Optimized correlation measures in holography

Cheng, Newton

doi:10.1103/physrevd.101.066009

Cited by 12 publications

(11 citation statements)

References 63 publications

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“…However, at least in some cases -e.g. for optimized (n-point) correlation measures -it was established in [138] that a minimization over semiclassical bulk spacetimes will in fact accomplish a global minimum over a holographic CFT's Hilbert space. The volume of the maximal volume slice of this spacetime is the obvious candidate to C P (ρ R ).…”

Section: Jhep01(2022)040 4 Discussionmentioning

confidence: 99%

General bounds on holographic complexity

Engelhardt

Folkestad

2022

J. High Energ. Phys.

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We prove a positive volume theorem for asymptotically AdS spacetimes: the maximal volume slice has nonnegative vacuum-subtracted volume, and the vacuum-subtracted volume vanishes if and only if the spacetime is identically pure AdS. Under the Complexity=Volume proposal, this constitutes a positive holographic complexity theorem. The result features a number of parallels with the positive energy theorem, including the assumption of an energy condition that excludes false vacuum decay (the AdS weak energy condition). Our proof is rigorously established in broad generality in four bulk dimensions, and we provide strong evidence in favor of a generalization to arbitrary dimensions. Our techniques also yield a holographic proof of Lloyd’s bound for a class of bulk spacetimes. We further establish a partial rigidity result for wormholes: wormholes with a given throat size are more complex than AdS-Schwarzschild with the same throat size.

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Section: Jhep01(2022)040 4 Discussionmentioning

confidence: 99%

General bounds on holographic complexity

Engelhardt

Folkestad

2022

J. High Energ. Phys.

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“…intractable problem, it was assumed that minimizing over geometric purifications was sufficient (for discussions of this point, see [31]). This conjecture, along with its multipartite generalizations, has received a lot of attention recently, although proofs or related computations have generally required various strong assumptions [13][14][15][32][33][34][35][36][37][38][39].…”

Section: E P Conjecture Vs Bipartite Entanglementmentioning

confidence: 99%

“…An important insight we gain here is that non-geometric tensor networks like the simplified network were crucial for the minimization in computing E P , at least for RSTNs. It would be interesting to understand if this is more generally true [31].…”

Section: Jhep04(2020)208mentioning

confidence: 99%

Entanglement wedge cross sections require tripartite entanglement

Akers

Rath

2020

J. High Energ. Phys.

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We argue that holographic CFT states require a large amount of tripartite entanglement, in contrast to the conjecture that their entanglement is mostly bipartite. Our evidence is that this mostly-bipartite conjecture is in sharp conflict with two wellsupported conjectures about the entanglement wedge cross section surface EW . If EW is related to either the CFT's reflected entropy or its entanglement of purification, then those quantities can differ from the mutual information at O( 1 G N ). We prove that this implies holographic CFT states must have O( 1G N ) amounts of tripartite entanglement. This proof involves a new Fannes-type inequality for the reflected entropy, which itself has many interesting applications.

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“…First, we will assume that for any optimized correlation measure and any holographic mixed state, the optimal purification is holographic. Arguments supporting this assumption were presented in [28]. Second, we take the optimal purification (before dividing it into n subsystems) to be the closed surface formed by the boundary of the n-partite entanglement wedge.…”

Section: But What Other Geometric Purifications Are Possible?mentioning

confidence: 99%

“…In [20], the log negativity [21] was proposed as the EWCS dual, while in [22], a quantity called the odd entanglement entropy was argued for. Indeed, investigations of the EWCS and its proposed boundary duals have been the subject of a large body of work [23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41]. Many of these proposed dualities coincide with E P in the limit of classical geometry.…”

Section: Introductionmentioning

confidence: 99%

Multipartite optimized correlation measures and holography

2020

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We explore ways to quantify multipartite correlations, in quantum information and in holography. We focus on optimized correlation measures, linear combinations of entropies minimized over all possible purifications of a state that satisfy monotonicity conditions. These contain far more information about correlations than entanglement entropy alone. We present a procedure to derive such quantities and construct a menagerie of symmetric optimized correlation measures on three parties. These include tripartite generalizations of the entanglement of purification, the squashed entanglement, and the recently introduced Q correlation and R correlation. Some correlation measures vanish only on product states and, thus, quantify both classical and quantum correlations; others vanish on any separable state, capturing quantum correlations alone. We then use a procedure motivated by the surface-state correspondence to construct holographic duals for the correlation measures as linear combinations of bulk surfaces. The geometry of the surfaces can preserve, partially break, or fully break the symmetry of the correlation measure. The optimal purification is encoded in the locations of certain points, whose locations are fixed by constraints on the areas of combinations of surfaces. This gives a new concrete connection between information theoretic quantities evaluated on a boundary state and detailed geometric properties of its dual.

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Optimized correlation measures in holography

Cited by 12 publications

References 63 publications

General bounds on holographic complexity

General bounds on holographic complexity

Entanglement wedge cross sections require tripartite entanglement

Multipartite optimized correlation measures and holography

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