Related papers: Wick's theorem for matrix product states
The generalization of matrix product states (MPS) to continuous systems, as proposed in the breakthrough paper [F. Verstraete, J.I. Cirac, Phys. Rev. Lett. 104, 190405(2010)], provides a powerful variational ansatz for the ground state of…
Permutation symmetries of multipartite quantum states are defined only when the constituent subsystems are of equal dimensions. In this work we extend this notion of permutation symmetry to heterogeneous systems, that is, systems composed…
We formulate a general framework for the study of operator systems arising from discrete groups. We study in detail the operator system of the free group on $n$ generators, as well as the operator systems of the free products of finitely…
The truncation or compression of the spectrum of Schmidt values is inherent to the matrix product state (MPS) approximation of one-dimensional quantum ground states. We provide a renormalization group picture by interpreting this…
We extend the formalism of pure state thermodynamics to matrix product states. In pure state thermodynamics finite temperature properties of quantum systems are derived without the need of statistical mechanics ensembles, but instead using…
Quantum collision models have proved to be useful for a clear and concise description of many physical phenomena in the field of open quantum systems: thermalization, decoherence, homogenization, nonequilibrium steady state, entanglement…
Multipartite entanglement is indispensable in the implementation of quantum technologies and the fundamental test of quantum mechanics. Here we study how the W state and W-like state may be generated in a quantum-dot array by controlling…
Pairwise quantum correlations in the ground state of a N-spins antiferromagnetic chain described by the Heisenberg model with nearest neighbor exchange coupling are investigated. By varying a single coupling between two neighboring sites it…
Matrix Product States (MPS) and Operators (MPO) have been proven to be a powerful tool to study quantum many-body systems but are restricted to moderately entangled states as the number of parameters scales exponentially with the…
We study the few-body physics of trapped atoms or molecules with electric or magnetic dipole moments aligned by an external field. Using exact numerical diagonalization appropriate for the strongly correlated regime, as well as a classical…
We derive a hierarchy of continuous-variable multipartite entanglement conditions in terms of second-order moments of position and momentum operators that generalizes existing criteria. Each condition corresponds to a convex optimization…
Entanglement, a defining feature of quantum mechanics, arises naturally from interactions between molecular systems. Yet the precise nature and quantification of entanglement in the products of molecular collisions and reactions remain…
Quantum entanglement plays an important role in quantum information processes, such as quantum computation and quantum communication. Experiments in laboratories are unquestionably crucial to increase our understanding of quantum systems…
We consider a general weak perturbation of a non-interacting quantum lattice system with a non-degenerate gapped ground state. We prove that the presence of isolated eigenvalues in the spectrum of the decoupled model leads to the existence…
We extend classical work by Janusz Czelakowski on the closure properties of the class of matrix models of entailment relations - nowadays more commonly called multiple-conclusion logics - to the setting of non-deterministic matrices…
Here we propose the Variational Discrete Action Theory (VDAT) to study the ground state properties of quantum many-body Hamiltonians. VDAT is a variational theory based on the sequential product density matrix (SPD) ansatz, characterized by…
This work gives a detailed investigation of matrix product state (MPS) representations for pure multipartite quantum states. We determine the freedom in representations with and without translation symmetry, derive respective canonical…
Quantum correlations, crucial for the advantage and advancement of quantum science and technology, arise from the impossibility of expressing a quantum state as a tensor product over a given set of parties. In this work, a generalized…
We study the quantum correlations of the radiation emitted by three level atoms (cascade type) interacting with two driving fields. In the linear regime, and in the Weisskopf-Wigner approximation, we show that the atomic and the two-photon…
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.