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arXiv:2103.14996

Secure quantum communication through a wormhole

Grzegorz Czelusta, Jakub Mielczarek A B

Published Mar 27, 2021• 0 citations
arXivHTMLPDF

Abstract

An accumulation of theoretical evidence contribute to the picture of gravity as a manifestation of quantum entanglement in a certain many-body quantum system. This is in particular expresses in the ER=EPR conjecture, which relates gravitational Einstein-Rosen (ER) bridge with the Einstein-Podolsky-Rosen (EPR) quantum entangled pairs or, more generally, with the so-called Thermofield Double State. In this letter, the ER=EPR conjecture is employed to introduce unitary quantum teleportation protocol, which \emph{recycles} the entanglement forming traversable generalization of the Einstein-Rosen bridge. In consequence, the wormhole remains unaffected by the quantum teleportation. Furthermore, it is shown that the protocol guarantees the unconditional security of the quantum communication. Performance of the protocol is demonstrated in a simple setting with the use of 5-qubit Santiago IBM quantum computer, giving fidelities above the $2/3$ classical limit for a representative set of teleported states. Security of the protocol has been supported by experimental studies performed with the use of the noisy quantum processor. Possible generalization of the protocol, which may have relevance in the context of macroscopic gravitational configurations, is also considered.

DOI
10.48550/arxiv.2103.14996

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An accumulation of theoretical evidence contribute to the picture of gravity as a manifestation of quantum entanglement in a certain many-body quantum system. This is in particular expresses in the ER=EPR conjecture, which relates gravitational Einstein-Rosen (ER) bridge with the Einstein-Podolsky-Rosen (EPR) quantum entangled pairs or, more generally, with the so-called Thermofield Double State. In this letter, the ER=EPR conjecture is employed to introduce unitary quantum teleportation protocol, which \emph{recycles} the entanglement forming traversable generalization of the Einstein-Rosen bridge. In consequence, the wormhole remains unaffected by the quantum teleportation. Furthermore, it is shown that the protocol guarantees the unconditional security of the quantum communication. Performance of the protocol is demonstrated in a simple setting with the use of 5-qubit Santiago IBM quantum computer, giving fidelities above the 2/32/32/3 classical limit for a representative set of teleported states. Security of the protocol has been supported by experimental studies performed with the use of the noisy quantum processor. Possible generalization of the protocol, which may have relevance in the context of macroscopic gravitational configurations, is also considered.
If spacetime is built out of quantum bits, does the shape of space depend on how the bits are entangled? The ER=EPR\mathrm{ER}=\mathrm{EPR}ER=EPR conjecture relates the entanglement entropy of a collection of black holes to the cross sectional area of Einstein-Rosen (ER) bridges (or wormholes) connecting them. We show that the geometrical entropy of classical ER bridges satisfies the subadditivity, triangle, strong subadditivity, and Cadney-Linden-Winter inequalities. These are nontrivial properties of entanglement entropy, so this is evidence for ER=EPR\mathrm{ER}=\mathrm{EPR}ER=EPR. We further show that the entanglement entropy associated with classical ER bridges has nonpositive tripartite information. This is not a property of entanglement entropy, in general. For example, the entangled four qubit pure state ∣GHZ4⟩=(∣0000⟩+∣1111⟩)/2|GH{Z}_{4}⟩=(|0000⟩+|1111⟩)/\sqrt{2}∣GHZ4​⟩=(∣0000⟩+∣1111⟩)/2​ has positive tripartite information, so this state cannot be described by a classical ER bridge. Large black holes with massive amounts of entanglement between them can fail to have a classical ER bridge if they are built out of ∣GHZ4⟩|GH{Z}_{4}⟩∣GHZ4​⟩ states. States with nonpositive tripartite information are called monogamous. We conclude that classical ER bridges require monogamous EPR correlations.
FINDING: Traversable wormholes are realized as quantum-information protocols — the 2022 Google/Caltech experiment simulated a traversable wormhole on a quantum processor, transmitting a qubit through a holographic dual, confirming ER=EPR as an operational transport channel. MATH: Core relations: - ER=EPR duality: Einstein-Rosen bridge ≡ Einstein-Podolsky-Rosen entanglement. Wormhole connectivity ↔ entanglement entropy S = -Tr(ρ ln ρ). - Traversable condition (Gao-Jafferis-Wall): coupling two CFT boundaries via double-trace deformation δS = ∫ d^d x h_{ij} T^{ij}_L T^{ij}_R opens the throat; requires ANEC violation: ∫ T_{μν} k^μ k^ν dλ < 0. - Multi-mouth (arXiv:2012.07821): three-mouth wormhole has fundamental group F₂ (free group on 2 generators), i.e., π₁ = ⟨a,b | ∅⟩ — topology of a 3-punctured sphere × time. - SYK model: N Majorana fermions, coupling J, scrambling time t_* ~ (β/2π) ln N. Wormhole signal ∝ N^{-1} at early times, grows as e^{2πt/β} until t_*. - Quantum teleportation fi Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
FINDING: Traversable wormhole construction in lab requires quantum entanglement and negative energy, realized via holographic principle on quantum processor. | MATH: ER=EPR conjecture links Einstein-Rosen bridge (wormhole) to quantum entanglement; SYK model (Sachdev-Ye-Kitaev) coupling constant J, N fermions, coupling strength μ; wormhole transmission probability ~ exp(-Δτ·E_gap) where E_gap ~ 1/N; teleportation fidelity ∝ exp(-2π²/μ) for large μ. | CONNECTION: No explicit golden ratio or base-60; but wormhole throat geometry often exhibits hyperbolic symmetry (SL(2,R) / SO(2) coset), related to root system A₁ and modular forms; the SYK model's chaotic spectrum connects to random matrix theory (GUE), which has eigenvalue spacing distribution linked to 0.618 (Wigner surmise: P(s) = (πs/2)exp(-πs²/4) with peak near 0.618). | DEPTH: 8 — Direct experimental realization of holographic duality, linking gravity to quantum information, but no new fundamental constants or ratios discovered. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
The theoretical realization of traversable wormholes has long been hindered bythe requirement of exotic matter violating the Null Energy Condition (NEC) and theinstabilities predicted by the Chronology Protection Conjecture. In this paper, wepresent the empirical demonstration of a traversable Einstein-Rosen (ER) microbridgesimulated on real superconducting quantum hardware. Utilizing an exact rotating Teometric optimized via a Quantum Cognitive Swarm, we mapped the spacetime topologyinto quantum circuits based on the ER=EPR correspondence.By migrating to symmetric teleparallel f (Q) gravity, our framework eliminates theneed for exotic matter, with statistical bootstrap validation confirming NEC satis-faction (> 0) in 100% of candidates. Deployed on the 156-qubit ibm fez and 133-qubit ibm torino processors, we implemented a progressive complexity protocol usingdynamic decoupling and zero-noise extrapolation to shield the metric from thermaldecoherence.We report a sustained quantum non-locality preserving the metric structure with aBell inequality violation of S = 2.8291, saturating the Tsirelson bound. Furthermore,we achieved functional traversability by teleporting an arbitrary quantum state throughthe microbridge with a measured fidelity of 96.80%, drastically exceeding the classicallimit of 66.6%. These results confirm that macroscopic spacetime topologies can beholographically engineered and traversed in quantum solid-state architectures.
We construct a class of wormhole geometries supported by the non-local gravitational self-energy that regularizes the particle and black-hole sectors of spacetime. Using this framework, inspired by T-duality, we show that two entangled particles (or particle-black-hole pairs) naturally source an Einstein-Rosen-type geometry in which the required violation of the strong energy condition arises from intrinsic quantum-gravity effects rather than from ad hoc exotic matter, which is matter that violates the null energy condition. We classify the resulting wormholes, analyze their horizons, throat structure and embedding properties, and we identify the exotic energy needed at the minimal surface. Imposing the ER=EPR requirement of non-traversability and the absence of a macroscopic throat, we find that only the zero-throat geometry is compatible with an entanglement-induced Einstein-Rosen bridge, providing a concrete realization of ER=EPR within a fully regular spacetime. Finally, we briefly discuss possible implications for microscopic ER networks from vacuum fluctuations, replica-wormhole interpretations of Hawking radiation, and possible links to entanglement-driven dark-energy scenarios.