[Paper Review] Quantum Teleportation with an Accelerated Observer and Black Hole Information

K. Shiokawa|ArXiv.org|Oct 9, 2009

Quantum Information and Cryptography4 references3 citations

TL;DR

This paper investigates quantum teleportation between a static and an accelerated observer in a relativistic setting, using oscillator variables coupled to a scalar quantum field vacuum. It shows that acceleration suppresses teleportation fidelity due to Unruh effects and environmental decoherence, with information loss arising from both intrinsic measurement processes and field interactions—key insights for the black hole information paradox.

ABSTRACT

Nonperturbative analysis of quantum entanglement and quantum teleportation protocol using oscillator variables carried by observers in relativistic motion under the continuous influence of the environment is given. The full time evolution of quantum entanglement among static and accelerated observers is studied. The environment plays a dual role. While it creates bipartite and tripartite entanglement among observers even when the initial state is separable, it suppresses the entanglement via decoherence. Motivated by the black hole information problem, we consider quantum teleportation between static and accelerated observers. Acceleration of the observer suppresses fidelity of teleportation. Some of the quantum information escapes outside of the horizon in the form of bipartite and tripartite entanglement during the teleportation process. Explicit calculation of information loss is provided. In addition to the loss due to the interaction with the environment, there is an intrinsic loss originated in a measurement process. We discuss the implications of our results on the black hole case.

Motivation & Objective

• To study the dynamical evolution of quantum entanglement and teleportation fidelity in relativistic motion, particularly between static and accelerated observers.
• To analyze the role of the environment (scalar vacuum field) in inducing both entanglement and decoherence in accelerated systems.
• To investigate how acceleration and interaction with the vacuum affect information loss during quantum teleportation, modeling black hole horizon physics.
• To provide a nonperturbative analysis of entanglement and fidelity, avoiding approximations that compromise positivity of the density matrix.
• To explore implications for the black hole information paradox, distinguishing intrinsic loss from environmental-induced loss.

Proposed method

• Formalism is generalized to describe entanglement among multiple observers using harmonic oscillator variables coupled to a scalar quantum field.
• The Minkowski vacuum is treated as a background environment; the reduced density matrix of observers is obtained by tracing out field modes.
• Nonperturbative exact solutions are derived for the time evolution of entanglement and fidelity, avoiding Born or Born-Markov approximations.
• Fidelity is computed for teleportation protocols with initial and final maximally entangled states, including cases with finite and infinite squeezing parameters.
• Asymptotic fidelity is evaluated in the long-time limit to assess information recovery, considering both vacuum interaction and postselection.
• The analysis distinguishes two sources of nonunitarity: intrinsic loss from measurement boundary conditions and induced loss from field interactions.

Experimental results

Research questions

• RQ1 How does constant acceleration affect the fidelity of quantum teleportation between static and accelerated observers?
• RQ2 To what extent does the interaction with the vacuum field induce tripartite entanglement and decoherence in the teleportation process?
• RQ3 What is the role of the Unruh effect in suppressing teleportation fidelity and causing information loss?
• RQ4 How do intrinsic measurement-induced losses and environment-induced decoherence compare in their contributions to information loss?
• RQ5 Can quantum error correction or postselection restore information in scenarios resembling black hole evaporation?

Key findings

• Fidelity in quantum teleportation decays due to acceleration, with maximum fidelity only achieved at initial time and approaching unity only in the limit of infinite squeezing parameters.
• In the absence of environmental interaction, fidelity reaches unity for maximally entangled final states with infinite squeezing, but decays under realistic conditions.
• With vacuum interaction, the asymptotic fidelity drops to approximately 0.7 if only Bob’s state is affected, and to 0.3 when all three parties interact with the vacuum, indicating failure of teleportation.
• The fidelity exhibits damped oscillations due to decoherence, showing a strong correlation between entanglement dynamics and teleportation fidelity.
• Information loss arises from two sources: intrinsic loss due to measurement boundary conditions and induced loss from interaction with the quantum vacuum field.
• The results suggest that black hole information may be recoverable only if vacuum-induced decoherence is negligible and proper postselection or error correction is applied.