117 citations · 434 across the 23 of their papers we have counts for
23 papers
Many bounded versions of undecidable problems are NP-hard
Andreas Klingler, Mirte van der Eyden, Sebastian Stengele +2
Several physically inspired problems have been proven undecidable; examples are the spectral gap problem and the membership problem for quantum correlations. Most of these results…
Magic squares: Latin, Semiclassical and Quantum
Gemma De las Cuevas, Tim Netzer, Inga Valentiner-Branth
Quantum magic squares were recently introduced as a 'magical' combination of quantum measurements. In contrast to quantum measurements, they cannot be purified (i.e. dilated to a q…
Halos and undecidability of tensor stable positive maps
Mirte van der Eyden, Tim Netzer, Gemma De las Cuevas
A map is tensor stable positive (tsp) if is positive for all , and essential tsp if it is not completely positive or completely co-positi…
Polynomial decompositions with invariance and positivity inspired by tensors
Gemma De las Cuevas, Andreas Klingler, Tim Netzer
We present a framework to decompose real multivariate polynomials while preserving invariance and positivity. This framework has been recently introduced for tensor decompositions,…
Quantum Information Theory and Free Semialgebraic Geometry: One Wonderland Through Two Looking Glasses
Gemma De Las Cuevas, Tim Netzer
We illustrate how quantum information theory and free (i.e. noncommutative) semialgebraic geometry often study similar objects from different perspectives. We give examples in the…
Classical spin Hamiltonians are context-sensitive languages
Sebastian Stengele, David Drexel, Gemma De las Cuevas
Classical spin Hamiltonians are a powerful tool to model complex systems, characterised by a local structure given by the local Hamiltonians. One of the best understood local struc…
Approximate tensor decompositions: disappearance of many separations
Gemma De las Cuevas, Andreas Klingler, Tim Netzer
It is well-known that tensor decompositions show separations, that is, that constraints on local terms (such as positivity) may entail an arbitrarily high cost in their representat…
Quantum magic squares: dilations and their limitations
Gemma De las Cuevas, Tom Drescher, Tim Netzer
Quantum permutation matrices and quantum magic squares are generalizations of permutation matrices and magic squares, where the entries are no longer numbers but elements from arbi…
Tensor decompositions on simplicial complexes with invariance
Gemma De las Cuevas, Matt Hoogsteder Riera, Tim Netzer
We develop a framework to analyse invariant decompositions of elements of tensor product spaces. Namely, we define an invariant decomposition with indices arranged on a simplicial…
Generalised ansatz for continuous Matrix Product States
Maria Balanzó-Juandó, Gemma De las Cuevas
Recently it was shown that continuous Matrix Product States (cMPS) cannot express the continuum limit state of any Matrix Product State (MPS), according to a certain natural defini…
Mixed states in one spatial dimension: decompositions and correspondence with nonnegative matrices
Gemma De las Cuevas, Tim Netzer
We study six natural decompositions of mixed states in one spatial dimension: the Matrix Product Density Operator (MPDO) form, the local purification form, the separable decomposit…
Optimal bounds on the positivity of a matrix from a few moments
Gemma de las Cuevas, Tobias Fritz, Tim Netzer
In many contexts one encounters Hermitian operators on a Hilbert space whose dimension is so large that it is impossible to write down all matrix entries in an orthonormal basi…
Continuum limits of Matrix Product States
Gemma De las Cuevas, Norbert Schuch, David Perez-Garcia +1
We determine which translationally invariant matrix product states have a continuum limit, that is, which can be considered as discretized versions of states defined in the continu…
Irreducible forms of Matrix Product States: Theory and Applications
Gemma De las Cuevas, J. Ignacio Cirac, Norbert Schuch +1
The canonical form of Matrix Product States (MPS) and the associated fundamental theorem, which relates different MPS representations of a state, are the theoretical framework unde…
Fundamental limitations in the purifications of tensor networks
G. De las Cuevas, T. S. Cubitt, J. I. Cirac +2
We show a fundamental limitation in the description of quantum many-body mixed states with tensor networks in purification form. Namely, we show that there exist mixed states which…
Simple universal models capture all classical spin physics
Gemma De las Cuevas, Toby S. Cubitt
Spin models are used in many studies of complex systems---be it condensed matter physics, neural networks, or economics---as they exhibit rich macroscopic behaviour despite their m…
A quantum information approach to statistical mechanics
Gemma De las Cuevas
We review some connections between quantum information and statistical mechanics. We focus on three sets of results for classical spin models. First, we show that the partition fun…
Purifications of multipartite states: limitations and constructive methods
Gemma De las Cuevas, Norbert Schuch, David Pérez-García +1
We analyze the description of quantum many-body mixed states using matrix product states and operators. We consider two such descriptions: (i) as a matrix product density operator…
Reducing Spacetime to Binary Information
Silke Weinfurtner, Gemma De las Cuevas, Miguel Angel Martin-Delgado +1
We present a new description of discrete space-time in 1+1 dimensions in terms of a set of elementary geometrical units that represent its independent classical degrees of freedom.…
Quantum algorithms for classical lattice models
G. De las Cuevas, W. Dür, M. Van den Nest +1
We give efficient quantum algorithms to estimate the partition function of (i) the six vertex model on a two-dimensional (2D) square lattice, (ii) the Ising model with magnetic fie…
Projective simulation for artificial intelligence
Hans J. Briegel, Gemma De las Cuevas
We propose a model of a learning agent whose interaction with the environment is governed by a simulation-based projection, which allows the agent to project itself into future sit…
Mapping all classical spin models to a lattice gauge theory
G. De las Cuevas, W. Dür, H. J. Briegel +1
In our recent work [Phys. Rev. Lett. 102, 230502 (2009)] we showed that the partition function of all classical spin models, including all discrete standard statistical models and…
Completeness of classical spin models and universal quantum computation
Gemma De las Cuevas, Wolfgang Dür, Maarten Van den Nest +1
We study mappings between distinct classical spin systems that leave the partition function invariant. As recently shown in [Phys. Rev. Lett. 100, 110501 (2008)], the partition fun…