Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Holographic Limitations and Corrections to Quantum Information Protocols

Stefano Pirandola

TL;DR

This work shows how the naive application of holographic corrections render perfect CV teleportation impossible, preclude uniform convergence in the teleportation simulation of lossy quantum channels, and impose a revised PLOB bound for quantum communication.

Abstract

We discuss the limitations imposed on entanglement distribution, quantum teleportation, and quantum communication by holographic bounds, such as the Bekenstein bound and Susskind's spherical entropy bound. For continuous-variable (CV) quantum information, we show how the naive application of holographic corrections disrupts well-established results. These corrections render perfect CV teleportation impossible, preclude uniform convergence in the teleportation simulation of lossy quantum channels, and impose a revised PLOB bound for quantum communication. While these mathematical corrections do not immediately impact practical quantum technologies, they are critical for a deeper theoretical understanding of quantum information theory.

Holographic Limitations and Corrections to Quantum Information Protocols

TL;DR

This work shows how the naive application of holographic corrections render perfect CV teleportation impossible, preclude uniform convergence in the teleportation simulation of lossy quantum channels, and impose a revised PLOB bound for quantum communication.

Abstract

We discuss the limitations imposed on entanglement distribution, quantum teleportation, and quantum communication by holographic bounds, such as the Bekenstein bound and Susskind's spherical entropy bound. For continuous-variable (CV) quantum information, we show how the naive application of holographic corrections disrupts well-established results. These corrections render perfect CV teleportation impossible, preclude uniform convergence in the teleportation simulation of lossy quantum channels, and impose a revised PLOB bound for quantum communication. While these mathematical corrections do not immediately impact practical quantum technologies, they are critical for a deeper theoretical understanding of quantum information theory.
Paper Structure (12 sections, 31 equations, 1 figure)

This paper contains 12 sections, 31 equations, 1 figure.

Table of Contents

  1. Introduction
  2. General scenario
  3. Holographic bounds
  4. Holographic limits from the Bekenstein bound
  5. Limitations from the spherical entropy bound
  6. Black-hole creation dynamics
  7. Holographic limitations to CV protocols
  8. Limits to Gaussian modulation and two-mode squeezing
  9. Holographic no-go for ideal CV teleportation
  10. No uniform convergence in teleportation simulation
  11. Holographic corrections to the quantum communication limit
  12. Conclusions

Figures (1)

  • Figure 1: Double-sphere scenario. An entanglement source is located at the origin $x=0$ of the position coordinate $x$, while Alice is at $-R-\varepsilon$ and Bob at $R+\varepsilon$, with $\varepsilon$ arbitrarily small. Alice's and Bob's local labs are within spheres of radius $R$. The middle source distributes $n$ Bell pairs to the remote parties, separated by $D=2R+2\varepsilon\simeq2R$. We call $D$ entanglement or teleportation distance.