Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1207.4275 · Physical Review A

Localized detection of quantum entanglement through the event horizon

Andrzej Dragan, Jason Doukas, Eduardo Martín-Martínez

Published May 28, 2013• 41 citations
arXivHTMLPDF

Abstract

We present a localized solution to the problem of entanglement degradation in noninertial frames. A two-mode squeezed state is considered from the viewpoint of two observers, Alice (inertial) and Rob (accelerated), each observing a single localized mode of the field. We study the state of these modes to determine how much entanglement the observers can extract from the initial state. The dominant source of degradation is an inevitable mode mismatch between the mode of the squeezed state Rob is given and the mode he is able to observe from his accelerated frame. Leakage of the initial mode through Rob's horizon places a limit on his ability to fully measure the state, leading to an inevitable degradation of entanglement that even in principle cannot be fully retrieved by any measurement device.

DOI
10.1103/physreva.87.052326

Related papers

Entanglement and discord: Accelerated observations of local and global modes

Jason Doukas, Eric G. Brown, Andrzej Dragan +1 more

We investigate the amount of entanglement and quantum discord extractable from a two-mode squeezed state as considered from the viewpoint of two observers, Alice (inertial) and Rob (accelerated). We find that using localized modes produces qualitatively different correlation properties for large accelerations than do Unruh modes. Specifically, the entanglement undergoes a sudden death as a function of acceleration, and the discord asymptotes to zero in the limit of infinite acceleration. We conclude that the previous Unruh mode analyses do not determine the acceleration-dependent entanglement and discord degradation of a given quantum state.

arXiv:1209.3461•Physical Review A•Jan 10, 2013•63 citations

Unveiling quantum entanglement degradation near a Schwarzschild black hole

Eduardo Martín-Martínez, Luis J. Garay, Juan León

We analyze the entanglement degradation provoked by the Hawking effect in a bipartite system Alice-Rob when Rob is in the proximities of a Schwarzschild black hole while Alice is free falling into it. We will obtain the limit in which the tools imported from the Unruh entanglement degradation phenomenon can be used properly, keeping control on the approximation. As a result, we will be able to determine the degree of entanglement as a function of the distance of Rob to the event horizon, the mass of the black hole, and the frequency of Rob's entangled modes. By means of this analysis we will show that all the interesting phenomena occur in the vicinity of the event horizon and that the presence of event horizons do not effectively degrade the entanglement when Rob is far off the black hole. The universality of the phenomenon is presented: There are not fundamental differences for different masses when working in the natural unit system adapted to each black hole. We also discuss some aspects of the localization of Alice and Rob states. All this study is done without using the single mode approximation.

arXiv:1006.1394•Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields•Sep 3, 2010•184 citations

Entanglement degradation in causal diamonds

Horacio E. Camblong, A. Chakraborty, P. Lopez-Duque +1 more

Entanglement degradation appears to be a generic prediction in relativistic quantum information whenever horizons restrict access to a region of spacetime. This property has been previously explored in connection with the Unruh effect, where a bipartite entangled system composed of an inertial observer (Alice) and a uniformly accelerated observer (Rob) was studied, with entanglement degradation caused by the relative acceleration---and with equivalent results for the case when Alice is freely falling into a black hole and Rob experiences a constant proper acceleration as a stationary near-horizon observer. In this work, we show that a similar degradation also occurs in the case of an entangled system composed of an inertial observer (Alice) and a ``diamond observer'' (Dave) with a finite lifetime. The condition of a finite lifetime is equivalent to the restriction of Dave's access within a causal diamond. Specifically, if the system starts in a maximally entangled state, prepared from Alice's perspective, entanglement degradation is enforced by the presence of the diamond's causal horizons.

arXiv:2402.10417•Physical review. D/Physical review. D.•May 2, 2024•15 citations

Continuous-variable entanglement sharing in noninertial frames

Gerardo Adesso, Ivette Fuentes, Marie Ericsson

We study the distribution of entanglement between modes of a free scalar field from the perspective of observers in uniform acceleration. We consider a two-mode squeezed state of the field from an inertial perspective, and analytically study the degradation of entanglement due to the Unruh effect, in the cases of either one or both observers undergoing uniform acceleration. We find that, for two observers undergoing finite acceleration, the entanglement vanishes between the lowest-frequency modes. The loss of entanglement is precisely explained as a redistribution of the inertial entanglement into multipartite quantum correlations among accessible and inaccessible modes from a noninertial perspective. We show that classical correlations are also lost from the perspective of two accelerated observers but conserved if one of the observers remains inertial.

arXiv:quant-ph/0701074•Physical Review A•Dec 27, 2007•159 citations

Correlation loss and multipartite entanglement across a black hole horizon (

Gerardo Adesso, Ivette Fuentes

We investigate the Hawking effect on entangled fields. By considering a scalar field which is in a two-mode squeezed state from the point of view of freely falling (Kruskal) observers crossing the horizon of a Schwarzschild black hole, we study the degradation of quantum and classical correlations in the state from the perspective of physical (Schwarzschild) observers confined outside the horizon. Due to monogamy constraints on the entanglement distribution, we show that the lost bipartite entanglement is recovered as multipartite entanglement among modes inside and outside the horizon. In the limit of a small-mass black hole, no bipartite entanglement is detected outside the horizon, while the genuine multipartite entanglement interlinking the inner and outer regions grows infinitely.

arXiv:quant-ph/0702001•Quantum Information and Computation•Jul 1, 2009•22 citations

Speeding up entanglement degradation

Robert B. Mann, Vı́ctor M. Villalba

We present a method for tracking time-dependent entanglement between different modes of a quantum system as measured by observers in different states of relative (nonuniform) motion. By describing states on a given spacelike hypersurface, observers or detectors in different states of motion can detect different modes of excitation in a quantum field at any desired instant and thereby track various measures of entanglement as function of time. We illustrate our method for a scalar field, showing how entanglement degrades as a function of time if one observer begins in a state of inertial motion but ends in a state of uniform acceleration while the other remains inertial.

arXiv:0902.1580•Physical Review A•Aug 4, 2009•38 citations
We present a localized solution to the problem of entanglement degradation in noninertial frames. A two-mode squeezed state is considered from the viewpoint of two observers, Alice (inertial) and Rob (accelerated), each observing a single localized mode of the field. We study the state of these modes to determine how much entanglement the observers can extract from the initial state. The dominant source of degradation is an inevitable mode mismatch between the mode of the squeezed state Rob is given and the mode he is able to observe from his accelerated frame. Leakage of the initial mode through Rob's horizon places a limit on his ability to fully measure the state, leading to an inevitable degradation of entanglement that even in principle cannot be fully retrieved by any measurement device.
We investigate the amount of entanglement and quantum discord extractable from a two-mode squeezed state as considered from the viewpoint of two observers, Alice (inertial) and Rob (accelerated). We find that using localized modes produces qualitatively different correlation properties for large accelerations than do Unruh modes. Specifically, the entanglement undergoes a sudden death as a function of acceleration, and the discord asymptotes to zero in the limit of infinite acceleration. We conclude that the previous Unruh mode analyses do not determine the acceleration-dependent entanglement and discord degradation of a given quantum state.
We analyze the entanglement degradation provoked by the Hawking effect in a bipartite system Alice-Rob when Rob is in the proximities of a Schwarzschild black hole while Alice is free falling into it. We will obtain the limit in which the tools imported from the Unruh entanglement degradation phenomenon can be used properly, keeping control on the approximation. As a result, we will be able to determine the degree of entanglement as a function of the distance of Rob to the event horizon, the mass of the black hole, and the frequency of Rob's entangled modes. By means of this analysis we will show that all the interesting phenomena occur in the vicinity of the event horizon and that the presence of event horizons do not effectively degrade the entanglement when Rob is far off the black hole. The universality of the phenomenon is presented: There are not fundamental differences for different masses when working in the natural unit system adapted to each black hole. We also discuss some aspects of the localization of Alice and Rob states. All this study is done without using the single mode approximation.
Entanglement degradation appears to be a generic prediction in relativistic quantum information whenever horizons restrict access to a region of spacetime. This property has been previously explored in connection with the Unruh effect, where a bipartite entangled system composed of an inertial observer (Alice) and a uniformly accelerated observer (Rob) was studied, with entanglement degradation caused by the relative acceleration---and with equivalent results for the case when Alice is freely falling into a black hole and Rob experiences a constant proper acceleration as a stationary near-horizon observer. In this work, we show that a similar degradation also occurs in the case of an entangled system composed of an inertial observer (Alice) and a ``diamond observer'' (Dave) with a finite lifetime. The condition of a finite lifetime is equivalent to the restriction of Dave's access within a causal diamond. Specifically, if the system starts in a maximally entangled state, prepared from Alice's perspective, entanglement degradation is enforced by the presence of the diamond's causal horizons.
We study the distribution of entanglement between modes of a free scalar field from the perspective of observers in uniform acceleration. We consider a two-mode squeezed state of the field from an inertial perspective, and analytically study the degradation of entanglement due to the Unruh effect, in the cases of either one or both observers undergoing uniform acceleration. We find that, for two observers undergoing finite acceleration, the entanglement vanishes between the lowest-frequency modes. The loss of entanglement is precisely explained as a redistribution of the inertial entanglement into multipartite quantum correlations among accessible and inaccessible modes from a noninertial perspective. We show that classical correlations are also lost from the perspective of two accelerated observers but conserved if one of the observers remains inertial.
We investigate the Hawking effect on entangled fields. By considering a scalar field which is in a two-mode squeezed state from the point of view of freely falling (Kruskal) observers crossing the horizon of a Schwarzschild black hole, we study the degradation of quantum and classical correlations in the state from the perspective of physical (Schwarzschild) observers confined outside the horizon. Due to monogamy constraints on the entanglement distribution, we show that the lost bipartite entanglement is recovered as multipartite entanglement among modes inside and outside the horizon. In the limit of a small-mass black hole, no bipartite entanglement is detected outside the horizon, while the genuine multipartite entanglement interlinking the inner and outer regions grows infinitely.
We present a method for tracking time-dependent entanglement between different modes of a quantum system as measured by observers in different states of relative (nonuniform) motion. By describing states on a given spacelike hypersurface, observers or detectors in different states of motion can detect different modes of excitation in a quantum field at any desired instant and thereby track various measures of entanglement as function of time. We illustrate our method for a scalar field, showing how entanglement degrades as a function of time if one observer begins in a state of inertial motion but ends in a state of uniform acceleration while the other remains inertial.