Fermionic Projected Entangled Pair States (2009)
Kraus, Christina V., Schuch, Norbert, Verstraete, Frank, Cirac, J. Ignacio
We introduce a family of states, the fPEPS, which describes fermionic systems on lattices in arbitrary spatial dimensions. It constitutes the natural extension of another family of states, the PEPS,...
Simulation of interacting fermions with entanglement renormalization (2009)
Corboz, Philippe, Evenbly, Glen, Verstraete, Frank, Vidal, Guifre
We propose and test an algorithm to simulate a lattice system of interacting fermions in two spatial dimensions. The approach is an extension of the entanglement renormalization technique [Phys. Rev....
Quantum circuits for strongly correlated quantum systems (2008)
Verstraete, Frank, Cirac, J. Ignacio, Latorre, Jose I.
In recent years, we have witnessed an explosion of experimental tools by which quantum systems can be manipulated in a controlled and coherent way. One of the most important goals now is to build...
Verstraete, Frank, Wolf, Michael M., Cirac, J. Ignacio
We investigate the computational power of creating steady-states of quantum dissipative systems whose evolution is governed by time-independent and local couplings to a memoryless environment. We...
The computational difficulty of finding MPS ground states (2008)
Schuch, Norbert, Cirac, Ignacio, Verstraete, Frank
We determine the computational difficulty of finding ground states of one-dimensional (1D) Hamiltonians which are known to be Matrix Product States (MPS). To this end, we construct a class of 1D...
Sequentially generated states for the study of two dimensional systems (2008)
Bañuls, Mari-Carmen, Pérez-García, David, Wolf, Michael M., Verstraete, Frank, Cirac, J. Ignacio
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...
Entropy Scaling and Simulability by Matrix Product States (2008)
Schuch, Norbert, Wolf, Michael M., Verstraete, Frank, Cirac, J. Ignacio
Area Laws in Quantum Systems: Mutual Information and Correlations (2008)
Wolf, Michael M., Verstraete, Frank, Hastings, Matthew B., Cirac, J. Ignacio
String order and symmetries in quantum spin lattices (2008)
Pérez-García, David, Wolf, Michael M., Sanz Riuz, Mikel, Verstraete, Frank, Cirac, J. Ignacio
Sequentially generated states for the study of two-dimensional systems (2008)
Bañuls, Mari Carmen, Pérez-García, David, Wolf, Michael M., Verstraete, Frank, Cirac, J. Ignacio
Computational difficulty of finding matrix product ground states (2008)
Schuch, Norbert, Cirac, J. Ignacio, Verstraete, Frank
We determine the computational difficulty of finding ground states of one-dimensional (1D) Hamiltonians, which are known to be matrix product states (MPS). To this end, we construct a class of 1D...
PEPS as unique ground states of local Hamiltonians (2008)
Perez-García, David, Verstraete, Frank, Wolf, Michael M., Cirac, J. Ignacio
Interacting electrons, Density Functional Theory, and Quantum Merlin Arthur (2007)
Schuch, Norbert, Verstraete, Frank
During the last decades, computational complexity has played a central role in advancing the understanding of spin glasses and in explaining the difficulty of simulating problems in statistical...
Strings, Projected Entangled Pair States, and variational Monte Carlo methods (2007)
Schuch, Norbert, Wolf, Michael M., Verstraete, Frank, Cirac, J. Ignacio
We introduce string-bond states, a class of states obtained by placing strings of operators on a lattice, which encompasses the relevant states in Quantum Information. For string-bond states,...
PEPS as unique ground states of local Hamiltonians (2007)
Perez-Garcia, David, Verstraete, Frank, Cirac, J. Ignacio, Wolf, Michael M.
In this paper we consider projected entangled pair states (PEPS) on arbitrary lattices. We construct local parent Hamiltonians for each PEPS and isolate a condition under which the state is the...
Entropy scaling and simulability by Matrix Product States (2007)
Schuch, Norbert, Wolf, Michael M., Verstraete, Frank, Cirac, J. Ignacio
We investigate the relation between the scaling of block entropies and the efficient simulability by Matrix Product States (MPS), and clarify the connection both for von Neumann and Renyi entropies...
Computational Complexity of Projected Entangled Pair States (2007)
Schuch, Norbert, Wolf, Michael M., Verstraete, Frank, Cirac, J. Ignacio
Matrix product state representations (2007)
Perez-García, David, Verstraete, Frank, Wolf, Michael M., Cirac, J. Ignacio
The computational complexity of PEPS (2006)
Schuch, Norbert, Wolf, Michael M., Verstraete, Frank, Cirac, J. Ignacio
We determine the computational power of preparing Projected Entangled Pair States (PEPS), as well as the complexity of classically simulating them, and generally the complexity of contracting tensor...
Monogamy of Bell correlations and Tsirelson's bound (2006)
Toner, Benjamin, Verstraete, Frank
We consider three parties, A, B, and C, each performing one of two local measurements on a shared quantum state of arbitrary dimension. We characterize the trade-off between the nonlocality of the...
Quantum Phase Transitions in Matrix Product Systems (2006)
Wolf, Michael M., Ortiz, Gerardo, Verstraete, Frank, Cirac, J. Ignacio
We investigate quantum phase transitions (QPTs) in spin chain systems characterized by local Hamiltonians with matrix product ground states. We show how to theoretically engineer such QPT points...
General Monogamy Inequality for Bipartite Qubit Entanglement (2006)
Osborne, Tobias J., Verstraete, Frank
We consider multipartite states of qubits and prove that their bipartite quantum entanglement, as quantified by the concurrence, satisfies a monogamy inequality conjectured by Coffman, Kundu, and...
Numerical Computation of Localizable Entanglement in Spin Chains (2006)
Popp,Markus, Verstraete,Frank, Martin-Delgado,M. A., Cirac,J. Ignacio
Numerical Computation of Localizable Entanglement in Spin Chains (2006)
Popp, Markus, Verstraete, Frank, Martin-Delgado, M. A., Cirac, J. Ignacio
Criticality, the area Law, and the Computational Power of Projected Entangled Pair States (2006)
Verstraete, Frank, Wolf, Michael M., Pérez-García, David, Cirac, J. Ignacio
Quantum Phase Transitions in Matrix Product Systems (2006)
Wolf, Michael M., Ortiz, Gerardo, Verstraete, Frank, Cirac, J. Ignacio
Projected Entangled States: Properties and Applications (2006)
Verstraete, Frank, Wolf, Michael, Pérez-García, David, Cirac, J. Ignacio
Quantum phase transitions in matrix product systems (2005)
Wolf, Michael M., Ortiz, Gerardo, Verstraete, Frank, Cirac, J. Ignacio
We investigate quantum phase transitions (QPTs) in spin chain systems characterized by local Hamiltonians with matrix product ground states. We show how to theoretically engineer such QPT points...
Entanglement of assistance and multipartite state distillation (2005)
Smolin, John A., Verstraete, Frank, Winter, Andreas
We find that the asymptotic entanglement of assistance of a general bipartite mixed state is equal to the smaller of its two local entropies. Our protocol gives rise to the asymptotically optimal...
Sequential Generation of Entangled Multiqubit States (2005)
Schön,Christian, Solano,Enrique, Verstraete,Frank, Cirac,J. Ignacio, Wolf,Michael M.
Entanglement of assistance and multipartite state distillation (2005)
Smolin, John A., Verstraete, Frank, Winter, Andreas
We find that the asymptotic entanglement of assistance of a general bipartite mixed state is equal to the smaller of its two local entropies. Our protocol gives rise to the asymptotically optimal EPR...
Localizable entanglement (2005)
Popp,Markus, Verstraete,Frank, Martín-Delgado,Miguel Angel, Cirac,J. Ignacio
Renormalization-Group Transformations on Quantum States (2005)
Verstraete,Frank, Cirac,J. Ignacio, Latorre,J. I., Rico,E., Wolf,Michael M.
General Monogamy Inequality for Bipartite Qubit Entanglement (2005)
Osborne, Tobias J., Verstraete, Frank
We consider multipartite states of qubits and prove that their bipartite quantum entanglement, as quantified by the concurrence, satisfies a monogamy inequality conjectured by Coffman, Kundu, and...
Renormalization-Group Transformations on Quantum States (2005)
Verstraete, Frank, Cirac, J. Ignacio, Latorre, J. I., Rico, E., Wolf, Michael M.
Localizable entanglement (2005)
Popp, Markus, Verstraete, Frank, Martín-Delgado, Miguel Angel, Cirac, J. Ignacio
Sequential Generation of Entangled Multiqubit States (2005)
Schön, Christian, Solano, Enrique, Verstraete, Frank, Cirac, J. Ignacio, Wolf, Michael M.
Interpolation of recurrence and hashing entanglement distillation protocols (2004)
Vollbrecht, Karl Gerd H., Verstraete, Frank
We construct new entanglement distillation protocols by interpolating between the recurrence and hashing protocols. This leads to asymptotic two-way distillation protocols, resulting in an...
Quantum entanglement theory in the presence of superselection rules (2004)
Schuch, Norbert, Verstraete, Frank, Cirac, J. Ignacio
Superselection rules severly constrain the operations which can be implemented on a distributed quantum system. While the restriction to local operations and classical communication gives rise to...
Matrix product density operators: Simulation of finite-temperature and dissipative systems (2004)
Verstraete, Frank, Garcia-Ripoll, Juan J., Cirac, J. Ignacio
Multipartite entanglement in 2 x 2 x n quantum systems (2003)
Miyake, Akimasa, Verstraete, Frank
We classify multipartite entangled states in the 2 x 2 x n (n >= 4) quantum system, for example the 4-qubit system distributed over 3 parties, under local filtering operations. We show that there...
Separable states can be used to distribute entanglement (2003)
Cubitt, Toby S., Verstraete, Frank, Dür, W., Cirac, J. Ignacio
Maximal entanglement versus entropy for mixed quantum states (2002)
Wei, Tzu-Chieh, Nemoto, Kae, Goldbart, Paul M., Kwiat, Paul G., Munro, William J., Verstraete, Frank
Maximally entangled mixed states are those states that, for a given mixedness, achieve the greatest possible entanglement. For two-qubit systems and for various combinations of entanglement and...
Local permutations of products of Bell states and entanglement distillation (2002)
Dehaene, Jeroen, Nest, Maarten Van Den, De Moor, Bart, Verstraete, Frank
We present new algorithms for mixed-state multi-copy entanglement distillation for pairs of qubits. Our algorithms perform significantly better than the best known algorithms. Better algorithms can...
On the fidelity of mixed states of two qubits (2002)
Verstraete, Frank, Verschelde, Henri
We consider a single copy of a mixed state of two qubits and show how its fidelity or maximal singlet fraction is related to the entanglement measures concurrence and negativity. We characterize the...
Verstraete, Frank, Verschelde, Henri
One of the most challenging open problems in quantum information theory is to clarify and quantify how entanglement behaves when part of an entangled state is sent through a quantum channel. Of...
Four qubits can be entangled in nine different ways. (2002)
Verstraete, Frank, DEHAENE, J, DE MOOR, B, Verschelde, Henri
A Study Of Entanglement In Quantum Information Theory (2002)
Frank Verstraete, Prof Dr. M. Fannes
Although the concept of quantum entanglement has been known for about seventy years, it only recently quit the realms of meta-theoretical discussions when it was discovered how entanglement can be...
Entanglement versus Bell violations and their behaviour under local filtering operations (2001)
Verstraete, Frank, Wolf, Michael M.
We discuss the relations between the violation of the CHSH Bell inequality for systems of two qubits on the one side and entanglement of formation, local filtering operations, and the entropy and...
The Lorentz singular value decomposition and its applications to pure states of 3 qubits (2001)
Verstraete, Frank, Dehaene, Jeroen, De Moor, Bart
All mixed states of two qubits can be brought into normal form by the action of SLOCC operations of the kind $\rho'=(A\otimes B)\rho(A\otimes B)^\dagger$. These normal forms can be obtained by...
A comparison of the entanglement measures negativity and concurrence (2001)
Verstraete, Frank, Audenaert, Koenraad, Dehaene, Jeroen, De Moor, Bart
In this paper we investigate two different entanglement measures in the case of mixed states of two qubits. We prove that the negativity of a state can never exceed its concurrence and is always...
On the geometry of entangled states (2001)
Verstraete, Frank, Dehaene, Jeroen, De Moor, Bart
The basic question that is addressed in this paper is finding the closest separable state for a given entangled state, measured with the Hilbert Schmidt distance. While this problem is in general...
Normal forms and entanglement measures for multipartite quantum states (2001)
Verstraete, Frank, Dehaene, Jeroen, De Moor, Bart
A general mathematical framework is presented to describe local equivalence classes of multipartite quantum states under the action of local unitary and local filtering operations. This yields...
Negativity and Concurrence of mixed 2X2 states (2000)
Audenaert, Koenraad, Verstraete, Frank, De Bie, Tijl, De Moor, Bart
We consider two measures of entanglement of mixed bipartite states of dimension 2X2: concurrence and negativity. We first prove the conjecture of Eisert and Plenio that concurrence can never be...
Maximally entangled mixed states of two qubits (2000)
Verstraete, Frank, Audenaert, Koenraad, De Bie, Tijl, De Moor, Bart
We consider mixed states of two qubits and show under which global unitary operations their entanglement is maximized. This leads to a class of states that is a generalization of the Bell states....
Local filtering operations on two qubits (2000)
Verstraete, Frank, Dehaene, Jeroen, De Moor, Bart
We consider one single copy of a mixed state of two qubits and investigate how its entanglement changes under local quantum operations and classical communications (LQCC) of the type $\rho'\sim...