution and possess arbitrary block-wise…
Matrix Product States (MPS) are a particular type of one dimensional tensor network states, that have been applied to the study of numerous quantum many body problems. One of their key features is the possibility to describe and encode…
These lecture notes provide a brief overview of methods of entanglement theory applied to the study of quantum many-body systems, as well as of tensor network states capturing quantum states naturally appearing in condensed-matter systems.