Holographic quantum entanglement negativity

Chaturvedi, Pankaj; Malvimat, Vinay; Sengupta, Gautam

doi:10.1007/jhep05(2018)172

Cited by 81 publications

(168 citation statements)

References 32 publications

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“…The above developments naturally lead to the interesting question of a holographic characterization of the entanglement negativity for bipartite pure and mixed states in dual CF T s [25,26]. In the recent past two of the present authors (VM and GS) in a collaboration, proposed a holographic construction for the entanglement negativity of bipartite pure and mixed states in a dual CF T 1+1 through AdS 3 /CF T 2 framework and its covariant extension [27,28]. This construction was rigorously substantiated through a large central charge analysis employing the monodromy technique in [29], although a bulk proof for this conjecture along the lines of [20] is an outstanding issue.…”

Section: Contentsmentioning

confidence: 93%

Time evolution of entanglement negativity from black hole interiors

Malvimat

Mondal

Sengupta

2019

J. High Energ. Phys.

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We investigate the time evolution of entanglement negativity following a global quench for mixed state configurations of two disjoint and adjacent intervals in a (1 + 1)-dimensional conformal field theory (CF T 1+1 ) dual to the eternal black hole sliced in half by an end of the world brane, through the AdS 3 /CF T 2 correspondence. To this end we obtain the time evolution of the holographic entanglement negativity for such mixed states from a dual bulk eternal black hole geometry and elucidate the relevant geodesic structures. The holographic entanglement negativity for such mixed states, following a global quench is described by half of the results for the eternal black hole. Significantly our results exactly match with the corresponding CF T 1+1 computations.ArXiv ePrint: 1812.04424

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Section: Contentsmentioning

confidence: 93%

Time evolution of entanglement negativity from black hole interiors

Malvimat

Mondal

Sengupta

2019

J. High Energ. Phys.

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“…We plan to return to these interesting questions in the future. Let us remark that in [9][10][11] it was suggested that in holographic framework the mutual information, multiplied by a constant, could be a dual to the entanglement negativity E. This was revised by a suggestion [14] that the entanglement wedge cross section E W , supplemented by the backreaction of the hanging minimal (cosmological) surfaces to the geometry, is actually a gravity dual of entanglement negativity. While lots of important work [4,6,7, has been carried out and most obvious inequalities tested, we feel that it is premature to identify E W one way or the other.…”

Section: Introductionmentioning

confidence: 99%

Notes on entanglement wedge cross sections

Jokela

Pönni

2019

J. High Energ. Phys.

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We consider the holographic candidate for the entanglement of purification E P , given by the minimal cross sectional area of an entanglement wedge E W . The E P is generally very complicated quantity to obtain in field theories, thus to establish the conjectured relationship one needs to test if E W and E P share common features. In this paper the entangling regions we consider are slabs, concentric spheres, and creases in field theories in Minkowski space. The latter two can be mapped to regions in field theories defined on spheres, thus corresponding to entangled caps and orange slices, respectively. We work in general dimensions and for slabs we also consider field theories at finite temperature and confining theories. We find that E W is neither a monotonic nor continuous function of a scale. We also study a full ten-dimensional string theory geometry dual to a non-trivial RG flow of a three-dimensional Chern-Simons matter theory coupled to fundamentals. We show that also in this case E W behaves non-trivially, which if connected to E P , lends further support that the system can undergo purification simply by expansion or reduction in scale. * niko.jokela@helsinki.fi † arttu.ponni@helsinki.fi

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“…For example, one can conceive of a Hamiltonian that keeps ρ T B positive semidefinite for some time interval, indicating a protracted separability or bound entanglement. In such a scenario the patterned derivatives may be functionally different from the Jacobian (20) or Hessian (36), and would need to be treated on a case-by-case basis. However, we have seen in Section III B that our expansion correctly predicts zero evolution of the negativity when ρ T B is positive semidefinite.…”

Section: Discussionmentioning

confidence: 99%

“…(32) to (34). All that remains is to merge the unpatterned Hessians as in (36) to obtain the Hessian with respect to a Hermitian variable. We show these computations in more detail in App.…”

Section: Second Derivative Of the Trace Normmentioning

confidence: 99%

Perturbative expansion of entanglement negativity using patterned matrix calculus

2019

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Negativity is an entanglement monotone frequently used to quantify entanglement in bipartite states. Because negativity is a non-analytic function of a density matrix, existing methods used in the physics literature are insufficient to compute its derivatives. To this end we develop techniques in the calculus of complex, patterned matrices and use them to conduct a perturbative analysis of negativity in terms of arbitrary variations of the density operator. The result is an easy-to-implement expansion that can be carried out to all orders. On the way we provide convenient representations of the partial transposition map appearing in the definition of negativity. Our methods are well-suited to study the growth and decay of entanglement in a wide range of physical systems, including the generic linear growth of entanglement in many-body systems, and have broad relevance to many functions of quantum states and observables.1 By most definitions, entanglement measures ought to reduce to the entanglement entropy [17,24] in the pure state case; negativity does not. Nevertheless, we alternate between calling it a monotone and measure depending on the subsystem dimensions.arXiv:1809.07772v2 [quant-ph]

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Holographic quantum entanglement negativity

Cited by 81 publications

References 32 publications

Time evolution of entanglement negativity from black hole interiors

Time evolution of entanglement negativity from black hole interiors

Notes on entanglement wedge cross sections

Perturbative expansion of entanglement negativity using patterned matrix calculus

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