Abstract We introduce a new class of quantum and classical correlation measures by generalizing the reflected entropy to multipartite states. We define the new measures for quantum systems in one spatial dimension. For quantum systems having gravity duals, we show that the holographic duals of these new measures are various types of minimal surfaces consist of different entanglement wedge cross sections. One special generalized reflected entropy is ∆R, with the holographic dual proportional to the so called multipartite entanglement wedge cross section ∆W defined before. We then perform a large c computation of ∆R and find evidence to support ∆R = 2∆W . This shows another candidate ∆R as the dual of 2∆W and also supports our holographic conjecture of the new class of generalized reflected entropies.Abstract We introduce a new class of quantum and classical correlation measures by generalizing the reflected entropy to multipartite states. We define the new measures for quantum systems in one spatial dimension. For quantum systems having gravity duals, we show that the holographic duals of these new measures are various types of minimal surfaces consist of different entanglement wedge cross sections. One special generalized reflected entropy is ∆R, with the holographic dual proportional to the so called multipartite entanglement wedge cross section ∆W defined before. We then perform a large c computation of ∆R and find evidence to support ∆R = 2∆W . This shows another candidate ∆R as the dual of 2∆W and also supports our holographic conjecture of the new class of generalized reflected entropies.

arXiv:1909.10456Journal of High Energy PhysicsMar 1, 202054 citations

Entropic methodology for entanglement measures

Wei Deng, Yong Deng

Physica A Statistical Mechanics and its ApplicationsAug 13, 201841 citations

Optimized correlation measures in holography

Newton Cheng

We consider a class of correlation measures for quantum states called optimized correlation measures defined as a minimization of a linear combination of von Neumann entropies over purifications of a given state. Examples include the entanglement of purification ${E}_{P}$ and squashed entanglement ${E}_{\mathrm{sq}}$ . We show that when evaluating such measures on ``nice" holographic states in the large- $N$ limit, the optimal purification has a semiclassical geometric dual. We then apply this result to confirm several holographic dual proposals, including the $n$ -party squashed entanglement. Moreover, our result suggests two new techniques for determining holographic duals: holographic entropy inequalities and direct optimization of the dual geometry.We consider a class of correlation measures for quantum states called optimized correlation measures defined as a minimization of a linear combination of von Neumann entropies over purifications of a given state. Examples include the entanglement of purification ${E}_{P}$ and squashed entanglement ${E}_{\mathrm{sq}}$. We show that when evaluating such measures on ``nice" holographic states in the large-$N$ limit, the optimal purification has a semiclassical geometric dual. We then apply this result to confirm several holographic dual proposals, including the $n$-party squashed entanglement. Moreover, our result suggests two new techniques for determining holographic duals: holographic entropy inequalities and direct optimization of the dual geometry.

arXiv:1909.09334Physical review. D/Physical review. D.Mar 12, 20207 citations

Measures of Quantum Entanglement

P. K. Aravind

Springer eBooksJan 1, 19962 citations

New multipartite entanglement measure and its holographic dual

Abhijit Gadde, Vineeth Krishna, Trakshu Sharma

In this paper we define a natural generalization of the von Neumann entropy to multiple parties that is symmetric with respect to all the parties. We call this measure multi-entropy. We show that for conformal field theories with holographic duals, the multi-entropy is computed by the area of an appropriate ``soap-film'' anchored on the boundary. We conjecture the quantum version of this prescription that takes into account the subleading corrections in ${G}_{N}$ .In this paper we define a natural generalization of the von Neumann entropy to multiple parties that is symmetric with respect to all the parties. We call this measure multi-entropy. We show that for conformal field theories with holographic duals, the multi-entropy is computed by the area of an appropriate ``soap-film'' anchored on the boundary. We conjecture the quantum version of this prescription that takes into account the subleading corrections in ${G}_{N}$.

arXiv:2206.09723Physical review. D/Physical review. D.Dec 2, 202241 citations

{E}_{P}

and squashed entanglement

{E}_{\mathrm{sq}}

. We show that when evaluating such measures on ``nice" holographic states in the large-

N

limit, the optimal purification has a semiclassical geometric dual. We then apply this result to confirm several holographic dual proposals, including the

n

-party squashed entanglement. Moreover, our result suggests two new techniques for determining holographic duals: holographic entropy inequalities and direct optimization of the dual geometry.

{G}_{N}