831 citations · 6k across the 58 of their papers we have counts for
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Matrix Product States and Projected Entangled Pair States: Concepts, Symmetries, and Theorems
Ignacio Cirac, David Perez-Garcia, Norbert Schuch +1
The theory of entanglement provides a fundamentally new language for describing interactions and correlations in many body systems. Its vocabulary consists of qubits and entangled…
Classification of phases for mixed states via fast dissipative evolution
Andrea Coser, David Perez-Garcia
We propose the following definition of topological quantum phases valid for mixed states: two states are in the same phase if there exists a time independent, fast and local Lindbl…
Undecidability of the Spectral Gap in One Dimension
Johannes Bausch, Toby Cubitt, Angelo Lucia +1
The spectral gap problem - determining whether the energy spectrum of a system has an energy gap above ground state, or if there is a continuous range of low-energy excitations - p…
Resource Quantification for the No-Programming Theorem
Aleksander M. Kubicki, Carlos Palazuelos, David Pérez-García
The no-programming theorem prohibits the existence of a Universal Programmable Quantum Processor. This statement has several implications in relation to quantum computation, but al…
Quantum conditional relative entropy and quasi-factorization of the relative entropy
Angela Capel, Angelo Lucia, David Pérez-García
The existence of a positive log-Sobolev constant implies a bound on the mixing time of a quantum dissipative evolution under the Markov approximation. For classical spin systems, s…
Locality at the boundary implies gap in the bulk for 2D PEPS
Michael J. Kastoryano, Angelo Lucia, David Perez-Garcia
Proving that the parent Hamiltonian of a Projected Entangled Pair State (PEPS) is gapped remains an important open problem. We take a step forward in solving this problem by showin…
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…
Superadditivity of quantum relative entropy for general states
Angela Capel, Angelo Lucia, David Pérez-García
The property of superadditivity of the quantum relative entropy states that, in a bipartite system , for every density operato…
Matrix Product Density Operators: Renormalization Fixed Points and Boundary Theories
J. I. Cirac, D. Perez-Garcia, N. Schuch +1
We consider the tensors generating matrix product states and density operators in a spin chain. For pure states, we revise the renormalization procedure introduced by F. Verstraete…
Comment on "On the uncomputability of the spectral gap"
Toby S. Cubitt, David Perez-Garcia, Michael M. Wolf
The aim of this short note is to clarify some of the claims made in the comparison made in [S. Lloyd, On the uncomputability of the spectral gap, arXiv:1602.05924] between our rece…
Size-Driven Quantum Phase Transitions
Johannes Bausch, Toby S. Cubitt, Angelo Lucia +2
Can the properties of the thermodynamic limit of a many-body quantum system be extrapolated by analysing a sequence of finite-size cases? We present a model for which such an appro…
Area law for fixed points of rapidly mixing dissipative quantum systems
Fernando G. S. L. Brandao, Toby S. Cubitt, Angelo Lucia +2
We prove an area law with a logarithmic correction for the mutual information for fixed points of local dissipative quantum system satisfying a rapid mixing condition, under either…
Undecidability of the Spectral Gap (full version)
Toby Cubitt, David Perez-Garcia, Michael M. Wolf
We show that the spectral gap problem is undecidable. Specifically, we construct families of translationally-invariant, nearest-neighbour Hamiltonians on a 2D square lattice of d-l…
Undecidability of the Spectral Gap (short version)
Toby Cubitt, David Perez-Garcia, Michael M. Wolf
The spectral gap - the energy difference between the ground state and first excited state - is central to quantum many-body physics. Many challenging open problems, such as the Hal…
Unbounded number of channel uses are required to see quantum capacity
Toby Cubitt, David Elkouss, William Matthews +3
Transmitting data reliably over noisy communication channels is one of the most important applications of information theory, and well understood when the channel is accurately mod…
Stability of local quantum dissipative systems
Toby S. Cubitt, Angelo Lucia, Spyridon Michalakis +1
Open quantum systems weakly coupled to the environment are modeled by completely positive, trace preserving semigroups of linear maps. The generators of such evolutions are called…
Preparing topological PEPS on a quantum computer
Martin Schwarz, Toby S. Cubitt, Kristan Temme +2
Simulating of exotic phases of matter that are not amenable to classical techniques is one of the most important potential applications of quantum information processing. We presen…
Entanglement, fractional magnetization and long-range interactions
Andrea Cadarso, Mikel Sanz, Michael M. Wolf +2
Based on the theory of Matrix Product States, we give precise statements and complete analytical proofs of the following claim: a large fractionalization in the magnetization or th…
Existence of an information unit as a postulate of quantum theory
Lluis Masanes, Markus P. Mueller, Remigiusz Augusiak +1
Does information play a significant role in the foundations of physics? Information is the abstraction that allows us to refer to the states of systems when we choose to ignore the…
Matrix Product States with long-range Localizable Entanglement
Thorsten B. Wahl, David Perez-Garcia, J. Ignacio Cirac
We derive a criterion to determine when a translationally invariant matrix product state (MPS) has long-range localizable entanglement, where that quantity remains finite in the th…
Joint system quantum descriptions arising from local quantumness
Tom Cooney, Marius Junge, Miguel Navascues +2
Bipartite correlations generated by non-signalling physical systems that admit a finite-dimensional local quantum description cannot exceed the quantum limits, i.e., they can alway…
Quantum Steering and Space-Like Separation
Miguel Navascues, David Perez-Garcia
In non-relativistic quantum mechanics, measurements performed by separate observers are modeled via tensor products. In Algebraic Quantum Field Theory, though, local observables co…
Matrix Product States, Random Matrix Theory and the Principle of Maximum Entropy
Benoit Collins, Carlos E. Gonzalez-Guillen, David Perez-Garcia
Using random matrix techniques and the theory of Matrix Product States we show that reduced density matrices of quantum spin chains have generically maximum entropy.