A holographic inequality for N = 7 regions

Czech, Bartłomiej; Wang, Yunfei

doi:10.1007/jhep01(2023)101

Cited by 9 publications

(2 citation statements)

References 28 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…As opposed to the mutual information, the tripartite information can be both positive and negative for different theories [32,33]. When a given theory satisfies I 3 ≤ 0 for arbitrary regions, the mutual information is said to be "monogamous", which is the case, for instance, of holographic theories [34,35] see also [36][37][38]. On the other hand, examples of theories which exhibit non-monogamous mutual informations include free fields [39].…”

Section: Jhep03(2023)246mentioning

confidence: 99%

Aspects of N-partite information in conformal field theories

Agón

Bueno

Andino

et al. 2023

J. High Energ. Phys.

View full text Add to dashboard Cite

We present several new results for the N-partite information, IN, of spatial regions in the ground state of d-dimensional conformal field theories. First, we show that IN can be written in terms of a single N-point function of twist operators. Using this, we argue that in the limit in which all mutual separations are much greater than the regions sizes, the N-partite information scales as IN ~ r−2N∆, where r is the typical distance between pairs of regions and ∆ is the lowest primary scaling dimension. In the case of spherical entangling surfaces, we obtain a completely explicit formula for the I4 in terms of 2-, 3- and 4-point functions of the lowest-dimensional primary. Then, we consider a three- dimensional scalar field in the lattice. We verify the predicted long-distance scaling and provide strong evidence that IN is always positive for general regions and arbitrary N for that theory. For the I4, we find excellent numerical agreement between our general formula and the lattice result for disk regions. We also perform lattice calculations of the mutual information for more general regions and general separations both for a free scalar and a free fermion, and conjecture that, normalized by the corresponding disk entanglement entropy coefficients, the scalar result is always greater than the fermion one. Finally, we verify explicitly the equality between the N-partite information of bulk and boundary fields in holographic theories for spherical entangling surfaces in general dimensions.

show abstract

Section: Jhep03(2023)246mentioning

confidence: 99%

Aspects of N-partite information in conformal field theories

Agón

Bueno

Andino

et al. 2023

J. High Energ. Phys.

View full text Add to dashboard Cite

show abstract

“…The discovery of monogamy of mutual information (MMI) [5,6] showed that for geometric states, i.e., states of holographic CFTs which are dual to classical geometries, the HRRT prescription [7,8] implies that the entropies of spatial subsystems in the boundary CFT satisfy constraints that in general do not hold for arbitrary quantum systems. Since then, new holographic entropy inequalities have been found, and the holographic entropy cone (HEC) [9] has been studied extensively [10][11][12][13][14][15][16][17][18][19][20][21].…”

Section: Introductionmentioning

confidence: 99%

On the relation between the subadditivity cone and the quantum entropy cone

He,

Hubeny,

Rota

2023

J. High Energ. Phys.

View full text Add to dashboard Cite

Given a multipartite quantum system, what are the possible ways to impose mutual independence among some subsystems, and the presence of correlations among others, such that there exists a quantum state which satisfies these demands? This question and the related notion of a pattern of marginal independence (PMI) were introduced in [1], and then argued in [2] to be central in the derivation of the holographic entropy cone. Here we continue the general information theoretic analysis of the PMIs allowed by strong subadditivity (SSA) initiated in [1]. We show how the computation of these PMIs simplifies when SSA is replaced by a weaker constraint, dubbed Klein’s condition (KC), which follows from the necessary condition for the saturation of subadditivity (SA). Formulating KC in the language of partially ordered sets, we show that the set of PMIs compatible with KC forms a lattice, and we investigate several of its structural properties. One of our main results is the identification of a specific lower dimensional face of the SA cone that contains on its boundary all the extreme rays (beyond Bell pairs) that can possibly be realized by quantum states. We verify that for four or more parties, KC is strictly weaker than SSA, but nonetheless the PMIs compatible with SSA can easily be derived from the KC-compatible ones. For the special case of 1-dimensional PMIs, we conjecture that KC and SSA are in fact equivalent. To make the presentation self-contained, we review the key ingredients from lattice theory as needed.

show abstract