@article{EisertCramerPlenio2010,
  author    = {Eisert, Jens and Cramer, Marcus and Plenio, Martin B.},
  title     = {Colloquium : area laws for the entanglement entropy},
  issn      = {0034-6861},
  doi       = {10.1103/RevModPhys.82.277},
  year      = {2010},
  abstract  = {Physical interactions in quantum many-body systems are typically local: Individual constituents interact mainly with their few nearest neighbors. This locality of interactions is inherited by a decay of correlation functions, but also reflected by scaling laws of a quite profound quantity: the entanglement entropy of ground states. This entropy of the reduced state of a subregion often merely grows like the boundary area of the subregion, and not like its volume, in sharp contrast with an expected extensive behavior. Such "area laws" for the entanglement entropy and related quantities have received considerable attention in recent years. They emerge in several seemingly unrelated fields, in the context of black hole physics, quantum information science, and quantum many-body physics where they have important implications on the numerical simulation of lattice models. In this Colloquium the current status of area laws in these fields is reviewed. Center stage is taken by rigorous results on lattice models in one and higher spatial dimensions. The differences and similarities between bosonic and fermionic models are stressed, area laws are related to the velocity of information propagation in quantum lattice models, and disordered systems, nonequilibrium situations, and topological entanglement entropies are discussed. These questions are considered in classical and quantum systems, in their ground and thermal states, for a variety of correlation measures. A significant proportion is devoted to the clear and quantitative connection between the entanglement content of states and the possibility of their efficient numerical simulation. Matrix-product states, higher-dimensional analogs, and variational sets from entanglement renormalization are also discussed and the paper is concluded by highlighting the implications of area laws on quantifying the effective degrees of freedom that need to be considered in simulations of quantum states.},
  language  = {en}
}
@article{CramerEisertPlenioetal.2006,
  author    = {Cramer, Marcus and Eisert, Jens and Plenio, Martin B. and Dreißig, Julian},
  title     = {Entanglement-area law for general bosonic harmonic lattice systems},
  doi       = {10.1103/Physreva.73.012309},
  year      = {2006},
  abstract  = {We demonstrate that the entropy of entanglement and the distillable entanglement of regions with respect to the rest of a general harmonic-lattice system in the ground or a thermal state scale at most as the boundary area of the region. This area law is rigorously proven to hold true in noncritical harmonic-lattice systems of arbitrary spatial dimension, for general finite-ranged harmonic interactions, regions of arbitrary shape, and states of nonzero temperature. For nearest-neighbor interactions-corresponding to the Klein-Gordon case-upper and lower bounds to the degree of entanglement can be stated explicitly for arbitrarily shaped regions, generalizing the findings of Phys. Rev. Lett. 94, 060503 (2005). These higher-dimensional analogs of the analysis of block entropies in the one-dimensional case show that under general conditions, one can expect an area law for the entanglement in noncritical harmonic many-body systems. The proofs make use of methods from entanglement theory, as well as of results on matrix functions of block- banded matrices. Disordered systems are also considered. We moreover construct a class of examples for which the two- point correlation length diverges, yet still an area law can be proven to hold. We finally consider the scaling of classical correlations in a classical harmonic system and relate it to a quantum lattice system with a modified interaction. We briefly comment on a general relationship between criticality and area laws for the entropy of entanglement},
  language  = {en}
}
@article{EisertPlenio2010,
  author    = {Eisert, Jens and Plenio, Martin B.},
  title     = {Focus on quantum information and many-body theory},
  issn      = {1367-2630},
  doi       = {10.1088/1367-2630/12/2/025001},
  year      = {2010},
  abstract  = {Quantum many-body models describing natural systems or materials and physical systems assembled piece by piece in the laboratory for the purpose of realizing quantum information processing share an important feature: intricate correlations that originate from the coherent interaction between a large number of constituents. In recent years it has become manifest that the cross-fertilization between research devoted to quantum information science and to quantum many- body physics leads to new ideas, methods, tools, and insights in both fields. Issues of criticality, quantum phase transitions, quantum order and magnetism that play a role in one field find relations to the classical simulation of quantum systems, to error correction and fault tolerance thresholds, to channel capacities and to topological quantum computation, to name but a few. The structural similarities of typical problems in both fields and the potential for pooling of ideas then become manifest. Notably, methods and ideas from quantum information have provided fresh approaches to long-standing problems in strongly correlated systems in the condensed matter context, including both numerical methods and conceptual insights.},
  language  = {en}
}
@article{FeitoBoiracLundeenColdenstrodtRongeetal.2009,
  author    = {Feito Boirac, Alvaro Felipe and Lundeen, Jeff S. and Coldenstrodt-Ronge, Hendrik and Eisert, Jens and Plenio, Martin B. and Walmsley, Ian A.},
  title     = {Measuring measurement : theory and practice},
  issn      = {1367-2630},
  doi       = {10.1088/1367-2630/11/9/093038},
  year      = {2009},
  abstract  = {Recent efforts have applied quantum tomography techniques to the calibration and characterization of complex quantum detectors using minimal assumptions. In this work, we provide detail and insight concerning the formalism, the experimental and theoretical challenges and the scope of these tomographical tools. Our focus is on the detection of photons with avalanche photodiodes and photon-number resolving detectors and our approach is to fully characterize the quantum operators describing these detectors with a minimal set of well-specified assumptions. The formalism is completely general and can be applied to a wide range of detectors.},
  language  = {en}
}
@article{FeitoLundeenColdenstrodtRongeetal.2009,
  author    = {Feito, Alvaro and Lundeen, Jeff and Coldenstrodt-Ronge, Hendrik and Eisert, Jens and Plenio, Martin B. and Walmsley, Ian A.},
  title     = {Measuring measurement : theory and practice},
  issn      = {1367-2630},
  doi       = {10.1088/1367-2630/11/9/093038},
  year      = {2009},
  abstract  = {Recent efforts have applied quantum tomography techniques to the calibration and characterization of complex quantum detectors using minimal assumptions. In this work, we provide detail and insight concerning the formalism, the experimental and theoretical challenges and the scope of these tomographical tools. Our focus is on the detection of photons with avalanche photodiodes and photon-number resolving detectors and our approach is to fully characterize the quantum operators describing these detectors with a minimal set of well-specified assumptions. The formalism is completely general and can be applied to a wide range of detectors.},
  language  = {en}
}
@article{HuebenerKruszynskaHartmannetal.2009,
  author    = {H{\"u}bener, Robert and Kruszynska, Caroline and Hartmann, Lorenz and Duer, Wolfgang and Verstraete, Frank and Eisert, Jens and Plenio, Martin B.},
  title     = {Renormalization algorithm with graph enhancement},
  issn      = {1050-2947},
  doi       = {10.1103/Physreva.79.022317},
  year      = {2009},
  abstract  = {We introduce a class of variational states to describe quantum many-body systems. This class generalizes matrix product states which underlie the density-matrix renormalization-group approach by combining them with weighted graph states. States within this class may (i) possess arbitrarily long-ranged two-point correlations, (ii) exhibit an arbitrary degree of block entanglement entropy up to a volume law, (iii) be taken translationally invariant, while at the same time (iv) local properties and two-point correlations can be computed efficiently. This variational class of states can be thought of as being prepared from matrix product states, followed by commuting unitaries on arbitrary constituents, hence truly generalizing both matrix product and weighted graph states. We use this class of states to formulate a renormalization algorithm with graph enhancement and present numerical examples, demonstrating that improvements over density-matrix renormalization-group simulations can be achieved in the simulation of ground states and quantum algorithms. Further generalizations, e.g., to higher spatial dimensions, are outlined.},
  language  = {en}
}
@article{HuebenerKruszynskaHartmannetal.2011,
  author    = {H{\"u}bener, Robert and Kruszynska, Caroline and Hartmann, Lorenz and Duer, Wolfgang and Plenio, Martin B. and Eisert, Jens},
  title     = {Tensor network methods with graph enhancement},
  series = {Physical review : B, Condensed matter and materials physics},
  volume    = {84},
  journal   = {Physical review : B, Condensed matter and materials physics},
  number    = {12},
  publisher = {American Physical Society},
  address   = {College Park},
  issn      = {1098-0121},
  doi       = {10.1103/PhysRevB.84.125103},
  pages     = {24},
  year      = {2011},
  abstract  = {We present applications of the renormalization algorithm with graph enhancement (RAGE). This analysis extends the algorithms and applications given for approaches based on matrix product states introduced in [Phys. Rev. A 79, 022317 (2009)] to other tensor-network states such as the tensor tree states (TTS) and projected entangled pair states. We investigate the suitability of the bare TTS to describe ground states, showing that the description of certain graph states and condensed-matter models improves. We investigate graph-enhanced tensor-network states, demonstrating that in some cases (disturbed graph states and for certain quantum circuits) the combination of weighted graph states with TTS can greatly improve the accuracy of the description of ground states and time-evolved states. We comment on delineating the boundary of the classically efficiently simulatable states of quantum many-body systems.},
  language  = {en}
}