Teleportation Through the Wormhole (1707.04354v1)

Abstract: ER=EPR allows us to think of quantum teleportation as communication of quantum information through space-time wormholes connecting entangled systems. The conditions for teleportation render the wormhole traversable so that a quantum system entering one end of the ERB will, after a suitable time, appear at the other end. Teleportation requires the transfer of classical information outside the horizon, but the classical bit-string carries no information about the teleported system; the teleported system passes through the ERB leaving no trace outside the horizon. In general the teleported system will retain a memory of what it encountered in the wormhole. This phenomenon could be observable in a laboratory equipped with quantum computers.

• The paper demonstrates that under the ER=EPR conjecture, quantum teleportation occurs through traversable wormholes, effectively reducing entanglement by the size of the teleported system.
• It employs circuit models to optimize the teleportation process, revealing that minimal operations on the receiver's side can significantly streamline quantum state transfer.
• The authors propose that laboratory experiments with quantum computers could verify these predictions, potentially advancing research in quantum gravity and spacetime geometry.

Teleportation Through the Wormhole: An Examination

The paper "Teleportation Through the Wormhole" by Leonard Susskind and Ying Zhao explores the implications of the ER=EPR conjecture, a theory that connects Einstein-Rosen bridges (wormholes) with quantum entanglement. This principle has far-reaching consequences in the context of quantum teleportation and spacetime geometry, suggesting a novel understanding of quantum information transfer between entangled systems through a wormhole.

Summary of the Paper

The authors begin by discussing quantum teleportation, a quantum information process originally developed by Bennett et al., and how it can be viewed in the light of wormhole traversal under the ER=EPR hypothesis. In traditional quantum teleportation, a quantum state is transferred from one location to another using entangled particles and classical communication, without a physical transfer of matter or energy. The paper suggests that this process can be understood geometrically as the transfer of information through a microscopic wormhole connecting two entangled particles or systems.

Key Points

1. Wormhole Traversability: The paper asserts that under the conditions specified by ER=EPR, wormholes become traversable for quantum information. Although these microscopic wormholes lack a classical geometric structure, they provide a conceptual model for teleportation.
2. Entanglement and Information Transfer: In this framework, the teleportation of a quantum state entails the transfer of classical information outside the horizon of a black hole. Importantly, the classical bit string involved conveys no actual content about the teleported state, which traverses the wormhole unaltered by local spacetime.
3. Laboratory Implications: The authors propose that the teleportation effect described could be observable in laboratory settings with quantum computers, potentially confirming ER=EPR without requiring observers to cross event horizons.

Numerical and Theoretical Insights

One central technical result is that the process of teleportation necessarily diminishes the quantum entanglement between the involved systems by at least the size (in qubits) of the teleported system. Additionally, theoretical estimations simplify the complexity of operations involved. For example, through circuit models, they demonstrate that the complexity of teleportation can be optimized, exploiting the switchback effect to minimize the operations required on Bob's end.

Contrasting Approaches

The paper contrasts this teleportation methodology with the protocol by Gao, Jafferis, and Wall, wherein the appearance of negative energy shockwaves makes wormholes traversable. Both approaches underscore the multi-faceted nature of ER=EPR, revealing different yet compatible means of enabling quantum state transfers through spacetime.

Implications and Speculation

Theoretical Implications: By reimagining quantum teleportation in terms of traversable wormholes, the authors provide a fresh perspective linking quantum information theory with spacetime geometry. This viewpoint not only supports the holographic principle but also bridges gaps between quantum mechanics, general relativity, and quantum gravity theories.

Practical Implications: In practical terms, these theoretical constructs suggest possibilities for future quantum computing and communication technologies, where information may be transferred with unprecedented efficiency and security.

Future Directions: As the paper implies, expanding the experimental tests of ER=EPR could lead to groundbreaking insights into the nature of spacetime. Further work could explore larger teleportation systems, improve the decoding complexity, and investigate variations in initial conditions to observe their effects on teleported states.

In conclusion, Susskind and Zhao's paper provides a compelling narrative for the merging of quantum teleportation with gravitational geometry. By cementing the conceptual equivalence of entangled states to traversable wormholes, it opens new vistas in the paper of quantum mechanics and spacetime, urging a deeper investigation into the intertwined fabric of the universe.