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arXiv:1210.2223 · Classical and Quantum Gravity

Observer-dependent entanglement

Paul M Alsing, Ivette Fuentes

Published Oct 18, 2012• 132 citations
arXivHTMLPDF

Abstract

Understanding the observer-dependent nature of quantum entanglement has been a central question in relativistic quantum information. In this paper, we will review key results on relativistic entanglement in flat and curved spacetime and discuss recent work which shows that motion and gravity have observable effects on entanglement between localized systems.

DOI
10.1088/0264-9381/29/22/224001

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Understanding the observer-dependent nature of quantum entanglement has been a central question in relativistic quantum information. In this paper, we will review key results on relativistic entanglement in flat and curved spacetime and discuss recent work which shows that motion and gravity have observable effects on entanglement between localized systems.
Recently, there has been increased interest in understanding entanglement and quantum communication in black hole spacetimes and in using quantum information techniques to address questions in gravity. Studies on relativistic entanglement show the emergence of conceptually important qualitative differences to a non-relativistic treatment. For instance, entanglement was found to be an observer-dependent property that changes from the perspective of accelerated observers moving in flat spacetime. Relativisitic quantum information theory uses well-known tools coming from quantum information and quantum optics to study quantum effects provoked by gravity to learn information about the spacetime. We can take advantage of our knowledge about quantum correlations and effects produced by the gravitational interaction to set the basis for experimental proposals ultimately aiming at finding corrections due to quantum gravity effects, too mild to be directly observed. This doctoral thesis dissertation summarises most of the research carried out during my PhD on this topic.
Abstract Quantum coherence is a basis-dependent resource whose operational meaning becomes particularly subtle when quantum fields are observed from non-inertial reference frames or propagate through curved spacetime. In relativistic settings, the distinction between particles, modes, and accessible subsystems depends on the observer, while gravitational or accelerated horizons can restrict portions of the field from direct measurement. These effects imply that coherence assigned to one set of field modes need not coincide with that reconstructed by another observer. The problem becomes more intricate under non-stationary relativistic conditions, where acceleration, spacetime geometry, or mode structure changes with time and no single global decomposition into positive- and negative-frequency components remains universally preferred. This study develops a conceptual framework for analysing observer-dependent quantum coherence in such environments. The discussion combines quantum field theory in curved spacetime, the Unruh and Hawking effects, relativistic quantum information, and the resource-theoretic description of quantum coherence. Curved-spacetime field theory establishes that the concept of a particle is not generally observer independent [1]. Algebraic and geometric formulations further demonstrate that physically meaningful observables can remain well defined even when global particle interpretations become ambiguous [2]. Resource theory provides a complementary language for distinguishing coherence intrinsic to a chosen state representation from changes caused by observer-dependent mode decomposition [7]. Particular attention is given to accelerated observers, horizons, Bogoliubov mode mixing, time-dependent acceleration, dynamically changing accessibility of field sectors, and the distinction between genuine decoherence and redistribution of coherence into inaccessible degrees of freedom. Non-stationary relativistic motion is treated as a dynamical source of basis change rather than merely a perturbation of a stationary accelerated frame.
Over the past few years, a new field of high research intensity has emerged that blends together concepts from gravitational physics and quantum computing. Known as relativistic quantum information, or RQI, the field aims to understand the relationship between special and general relativity and quantum information. Since the original discoveries of Hawking radiation and the Unruh effect, it has been known that incorporating the concepts of quantum theory into relativistic settings can produce new and surprising effects. However it is only in recent years that it has become appreciated that the basic concepts involved in quantum information science undergo significant revision in relativistic settings, and that new phenomena arise when quantum entanglement is combined with relativity. A number of examples illustrate that point. Quantum teleportation fidelity is affected between observers in uniform relative acceleration. Entanglement is an observer-dependent property that is degraded from the perspective of accelerated observers moving in flat spacetime. Entanglement can also be extracted from the vacuum of relativistic quantum field theories, and used to distinguish peculiar motion from cosmological expansion. The new quantum information-theoretic framework of quantum channels in terms of completely positive maps and operator algebras now provides powerful tools for studying matters of causality and information flow in quantum field theory in curved spacetimes. This focus issue provides a sample of the state of the art in research in RQI. Some of the articles in this issue review the subject while others provide interesting new results that will stimulate further research. What makes the subject all the more exciting is that it is beginning to enter the stage at which actual experiments can be contemplated, and some of the articles appearing in this issue discuss some of these exciting new developments. The subject of RQI pulls together concepts and ideas from special relativity, quantum optics, general relativity, quantum communication and quantum computation. The high level of current interest in these subjects is exemplified by the recent award of the 2012 Nobel Prize in Physics to Serge Haroche and David J Wineland for ground-breaking experimental methods that enable measuring and manipulation of individual quantum systems. It is our hope that this issue will encourage new researchers to enter this rapidly developing and exciting new field. R B Mann and T C Ralph Guest Editors
The purpose of this study is to calculate the entanglement measure for a bipartite system where the two subsystems interact via a central potential, and more importantly, to analyze the conceptual implication in the case of gravitational potential. Through numerical calculation, we confirm that the ground state of such quantum system is an entangled state. This raises a question whether a quantum ground state describing masses interacting through gravity can ever be a separable state. Entanglement seems to be an intrinsic characteristic for the ground state when mutual gravitational interaction is involved. Although the study is in the context of non-relativistic quantum mechanics, it provides hints for a quantum gravity theory in the limit of very weak field and low relative velocity. The entanglement of the ground state of two masses seems intrinsically connecting to the curvature of spacetime they create.
This is an idiosyncratic colloquium-style review of the idea that spacetime and gravity can emerge from entanglement. Drawing inspiration from the conjectured duality between quantum gravity in anti de Sitter space and certain conformal field theories, we argue that tensor networks can be used to define a discrete geometry that encodes entanglement geometrically. With the additional assumption that a continuum limit can be taken, the resulting geometry necessarily obeys Einstein's equations. The discussion takes the point of view that the emergence of spacetime and gravity is a mysterious phenomenon of quantum many-body physics that we would like to understand. We also briefly discuss possible experiments to detect emergent gravity in highly entangled quantum systems.