Bipartite Relativistic Quantum Information: An Effective Field Theory Approach to Entanglement Harvesting, Quantum Discord, and Nonlocality

Kernkonzepte

This paper explores how the principles of effective field theory (EFT) can be applied to understand relativistic quantum information (RQI), particularly focusing on entanglement harvesting, quantum discord, and nonlocality in a system of two Unruh-DeWitt (UDW) detectors interacting with a quantum field in the presence of a black hole.

Zusammenfassung

Bibliographic Information:

Feng-Li Lin and Sayid Mondal. Bipartite Relativistic Quantum Information from Effective Field Theory Approach with Implications to Contextual Meanings of Locality and Quantumness. arXiv preprint arXiv:2411.09409, 2024.

Research Objective:

This paper investigates the application of effective field theory (EFT) to study relativistic quantum information (RQI) phenomena, specifically focusing on entanglement harvesting, quantum discord, and nonlocality in a bipartite system of Unruh-DeWitt (UDW) detectors interacting with a quantum field in the presence of a black hole.

Methodology:

The authors employ an EFT approach where the high-energy degrees of freedom of a massless mediator field are integrated out, resulting in direct Coulombic interactions between the multipole moments of the UDW detectors and the black hole. This simplified framework allows for the calculation of the reduced final states of the UDW detectors, which are then used to analyze entanglement harvesting, quantum discord, and nonlocality.

Key Findings:

• The EFT approach successfully reproduces the patterns of entanglement harvesting observed in conventional RQI calculations based on master theory.
• Neglecting the direct interaction between UDW detectors, while retaining their interaction with the black hole, leads to no entanglement harvesting.
• The study reveals that the concepts of quantumness and locality may have different contextual meanings in quantum field theory (QFT) and RQI.
• While QFT and RQI agree on the presence of quantumness, they may differ in their assessment of locality.

Main Conclusions:

The EFT approach provides a valuable tool for studying RQI, offering a simplified framework for analyzing complex phenomena like entanglement harvesting and quantum correlations in relativistic settings. The findings highlight the nuanced and context-dependent nature of fundamental concepts like quantumness and locality when transitioning between QFT and RQI frameworks.

Significance:

This research contributes to the growing field of RQI by demonstrating the utility of EFT in analyzing complex quantum phenomena in relativistic settings. It sheds light on the subtle interplay between gravity, quantum fields, and quantum information, potentially impacting our understanding of black hole physics and quantum gravity.

Limitations and Future Research:

The study primarily focuses on static UDW detectors and a simplified EFT framework. Future research could explore dynamic detectors, higher-order EFT corrections, and the inclusion of quantum spin for the black hole to capture a more complete picture of RQI in curved spacetime.

Statistiken

The authors use a small energy gap of Ω = 0.001 for the UDW detectors.
The coupling constant g0 is set to 0.01 to ensure the validity of perturbative results.
The black hole and UDW detector sizes are fixed at ¯rB = ¯r1 = ¯r2 = 1.
The strengths of the multipole moments are set to q1 = q2 = 1.

Zitate

"The EFT is a low-energy approximation of the master field theory."
"The interactions in the PN EFT are spooky because they non-locally couple the internal quantum spins of UDW detectors, which may yield non-local resources such as quantum entanglement for the quantum information tasks."
"This indicates the EFT approach can be adopted as a framework for RQI."
"However, our understanding of important concepts such as quantumness and (non-)locality may have opposite meanings in different contexts, e.g., quantum field theory and quantum information."

Wichtige Erkenntnisse aus

Bipartite Relativistic Quantum Information from Effective Field Theory Approach with Implications to Contextual Meanings of Locality and Quantumness

by Feng-Li Lin,... um arxiv.org 11-15-2024

https://arxiv.org/pdf/2411.09409.pdf

Tiefere Fragen

How can the EFT framework be extended to incorporate the dynamics of UDW detectors and explore more complex RQI tasks beyond entanglement harvesting?

The provided text outlines an Effective Field Theory (EFT) approach to studying Relativistic Quantum Information (RQI) in the simplified scenario of static Unruh-DeWitt (UDW) detectors. To incorporate the dynamics of UDW detectors and delve into more intricate RQI tasks, several extensions to this framework can be considered:

Post-Newtonian (PN) Expansion: As briefly mentioned in the text, going beyond the leading-order Coulombic interaction of the 0PN EFT action (Eq. 2.2) is crucial for studying dynamic UDW detectors. By incorporating higher-order terms in the velocity expansion, we obtain a PN EFT that captures the effects of motion. The 1PN order, for instance, would introduce velocity-dependent potentials and allow for the study of entanglement harvesting and other RQI tasks in scenarios involving moving detectors.

Radiation Reaction: Incorporating radiation reaction into the EFT framework is essential for a complete description of dynamic systems. As UDW detectors move and interact, they emit radiation that backreacts on their dynamics. This backreaction can be systematically included in the EFT by considering half-integral PN orders. Including radiation reaction would enable the investigation of its impact on entanglement harvesting, decoherence, and other RQI protocols.

Time-Dependent Backgrounds: The text focuses on a static black hole background. Extending the EFT framework to time-dependent backgrounds, such as evaporating black holes or cosmological spacetimes, would open avenues for exploring RQI in more realistic and dynamic settings. This would involve incorporating the time dependence into the mode functions of the mediator field and the subsequent derivation of the effective action.

Beyond Entanglement Harvesting: While entanglement harvesting serves as a primary example, the EFT framework can be applied to a broader range of RQI tasks. These include:

Quantum Teleportation: Investigating the fidelity of quantum teleportation protocols in curved spacetime and the influence of the black hole's gravitational field.
Quantum Communication: Studying the capacity and fidelity of quantum communication channels in relativistic settings, considering the effects of spacetime curvature and horizons.
Quantum Metrology: Exploring the potential for enhanced precision in quantum metrology tasks by exploiting relativistic effects and the properties of quantum fields in curved spacetime.

By implementing these extensions, the EFT framework can provide a powerful tool for investigating the interplay between gravity, quantum information, and relativistic phenomena in a wide range of scenarios.

Could the observed discrepancy in the interpretation of locality between QFT and RQI point to a deeper underlying principle governing the interplay between gravity and quantum information?

The text hints at a potential discrepancy in the interpretation of locality when comparing Quantum Field Theory (QFT) and Relativistic Quantum Information (RQI). While the EFT approach seemingly employs a "classical" environment, it still predicts entanglement harvesting, a phenomenon typically associated with non-local quantum correlations. This observation could indeed point towards a deeper principle governing the relationship between gravity and quantum information.
Here's a breakdown of the potential implications:

Contextual Locality: The discrepancy might suggest that locality in QFT and RQI operates under different contextual frameworks. In QFT, locality is often defined through the commutation of field operators at spacelike separations. However, RQI introduces the concept of entanglement harvesting, where entanglement can be generated between spacelike separated detectors due to their interaction with a shared quantum field. This suggests that the presence of entanglement, and hence the manifestation of non-locality, might be observer-dependent or context-dependent in the presence of gravity.

Quantum Information as a Probe for Gravity: The observed discrepancy could imply that quantum information theory provides a unique lens through which to understand the non-local features of gravity. Entanglement, a fundamental concept in quantum information, might serve as a sensitive probe for exploring the subtle ways in which gravity departs from classical notions of locality.

Emergent Spacetime from Quantum Entanglement: Some theoretical frameworks propose that spacetime itself might be an emergent phenomenon arising from the entanglement structure of underlying quantum degrees of freedom. The observed discrepancy in locality could be a manifestation of this deeper connection, where the entanglement harvested by UDW detectors reflects the underlying entanglement structure of spacetime.
Further investigation into these discrepancies could lead to a more profound understanding of the interplay between gravity and quantum information. It might reveal novel principles governing the emergence of spacetime, the nature of quantum correlations in gravitational settings, and the limits of classical notions of locality.

If the "classical" environment in EFT can lead to entanglement harvesting, does this challenge the traditional understanding of classicality in the context of quantum information theory?

The text's observation that a seemingly "classical" environment in EFT can still result in entanglement harvesting does raise intriguing questions about the traditional understanding of classicality within quantum information theory.
Here's a nuanced perspective on this challenge:

Classicality in EFT: It's crucial to recognize that the term "classical" in the context of EFT carries a specific meaning. It refers to the fact that the EFT approach integrates out the high-energy degrees of freedom of the mediator field, effectively treating it as a classical background field. However, this classical background field still inherits crucial quantum properties from the underlying quantum field theory, particularly the thermal nature of the black hole's environment.

Entanglement Harvesting and Non-Classical Correlations: Entanglement harvesting fundamentally relies on the non-classical correlations present in the vacuum state of the quantum field. Even though the EFT treats the mediator field classically, it still captures these non-classical correlations through the spectral density of the blackbody and the resulting effective interactions between the UDW detectors.

Redefining Classicality: This observation suggests that the traditional dichotomy between classical and quantum environments might be too simplistic in the context of relativistic quantum information. The EFT approach highlights that even seemingly classical environments can exhibit non-classical features when gravity is involved. This calls for a more nuanced understanding of classicality, one that considers the potential for non-classical correlations to persist even in systems where certain degrees of freedom are treated classically.

LOCC vs. "Classical" EFT Environment: The text correctly points out that the "classical" environment in EFT differs significantly from Local Operations and Classical Communication (LOCC) in quantum information tasks. LOCC operations are fundamentally incapable of creating entanglement, while the "classical" EFT environment can lead to entanglement harvesting. This distinction arises because the EFT environment still encodes non-classical correlations inherited from the underlying quantum field theory, while LOCC operations are strictly limited to local quantum operations and classical communication.
In conclusion, the observation of entanglement harvesting in a "classical" EFT environment prompts a reevaluation of classicality in relativistic quantum information. It suggests that non-classical correlations can persist in seemingly classical settings when gravity is involved, highlighting the need for a more nuanced understanding of the classical-quantum boundary in these scenarios.