Can Topology and Geometry be Measured by an Operator Measurement in Quantum Gravity?

Berenstein, David; Miller, Alexandra C.

doi:10.1103/physrevlett.118.261601

Cited by 22 publications

(29 citation statements)

References 23 publications

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“…It is further found that the norm squared of the overlaps is bounded above by the inverse powers of the exponential of the entanglement entropies. Our results put into firmer footing the insights and observations in [11,33,34]. Incidentally, we also find that the overlap of any state with the coherent state defined in Section 3, is a symmetric function associated with that state.…”

Section: Discussionsupporting

confidence: 75%

Detecting topology change via correlations and entanglement from gauge/gravity correspondence

Lin

Zeng

2018

Journal of Mathematical Physics

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We compute a momentum space version of the entanglement spectrum and entanglement entropy of general Young tableau states, and one-point functions on Young tableau states. These physical quantities are used to measure the topology of the dual spacetime geometries in the context of gauge/gravity correspondence. The idea that Young tableau states can be obtained by superposing coherent states is explicitly verified. In this quantum superposition, a topologically distinct geometry is produced by superposing states dual to geometries with a trivial topology. Furthermore we have a refined bound for the overlap between coherent states and the rectangular Young tableau state, by using the techniques of symmetric groups and representations. This bound is exponentially suppressed by the total edge length of the Young tableau. It is also found that the norm squared of the overlaps is bounded above by inverse powers of the exponential of the entanglement entropies. We also compute the overlaps between Young tableau states and other states including squeezed states and multi-mode entangled states which have similarities with those appeared in quantum information theory.

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Section: Discussionsupporting

confidence: 75%

Detecting topology change via correlations and entanglement from gauge/gravity correspondence

Lin

Zeng

2018

Journal of Mathematical Physics

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“…It is natural to wonder whether entanglement entropy in the R-charge Hilbert space provides a similar understanding for the compact transverse space. The work in [116,118] supports this expectation. The quantum mechanical fermion picture and its semiclassical phase space realisation in the LLM plane provide an alternative factorisation of the Hilbert space to study entanglement in R-charge "real space", the conjugate to R-charge momentum.…”

Section: Free Fermion Qm Perspectivesupporting

confidence: 55%

“…To circumvent the difficulty of having a properly factorised Hilbert space, one can consider the effective factorisation in the N fermion quantum mechanics, recently advocated in [116] and subsequently pursued in [20,117,118] 32 .…”

Section: Entangled Gas Of Gravitonsmentioning

confidence: 99%

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Correlations vs connectivity in R-charge

Simón

2018

J. High Energ. Phys.

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The holographic relation between quantum correlations and connectivity of spacetime is explored for single R-charged AdS 5 black holes and their half-BPS limits (superstars). In a two boundary set-up, the wormhole between both universes reduces to a designable and computable quantum mechanical correlation between the dual microscopic degrees of freedom in the BPS limit. This quantum connectivity is seen as a naked singularity by a single sided observer. In a single boundary set-up, as a small step towards the description of entangled black holes, we describe quantum teleportation between two labs in different locations of the transverse 5-sphere using entangled gravitons in a reference state that provides a classical channel between both labs.

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“…In fact, it is known that reconstructing the interior geometry and topology of LLM spacetimes from the dual field theory using just local operator measurements would require access to trans-Planckian physics [17,18]. In particular, around configurations with non-trivial topology there is entanglement between the effective dynamical degrees of freedom and UV modes that are beyond the Planck scale [19][20][21].…”

Section: Introductionmentioning

confidence: 99%

Entanglement shadows in LLM geometries

Balasubramanian

Lawrence

Rolph

et al. 2017

J. High Energ. Phys.

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We find a new example of an asymptotically AdS 5 × S 5 geometry which has an entanglement shadow: that is, a region of spacetime which no Ryu-Takayanagi minimal surface enters. Our example is a particular case of the supersymmetric LLM geometries. Our results illustrate how minimal surfaces, which holographically geometrize entanglement entropy, can fail to probe the whole of spacetime, posing a challenge for attempts to directly reconstruct holographic geometries from the entanglement entropies of the dual field theory. We also comment on the relation to previous investigations of minimal surfaces localised in the S 5 factor of AdS 5 × S 5 .

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Can Topology and Geometry be Measured by an Operator Measurement in Quantum Gravity?

Cited by 22 publications

References 23 publications

Detecting topology change via correlations and entanglement from gauge/gravity correspondence

Detecting topology change via correlations and entanglement from gauge/gravity correspondence

Correlations vs connectivity in R-charge

Entanglement shadows in LLM geometries

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