Topological entanglement entropy in Chern-Simons theories and quantum Hall fluids

Dong, Shiying; Fradkin, Eduardo; Leigh, Robert G.; Nowling, Sean

doi:10.1088/1126-6708/2008/05/016

Cited by 200 publications

(334 citation statements)

References 80 publications

(176 reference statements)

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“…It is only important that we have a pair of lumps propagating in the opposite directions and that one of the members of the pair is inside the entangling region of an arbitrary shape (in 1d either a finite or semi-infinite interval) while the other member remains outside. This strongly hints to the topological nature of this quantity (see also [25] and the discussion section).…”

Section: Derivative Of a Primarymentioning

confidence: 66%

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Entanglement constant for conformal families

Caputa

Véliz-Osorio

2015

Phys. Rev. D

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We show that in 1+1 dimensional conformal field theories, exciting a state with a local operator increases the Rényi entanglement entropies by a constant which is the same for every member of the conformal family. Hence, it is an intrinsic parameter that characterises local operators from the perspective of quantum entanglement. In rational conformal field theories this constant corresponds to the logarithm of the quantum dimension of the primary operator. We provide several detailed examples for the second Rényi entropies and a general derivation.arXiv:1507.00582v2 [hep-th] 16 Sep 2015

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Section: Derivative Of a Primarymentioning

confidence: 66%

“…In fact it was shown in [25] that for a given region A the increase of the topological entanglement entropy due to excitation a is equal ∆S top = log(d a ) (5.5) where d a is the quantum dimension of the excitation.…”

Section: Conclusion and Discussionmentioning

confidence: 99%

Entanglement constant for conformal families

Caputa

Véliz-Osorio

2015

Phys. Rev. D

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“…This finding, which showed that entanglement entropy is sensitive to fundamental characteristics of a quantum system, motivated many further studies in which entanglement entropy has been used as a tool to analyze many-body states of a variety of different systems [6,7,8,9,10,11,12,13,14,15,16,17]. Entanglement entropy, serving as a general characteristic describing quantum many-body correlations between two parts of a quantum system, provided a framework for analyzing quantum critical phenomena [6,7,8] and quantum quenches [9,10,11,12].…”

Section: Introductionmentioning

confidence: 92%

Many-Body Entanglement: a New Application of the Full Counting Statistics

Klich¹,

Levitov²,

Лебедев³

et al. 2009

AIP Conference Proceedings

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Entanglement entropy is a measure of quantum correlations between separate parts of a manybody system, which plays an important role in many areas of physics. Here we review recent work in which a relation between this quantity and the Full Counting Statistics description of electron transport was established for noninteracting fermion systems. Using this relation, which is of a completely general character, we discuss how the entanglement entropy can be directly measured by detecting current fluctuations in a driven quantum system such as quantum point contact.

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“…The notion of entanglement entropy has provided a framework for analyzing quantum critical phenomena [3,4,5] and quantum quenches [6,7,8,9]. Recently it was used as a probe of complexity of topologically ordered states [10,11,12]. In addition, this quantity is of fundamental interest for quantum information theory as a measure of the resources available for quantum computation [13] as well as for numerical approaches to strongly correlated systems [14].…”

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confidence: 99%

Quantum Noise as an Entanglement Meter

2009

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Entanglement entropy, which is a measure of quantum correlations between separate parts of a many-body system, has emerged recently as a fundamental quantity in broad areas of theoretical physics, from cosmology and field theory to condensed matter theory and quantum information. The universal appeal of the entanglement entropy concept is related, in part, to the fact that it is defined solely in terms of the many-body density matrix of the system, with no relation to any particular observables. However, for the same reason, it has not been clear how to access this quantity experimentally. Here we derive a universal relation between entanglement entropy and the fluctuations of current flowing through a quantum point contact (QPC) which opens a way to perform a direct measurement of entanglement entropy. In particular, by utilizing space-time duality of 1d systems, we relate electric noise generated by opening and closing the QPC periodically in time with the seminal S = 1 3 log L prediction of conformal field theory.Recent years have witnessed a burst of interest in the phenomena of quantum entanglement, and in particular, in entanglement entropy, a fundamental characteristic describing quantum many-body correlations between two parts of a quantum system. This quantity first emerged in field theory and cosmology [1,2] under the name of "geometric entropy," and subsequently was adopted by quantum information theory. The notion of entanglement entropy has provided a framework for analyzing quantum critical phenomena [3,4,5] and quantum quenches [6,7,8,9]. Recently it was used as a probe of complexity of topologically ordered states [10,11,12]. In addition, this quantity is of fundamental interest for quantum information theory as a measure of the resources available for quantum computation [13] as well as for numerical approaches to strongly correlated systems [14].Can the entanglement entropy be measured? Here we identify a system where such a measurement is possible, thereby offering an affirmative answer to this question. In particular, we establish a relation between the entropy and quantum noise in a quantum point contact (QPC) [15], an electron beam-splitter with tunable transmission and reflection. In essense, the QPC serves as a door between electron reservoirs, which can be opened and closed on demand (see Fig.1). We show that the fluctuations of electric current flowing through the QPC can be used to quantify the entanglement generated by the connection, and thereby measure the entanglement entropy.On some level, the very idea of measuring a quantity that encodes information about many-body correlations of a large number of particles, which is what the entanglement entropy is, may seem totally bizarre. Yet, as we shall see, the situation with the entanglement entropy is different from, for example, the many-body density matrix that depends on coordinates of all particles in the system and is thus indeed very difficult to measure. In the free fermion QPC problem analyzed below, all multiparticle correlati...

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Topological entanglement entropy in Chern-Simons theories and quantum Hall fluids

Cited by 200 publications

References 80 publications

Entanglement constant for conformal families

Entanglement constant for conformal families

Many-Body Entanglement: a New Application of the Full Counting Statistics

Quantum Noise as an Entanglement Meter

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