Complexity and entanglement in non-local computation and holography

May, Alex

doi:10.48550/arxiv.2204.00908

Cited by 2 publications

(3 citation statements)

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“…In holography, even for n = 2 the boundary protocol is most naturally modeled as an EAQECC: the particles fall into the bulk is the encoding step, then logical operations are performed on the encoded systems in tensor product form, then the systems are decoded, pulling them out from the bulk. Given the tension between the efficiency, in terms of entanglement use, in AdS/CFT vs in existing non-local computation protocols in quantum information [29], it is natural to explore EAQECC based non-local computation protocols in more detail. A simple starting point may be to adapt the code based strategies of [56] to use entanglement-assisted codes.…”

Section: Why No N-to-m Theorem For N = M?mentioning

confidence: 99%

“…In fact, having a large amount of entanglement between these regions is also sufficient to reproduce any bulk interaction, though many questions remain as to how much entanglement is needed for a given interaction. See e.g [29]. for a discussion.…”

mentioning

confidence: 99%

“…See[29] for a recent investigation of related issues 17. By "high probability," we mean a probability that converges exponentially to 1 in the limit n → ∞.…”

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confidence: 99%

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The connected wedge theorem and its consequences

May

Sorce

Yoshida

2022

J. High Energ. Phys.

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In the AdS/CFT correspondence, bulk causal structure has consequences for boundary entanglement. In quantum information science, causal structures can be replaced by distributed entanglement for the purposes of information processing. In this work, we deepen the understanding of both of these statements, and their relationship, with a number of new results. Centrally, we present and prove a new theorem, the n-to-n connected wedge theorem, which considers n input and n output locations at the boundary of an asymptotically AdS2+1 spacetime described by AdS/CFT. When a sufficiently strong set of causal connections exists among these points in the bulk, a set of n associated regions in the boundary will have extensive-in-N mutual information across any bipartition of the regions. The proof holds in three bulk dimensions for classical spacetimes satisfying the null curvature condition and for semiclassical spacetimes satisfying standard conjectures. The n-to-n connected wedge theorem gives a precise example of how causal connections in a bulk state can emerge from large-N entanglement features of its boundary dual. It also has consequences for quantum information theory: it reveals one pattern of entanglement which is sufficient for information processing in a particular class of causal networks. We argue this pattern is also necessary, and give an AdS/CFT inspired protocol for information processing in this setting.Our theorem generalizes the 2-to-2 connected wedge theorem proven in [3]. We also correct some errors in the proof presented there, in particular a false claim that existing proof techniques work above three bulk dimensions.

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Section: Why No N-to-m Theorem For N = M?mentioning

confidence: 99%

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The connected wedge theorem and its consequences

May

Sorce

Yoshida

2022

J. High Energ. Phys.

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The connected wedge theorem and its consequences

May¹,

Sorce²,

Yoshida³

2022

Preprint

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In the AdS/CFT correspondence, bulk causal structure has consequences for boundary entanglement. In quantum information science, causal structures can be replaced by distributed entanglement for the purposes of information processing. In this work, we deepen the understanding of both of these statements, and their relationship, with a number of new results. Centrally, we present and prove a new theorem, the n-to-n connected wedge theorem, which considers n input and n output locations at the boundary of an asymptotically AdS 2+1 spacetime described by AdS/CFT. When a sufficiently strong set of causal connections exists among these points in the bulk, a set of n associated regions in the boundary will have extensive-in-N mutual information across any bipartition of the regions. The proof holds in three bulk dimensions for classical spacetimes satisfying the null curvature condition and for semiclassical spacetimes satisfying standard conjectures. The n-to-n connected wedge theorem gives a precise example of how causal connections in a bulk state can emerge from large-N entanglement features of its boundary dual. It also has consequences for quantum information theory: it reveals one pattern of entanglement which is sufficient for information processing in a particular class of causal networks. We argue this pattern is also necessary, and give an AdS/CFT inspired protocol for information processing in this setting.Our theorem generalizes the 2-to-2 connected wedge theorem proven in arXiv:1912.05649. We also correct some errors in the proof presented there, in particular a false claim that existing proof techniques work above three bulk dimensions.

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Complexity and entanglement in non-local computation and holography

Cited by 2 publications

References 52 publications

The connected wedge theorem and its consequences

The connected wedge theorem and its consequences

The connected wedge theorem and its consequences

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