Entangled rings

O’Connor, Kevin; Wootters, William K.

doi:10.1103/physreva.63.052302

Cited by 366 publications

(361 citation statements)

References 26 publications

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“…The structure of the reduced density matrix, necessary to calculate the concurrence follows from the symmetry properties of the Hamiltonian. Reality and parity conservation of H together with translational invariance fix the structure of ρ to be real symmetric with ρ11, ρ22 = ρ33, ρ23, ρ14, ρ44 as the only non-zero entries.O'Connors and Wootters showed that in the Heisenberg chain the maximization of the entanglement at zero temperature is related to the energy minimization [11]. It is known that Werner states [12] can be generated in a one dimensional XY model [13] and that temper-1…”

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confidence: 99%

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Scaling of entanglement close to a quantum phase transition

Osterloh¹,

Amico

Falci

et al. 2002

Nature

1,846

2,051

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In this Letter we discuss the entanglement near a quantum phase transition by analyzing the properties of the concurrence for a class of exactly solvable models in one dimension. We find that entanglement can be classified in the framework of scaling theory. Further, we reveal a profound difference between classical correlations and the non-local quantum correlation, entanglement: the correlation length diverges at the phase transition, whereas entanglement in general remains short ranged.Classical phase transitions occur when a physical system reaches a state below a critical temperature characterized by a macroscopic order [1]. Quantum phase transitions occur at absolute zero; they are induced by the change of an external parameter or coupling constant [2], and are driven by fluctuations. Examples include transitions in quantum Hall systems [3], localization in Si-MOSFETs (metal oxide silicon field-effect transistors; Ref. [4]) and the superconductor-insulator transition in two-dimensional systems [5,6]. Both classical and quantum critical points are governed by a diverging correlation length, although quantum systems possess additional correlations that do not have a classical counterpart. This phenomenon, known as entanglement [7], is the resource that enables quantum computation and communication [8]. The role of the entanglement at a phase transition is not captured by statistical mechanics -a complete classification of the critical many-body state requires the introduction of concepts from quantum information theory [9]. Here we connect the theory of critical phenomena with quantum information by exploring the entangling resources of a system close to its quantum critical point. We demonstrate, for a class of one-dimensional magnetic systems, that entanglement shows scaling behaviour in the vicinity of the transition point.There are various questions that emerge in the study of this problem. Since the ground state wave-function undergoes qualitative changes at a quantum phase transition, it is important to understand how its genuine quantum aspects evolve throughout the transition. Will entanglement between distant subsystems be extended over macroscopic regions, as correlations are? Will it carry distinct features of the transition itself and show scaling behaviour? Answering these questions is important for a deeper understanding of quantum phase transitions and also from the perspective of quantum information theory. So results that bridge these two areas of research are of great relevance. We study a set of localized spins coupled through exchange interaction and subject to an external magnetic field (we consider only spin-1/2 particles), a model central both to condensed matter and information theory and subject to intense study [10]. FIG. 1. The change in the ground state wave-function in the critical region is analyzed considering ∂ λ C(1) as a function of the reduced coupling strength λ. The curves correspond to different lattice sizes N = 11, 41, 101, 251, 401, ∞. We choose N odd to avoid the sub...

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mentioning

confidence: 99%

“…O'Connors and Wootters showed that in the Heisenberg chain the maximization of the entanglement at zero temperature is related to the energy minimization [11]. It is known that Werner states [12] can be generated in a one dimensional XY model [13] and that temper-1…”

mentioning

confidence: 99%

Scaling of entanglement close to a quantum phase transition

Osterloh¹,

Amico

Falci

et al. 2002

Nature

1,846

2,051

View full text Add to dashboard Cite

show abstract

“…Along the same line of realizing a bridge between quantum information science and conventional many-body theory it has been discussed entanglement in magnetic systems [11,12,13,14,15]. In particular entanglement in both the ground state [11,12] and thermal state [13,14,15] of a spin-1/2 Heisenberg spin chain have been analyzed in the literature.…”

Section: Introductionmentioning

confidence: 99%

“…In particular entanglement in both the ground state [11,12] and thermal state [13,14,15] of a spin-1/2 Heisenberg spin chain have been analyzed in the literature. In this situation the system state is given by the Gibb's density operator ρ T = exp (−H/kT ) /Z, where Z =tr[exp (−H/kT )] is the partition function, H the system Hamiltonian, k is Boltzmann's constant which we henceforth will take equal to 1, and T the temperature.…”

Section: Introductionmentioning

confidence: 99%

Fermionic entanglement in itinerant systems

Zanardi

Wang

2002

J. Phys. A: Math. Gen.

119

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“…Since the entanglement is very fragile, the problem of how to create stable entanglement remains a main focus of recent studies in the field of QIP. The thermal entanglement, which differs from the other kinds of entanglement by its advantages of stability and requires neither measurement nor controlled switching of interactions in the preparing process, is an attractive topic that has been extensively studied for various systems including isotropic [3,4,5,6] and anisotropic [7,8] Heisenberg chains, Ising model in an arbitrarily directed magnetic field [9], and cavity-QED [10] since the seminal works by Arnesen et al [3] and Nielsen [11]. Based on the method developed in the context of quantum information, the relaxation of a quantum system towards the thermal equilibrium is investigated [12] and provides us an alternative mechanism to model the spin systems of the spin-1 2 case for the approaching of the thermal entangled states [3,4,5,6,7].…”

Section: Introductionmentioning

confidence: 99%

The effects of nonlinear couplings and external magnetic field on the thermal entanglement in a two-spin-qutrit system

Zhang

2006

Optics Communications

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We investigate the effects of nonlinear couplings and external magnetic field on the thermal entanglement in a two-spin-qutrit system by applying the concept of negativity. It is found that the nonlinear couplings favor the thermal entanglement creating. Only when the nonlinear couplings |K| are larger than a certain critical value does the entanglement exist. The dependence of the thermal entanglement in this system on the magnetic field and temperature is also presented. The critical magnetic field increases with the increasing nonlinear couplings constant |K|. And for a fixed nonlinear couplings constant, the critical temperature is independent of the magnetic field B.

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Entangled rings

Cited by 366 publications

References 26 publications

Scaling of entanglement close to a quantum phase transition

Scaling of entanglement close to a quantum phase transition

Fermionic entanglement in itinerant systems

The effects of nonlinear couplings and external magnetic field on the thermal entanglement in a two-spin-qutrit system

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