Constraining the doability of relativistic quantum tasks

Dolev, Kfir

doi:10.48550/arxiv.1909.05403

Cited by 6 publications

(24 citation statements)

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“…In that case, no simple procedure for completing that computation nonlocally is known. The only known procedures consume exponential entanglement [41][42][43] -for example, using port-teleportation [44]. More precisely, completing the task with p suc = 1 − on n qubits requires a mutual information of order n2 n / .…”

Section: General Relativity As a Quantum Information Theoristmentioning

confidence: 99%

Holographic scattering requires a connected entanglement wedge

May,

Penington,

Sorce

2019

Preprint

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In AdS/CFT, there can exist local 2-to-2 bulk scattering processes even when local scattering is not possible on the boundary; these have previously been studied in connection with boundary correlation functions. We show that boundary regions associated with these scattering configurations must have O(1/G N ) mutual information, and hence a connected entanglement wedge. One of us previously argued for this statement from the boundary theory using operational tools in quantum information theory. We improve that argument to make it robust to small errors and provide a proof in the bulk using focusing arguments in general relativity. We also provide a direct link to entanglement wedge reconstruction by showing that the bulk scattering region must lie inside the connected entanglement wedge. Our construction implies the existence of nonlocal quantum computation protocols that are exponentially more efficient than the optimal protocols currently known.

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Section: General Relativity As a Quantum Information Theoristmentioning

confidence: 99%

Holographic scattering requires a connected entanglement wedge

May,

Penington,

Sorce

2019

Preprint

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“…Using monogamy-of-entanglement games that exploit constructions of mutually unbiased bases in large dimensions [44][45][46], one can obtain p suc (ρ 13 Inserted in eq. (19), this leads to…”

Section: Definition 5 N Lqc Amentioning

confidence: 99%

“…The puzzle is resolved by the observation that local interactions plus shared entanglement in the more restrictive boundary geometry can be used to reproduce local interactions in the higher dimensional bulk. In fact, even general scenarios, with more inputs and outputs and requiring computations in multiple spacetime locations from a bulk perspective, can always be reproduced in the boundary with sufficient entanglement [19].…”

Section: Holography Implements Non-local Computationsmentioning

confidence: 99%

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Complexity and entanglement in non-local computation and holography

May¹

2022

Preprint

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Does gravity constrain computation?We study this question using the AdS/CFT correspondence, where computation in the presence of gravity can be related to non-gravitational physics in the boundary theory. In AdS/CFT, computations which happen locally in the bulk are implemented in a particular non-local form in the boundary, which in general requires distributed entanglement. In more detail, we recall that for a large class of bulk subregions the area of a surface called the ridge is equal to the mutual information available in the boundary to perform the computation non-locally. We then argue the complexity of the local operation controls the amount of entanglement needed to implement it non-locally, and in particular complexity and entanglement cost are related by a polynomial. If this relationship holds, gravity constrains the complexity of operations within these regions to be polynomial in the area of the ridge.

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“…A causal network has "input" vertices, where all edges are outgoing, and "output" vertices, where all edges are ingoing. They appear in varied contexts in quantum information theory, including in relativistic quantum information [5][6][7][8][9] and position based cryptography [10][11][12][13], while similar objects appear in network coding [14] and quantum foundations [15]. In these contexts, one asks: For a given network, what operations can be performed on a quantum system distributed across its input vertices?…”

Section: Introductionmentioning

confidence: 99%

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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Constraining the doability of relativistic quantum tasks

Cited by 6 publications

References 0 publications

Holographic scattering requires a connected entanglement wedge

Holographic scattering requires a connected entanglement wedge

Complexity and entanglement in non-local computation and holography

The connected wedge theorem and its consequences

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