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Entanglement in manybody systems
 quantph/0703044, 2007. in the quantum Ising model 43
"... The recent interest in aspects common to quantum information and condensed matter has prompted a flory of activity at the border of these disciplines that were far distant untill few years ago. Numerous interesting questions have been addressed so far. Here we review an important part of this field, ..."
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The recent interest in aspects common to quantum information and condensed matter has prompted a flory of activity at the border of these disciplines that were far distant untill few years ago. Numerous interesting questions have been addressed so far. Here we review an important part of this field, the properties of the entanglement in manybody systems. We discuss the zero and finite temperature properties of entanglement in interacting spin, fermion and boson model systems. Both bipartite and multipartite entanglement will be considered. In equilibrium we show how entanglement is tightly connected to the characteristics of the phase diagram. The behavior of entanglement can be related, via certain witnesses, to thermodynamic quantities thus offering interesting possibilities for an experimental test. Out of equilibrium we discuss how to generate and manipulate entangled states by means of manybody Hamiltonians. Contents
Entanglement detection
 Physics Reports
"... How can one prove that a given state is entangled? In this paper we review different methods that have been proposed for entanglement detection. We first explain the basic elements of entanglement theory for two or more particles and then entanglement verification procedures such as Bell inequalitie ..."
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How can one prove that a given state is entangled? In this paper we review different methods that have been proposed for entanglement detection. We first explain the basic elements of entanglement theory for two or more particles and then entanglement verification procedures such as Bell inequalities, entanglement witnesses, the determination of nonlinear properties of a quantum state via measurements on several copies, and spin squeezing inequalities. An emphasis is given to the theory and application of entanglement witnesses. We also discuss several experiments, where some of the presented methods have been implemented.
Entanglement Theory and the Quantum Simulation Of Manybody Physics
, 2008
"... Quantum mechanics led us to reconsider the scope of physics and its building principles, such as the notions of realism and locality. More recently, quantum theory has changed in an equally dramatic manner our understanding of information processing and computation. On one hand, the fundamental prop ..."
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Quantum mechanics led us to reconsider the scope of physics and its building principles, such as the notions of realism and locality. More recently, quantum theory has changed in an equally dramatic manner our understanding of information processing and computation. On one hand, the fundamental properties of quantum systems can be harnessed to transmit, store, and manipulate information in a more efficient and secure way than possible in the realm of classical physics. On the other hand, the development of systematic procedures to manipulate systems of a large number of particles in the quantum regime, crucial to the implementation of quantumbased information processing, has triggered new possibilities in the exploration of quantum manybody physics and related areas. In this thesis, we present new results relevant to two important problems in quantum information science: the development of a theory of entanglement, intrinsically quantum correlations, and the exploration of the use of controlled quantum systems to the computation and simulation of quantum manybody phenomena. In the first part we introduce a new approach to the study of entanglement
The structural physical approximations and optimal entanglement witnesses, preprint
"... We introduce the notions of positive and copositive types for entanglement witnesses, depending on the distance to the positive part and copositive part. An entanglement witness W is of positive type if and only if its partial transpose W Γ is of copositive type. We show that if the structural physi ..."
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We introduce the notions of positive and copositive types for entanglement witnesses, depending on the distance to the positive part and copositive part. An entanglement witness W is of positive type if and only if its partial transpose W Γ is of copositive type. We show that if the structural physical approximation of W is separable then W should be of copositive type, and the SPA of W Γ is never separable unless W is of both positive and copositive type. This shows that the SPA conjecture is meaningful only for those of copositive type. We provide examples to show that the SPA conjecture fails even for the case of copositive types.
Epsilonnet method for optimizations over separable states
 In Proceedings of the 39th International Colloquium on Automata, Languages and Programming (ICALP 2012
, 2012
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Approximation, proof systems, and correlations in a quantum world
, 2013
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Visualizing two qubits
 J. Math. Phys
"... We show that notions of entanglement, witnesses, and certain Bell inequalities can be visualized in three dimensions. This allows us to give “proofs by inspection ” of the result that for two qubits, Peres test is iff, and to “solve by inspection ” the optimization problem of the CHSH inequality vio ..."
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We show that notions of entanglement, witnesses, and certain Bell inequalities can be visualized in three dimensions. This allows us to give “proofs by inspection ” of the result that for two qubits, Peres test is iff, and to “solve by inspection ” the optimization problem of the CHSH inequality violation. Finally, we give numerical evidence that, remarkably, allowing Alice and Bob to use more measurements, three rather than two, does not help them to distinguish any new entangled SLOCC equivalence class beyond the CHSH class. 1
THE PROBABILITY OF ENTANGLEMENT
, 712
"... Abstract. We show that states on tensor products of matrix algebras whose ranks are relatively small are almost surely entangled, but that states of maximum rank are not. More precisely, let M = Mm(C) and N = Mn(C) be full matrix algebras with m ≥ n, fix an arbitrary state ω of N, and let E(ω) be th ..."
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Abstract. We show that states on tensor products of matrix algebras whose ranks are relatively small are almost surely entangled, but that states of maximum rank are not. More precisely, let M = Mm(C) and N = Mn(C) be full matrix algebras with m ≥ n, fix an arbitrary state ω of N, and let E(ω) be the set of all states of M ⊗N that extend ω. The space E(ω) contains states of rank r for every r = 1, 2,..., m · rank ω, and it has a filtration into compact subspaces E 1 (ω) ⊆ E 2 (ω) ⊆ · · · ⊆ E m·rank ω = E(ω), where E r (ω) is the set of all states of E(ω) having rank ≤ r. We show first that for every r, there is a realanalytic manifold V r, homogeneous under a transitive action of a compact group G r, which parameterizes E r (ω). The unique G rinvariant probability measure on V r promotes to a probability measure P r,ω on E r (ω), and P r,ω assigns probability 1 to states of rank r. The resulting probability space (E r (ω),P r,ω) represents “choosing a rank r extension of ω at random”. Main results: Among the extensions of maximum rank, the probability of entanglement satisfies 0 < p < 1. However, for every r = 1, 2,..., [rank ω/2], states of (E r (ω),P r,ω) are almost surely entangled. 1.
Entanglement Generation in Spatially Separated Systems Using Quantum Walk
, 2012
"... We present a scheme for generating entanglement between two spatially separated systems from the spatial entanglement generated by the interference effect during the evolution of a singleparticle quantum walk. Any two systems which can interact with the spatial modes entangled during the walk evol ..."
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We present a scheme for generating entanglement between two spatially separated systems from the spatial entanglement generated by the interference effect during the evolution of a singleparticle quantum walk. Any two systems which can interact with the spatial modes entangled during the walk evolution can be entangled using this scheme. A notable feature is the ability to control the quantum walk dynamics and its localization at desired pair lattice sites irrespective of separation distance resulting in a substantial control and improvement in the entanglement output. Implementation schemes to entangle spatially separated atoms using quantum walk on a single atom is also presented.