Global entanglement in multiparticle systems

Meyer, David; Wallach, Nolan R.

doi:10.1063/1.1497700

Cited by 492 publications

(546 citation statements)

References 37 publications

(38 reference statements)

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“…Many-body entanglement [1] is difficult to quantify, so entanglement measures are often restricted to the pure, zero temperature case, for example von Neumann entropy [4] or the Meyer-Wallach measure [5], or to a small number of possibly mixed qubits such as concurrence [6]. On the other hand, it is, in general, hard to quantitatively study the entanglement of thermal states due to the absence of efficient separability criterion for mixed states in many-body systems.…”

Section: Introductionmentioning

confidence: 99%

Entanglement and the interplay between staggered fields and couplings

2012

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We investigate how the interplay between a staggered magnetic field and staggered coupling strength affects both ground state and thermal entanglement. Upon analytically calculating thermodynamic quantities and the correlation functions for such a system, we consider both the global Meyer-Wallach measure of entanglement and the concurrence between pairs of spins. We discover two quantum phase transitions present in the model and show that the quantum phase transitions are reflected in the behaviour of the entanglement at zero temperature. We discover that increasing the alternating field and alternating coupling strength can actually increase the amount of entanglement present at both zero temperature and for thermal states of the system.

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Section: Introductionmentioning

confidence: 99%

Entanglement and the interplay between staggered fields and couplings

2012

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“…Following recent studies on the structures of genuine multipartite entanglement [4,5,6], researchers have proposed many quantitative measures for different classes of multipartite entanglement [7,8,9,10,11]. A particular interesting proposal is Osterloh and Siewert [12,13]'s N-qubit entanglement monotones (for an N-qubit system) constructed with antilinear operators.…”

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confidence: 99%

Permutation-invariant monotones for multipartite entanglement characterization

et al. 2008

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In this work we consider the permutational properties of multipartite entanglement monotones.Based on the fact that genuine multipartite entanglement is a property of the entire multi-qubit system, we argue that ideal definitions for its characterizing quantities must be permutationinvariant. Using this criterion, we examine the three 4-qubit entanglement monotones introduced by Osterloh and Siewert [Phys. Rev. A. 72, 012337]. By expressing them in terms of quantities whose permutational properties can be easily derived, we find that one of these monotones is not permutation-invariant. We propose a permutation-invariant entanglement monotone to replace it, and show that our new monotone properly measures the genuine 4-qubit entanglement in 4-qubit cluster-class states. Our results provide some useful insights in understanding multipartite entanglement.

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“…Accordingly, we examine the l 2 -distance between P P T (y) and the PR state distribution. The second test function we employ is the average subsystem entanglement, expressed in terms of the Meyer-Wallach entanglement measure [20,21],…”

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confidence: 99%

Quantum pseudorandomness from cluster-state quantum computation

2008

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We show how to efficiently generate pseudo-random states suitable for quantum information processing via cluster-state quantum computation. By reformulating pseudo-random algorithms in the cluster-state picture, we identify a strategy for optimizing pseudo-random circuits by properly choosing single-qubit rotations. A Markov chain analysis provides the tool for analyzing convergence rates to the Haar measure and finding the optimal single-qubit gate distribution. Our results may be viewed as an alternative construction of approximate unitary 2-designs.PACS numbers: 03.67. Mn, 03.67.Lx, 03.67.Bg, Methods for characterizing and efficiently generating random quantum states and unitary operators have broad conceptual and practical significance across quantum physics. From a fundamental standpoint, a main motivation stems from the challenge of modeling complex quantum behavior, including quantum chaos [1] and typical entanglement in many-body systems [2,3,4,5,6,7,8]. Within quantum information science, states and unitaries sampled from the appropriate uniform (Haar) distribution provide the enabling resource in a growing number of algorithms and protocols. Remarkably, random pure states saturate the classical communication capacity of a noisy quantum channel [9], and allow superdense coding of arbitrary quantum states [10]. Random unitaries find applications in tasks ranging from approximate encryption and remote state preparation [11] to unbiased noise estimation [12,13] and selective process tomography [14].However, implementing exact randomization on a quantum computer is inefficient, as the number of required elementary gates grows exponentially with the number of qubits. Still, it has been shown [5,12,15] that one can generate pseudo-random (PR) quantum states and unitary operators which satisfy certain practical tests of randomness using only a polynomial number of gates. In particular, a framework for quantifying to what extent pseudo-randomness may simulate the Haar distribution for an intended randomization task is offered by the notion of a t-design [16]. In its essence, a state (unitary) tdesign is a probability distribution over pure states (unitaries) whose statistical moments up to order t equal those from the Haar distribution. While efficient exact unitary 2-designs are known [16], constructions of approximate 2-designs as well as alternative schemes tackling higher-order moments are actively investigated [5,6,7]. So far, existing studies have focused only on the circuit model of quantum computation (QC).In this work, we construct an efficient algorithm for PR state generation in the cluster-state paradigm of QC [17]. This is crucial from an implementation perspective, in that many of the above-mentioned applications of random states originate in quantum communication protocols, for which photonic entanglement and clusterstate QC provide a leading approach [18]. Furthermore, we find that reformulating PR algorithms in a clusterstate picture suggests a path to optimize existing circuit constructions. I...

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Global entanglement in multiparticle systems

Cited by 492 publications

References 37 publications

Entanglement and the interplay between staggered fields and couplings

Entanglement and the interplay between staggered fields and couplings

Permutation-invariant monotones for multipartite entanglement characterization

Quantum pseudorandomness from cluster-state quantum computation

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