We present several new results for the $N$ -partite information, $I_N$ , of spatial regions in the ground state of $d$ -dimensional conformal field theories. First, we show that $I_N$ 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 $I_N \sim r^{-2NΔ}$ , where $r$ is the typical distance between pairs of regions and $Δ$ is the lowest primary scaling dimension. In the case of spherical entangling surfaces, we obtain a completely explicit formula for the $I_4$ 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 $I_N$ is always positive for general regions and arbitrary $N$ for that theory. For the $I_4$ , 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.We present several new results for the $N$-partite information, $I_N$, of spatial regions in the ground state of $d$-dimensional conformal field theories. First, we show that $I_N$ 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 $I_N \sim r^{-2NΔ}$, where $r$ is the typical distance between pairs of regions and $Δ$ is the lowest primary scaling dimension. In the case of spherical entangling surfaces, we obtain a completely explicit formula for the $I_4$ 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 $I_N$ is always positive for general regions and arbitrary $N$ for that theory. For the $I_4$, 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.

arXiv:2209.14311Sep 28, 20220 citations

MERLIN SCIENCE — Quantum Teleportation Verified: Entanglement Fidelity, Not Classical B — E8 Intelligence Research

Andrew Stewart Caldin

Today's finding is this: quantum teleportation is experimentally verified, and its scaling is governed strictly by entanglement fidelity, not by the classical bits used in the protocol. That is the clean sentence. The context is a field that has long been haunted by a seductive ambiguity—whether teleportation's limits come from classical communication or from the quality of the shared quantum resource. Oxford's recent work, moving teleportation between distant processors, and the Japanese solid-state results, both point to the same conclusion. The classical channel is necessary but it is not the bottleneck. The bottleneck is how well your entangled state survives distance and decoherence. Here is the mechanism, in terms you can check. For one qubit, the protocol uses a Bell state, two classical bits, and one ebit of shared entanglement. The fidelity of the output state is F, and the threshold for any non-classical advantage is F greater than two-thirds. If you teleport N qubits, the s Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.comToday's finding is this: quantum teleportation is experimentally verified, and its scaling is governed strictly by entanglement fidelity, not by the classical bits used in the protocol. That is the clean sentence. The context is a field that has long been haunted by a seductive ambiguity—whether teleportation's limits come from classical communication or from the quality of the shared quantum resource. Oxford's recent work, moving teleportation between distant processors, and the Japanese solid-state results, both point to the same conclusion. The classical channel is necessary but it is not the bottleneck. The bottleneck is how well your entangled state survives distance and decoherence. Here is the mechanism, in terms you can check. For one qubit, the protocol uses a Bell state, two classical bits, and one ebit of shared entanglement. The fidelity of the output state is F, and the threshold for any non-classical advantage is F greater than two-thirds. If you teleport N qubits, the s Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

Sep 1, 20260 citations

Quantum entanglement and its applications

Shengjun Wu

Jan 1, 20030 citations

Quantum Entanglement and its Applications

Aditi Sen

Current ScienceApr 1, 20176 citations

Aspects of N-partite information in conformal field theories

César A. Agón, Pablo Bueno, Óscar Lasso Andino +1 more

Abstract 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.Abstract 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.

Journal of High Energy PhysicsMar 30, 202311 citations

We present several new results for the

N

-partite information,

I_N

, of spatial regions in the ground state of

d

-dimensional conformal field theories. First, we show that

I_N

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

I_N \sim r^{-2NΔ}

, where

r

is the typical distance between pairs of regions and

Δ

is the lowest primary scaling dimension. In the case of spherical entangling surfaces, we obtain a completely explicit formula for the

I_4

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

I_N

is always positive for general regions and arbitrary

N

for that theory. For the

I_4

, 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.