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Entangling Moving Cavities in Noninertial Frames

T. G. Downes,1,* I. Fuentes,2,3 and T. C. Ralph1

1Centre for Quantum Computer Technology, Department of Physics, The University of Queensland, Brisbane 4072 Australia 2School of Mathematical Sciences, University of Nottingham, Nottingham NG7 2RD, United Kingdom

3Institute for Theoretical Physics, Technical University of Berlin, Hardenbergstr. 36, D-10623, Berlin, Germany (Received 14 May 2010; published 25 May 2011)

An open question in the field of relativistic quantum information is how parties in arbitrary motion may distribute and store quantum entanglement. We propose a scheme for storing quantum information in the field modes of cavities moving in flat space-time and analyze it in a quantum field theoretical framework. In contrast with previous work that found entanglement degradation between observers moving with uniform acceleration, we find the quantum information in such systems is protected. We further discuss a method for establishing the entanglement in the first place and show that in principle it is always possible to produce maximally entangled states between the cavities. ...

A key step is to find suitable ways to distribute and store quantum entanglement in relativistic scenarios. Entanglement is an essential resource for most quantum information protocols ...

Here we reconsider the idea of using moving cavities in space-time to store quantum information including the boundary conditions necessary to describe the field inside the cavities. When such boundary conditions are taken into account, it becomes clear that the cavity walls protect the entanglement once it has been created. Furthermore, we show that entangling an inertial and a noninertial cavity is nontrivial but that it can always be achieved in principle. Thus we demonstrate that there is no theoretical upper bound to the quality of the entanglement that can be shared between an inertial and uniformly accelerated observer.

it is always possible to create and store a maximally entangled state for any finite acceleration; however, the probability of success will decrease with increasing acceleration [13]. "

Of course with warp - wormhole technology there is no need to covariantly accelerate the Star Ship. Also remember how tiny the disentanglement from Unruh effect is.

"Entanglement is a key resource in quantum computational

tasks [1] such as teleportation[2], communication,

quantum control [3] and quantum simulations [4]. It is a

property of multipartite quantum states that arises from

the superposition principle and the tensor product structure

of Hilbert space. It can be quantified uniquely for

non-relativistic bipartite pure states by the von Neumann

entropy, and several measures such as entanglement cost,

distillable entanglement and logarithmic negativity have

been proposed for mixed states [5].

Understanding entanglement in a relativistic setting is

important both for providing a more complete framework

for theoretical considerations, and for practical situations

such as the implementation of quantum computational

tasks performed by observers in arbitrary relative motion.

For observers in uniform relative motion the total

amount of entanglement is the same in all inertial

frames [6], although different inertial observers may see

these correlations distributed differently amongst various

degrees of freedom."

How does this affect geodesic deviation curvature measurements?

"However for observers in relative

uniform acceleration a communication horizon appears,

limiting access to information about the whole of

spacetime, resulting in a degradation of entanglement as

demonstrated for scalars [7, 8] and fermions [9], and restricting

the fidelity of processes such as teleportation

[10], and other communication protocols [11].

The most general situation is that of observers in different

states of non-uniform motion. This situation is

relevant even for inertial observers in curved spacetime,

who will undergo relative non-uniform acceleration due

to the geodesic deviation equation, and therefore disagree

on the degree of entanglement in a given bipartite quantum

state. While it is expected such entanglement will

be time-dependent, there is presently no approach for determining

how the entanglement changes throughout the

course of the motion.

We address this issue by constructing a new method

for determining such time-dependent entanglement measures.

By considering the description of the field modes

on a given spacelike hypersurface we are able to compute

the Bogoliubov transformations between states of instantaneous

positive and negative frequency as determined

by observers in different states of non-uniform motion.

We illustrate our approach by considering specifically the

entanglement between two modes of a non-interacting

scalar field when one of the observers describing the state

begins in a state of inertial motion and ends in a state

of uniform acceleration. From the perspective of the inertial

observer (Alice) the state is a maximally entangled

pure state. However the non-uniformly accelerated

(NUA) observer (Vic) finds that the entanglement degrades

as a function of time, approaching at late times

the constant value measured by an observer (Rob) undergoing

the same asymptotic uniform acceleration. The

paper is structured as follows: In Sec II we solve the Klein

Gordon equation in the NUA coordinates and compute

the Bogoliubov coefficients. In Sec. III, we quantify the

degree of entanglement with the help of the logarithmic

negativity N and mutual information I. Finally, we summarize

our results in the conclusions. ...

A given mode seen by an inertial observer

corresponds for the Uniformly Accelerated observer to a two-mode

squeezed state, associated with the field observed in the

two distinct Rindler regions.

The UA observer can

neither access nor influence field modes in the causally

disconnected region and so information is lost about the

quantum state, resulting in detection of a thermal state,

a phenomenon known as the Unruh effect [13]. ...

Our method for tracking the time-dependence of measures

of quantum information via a sequence of measurements

on hypersurfaces where positive/negative frequencies

can be defined is quite general and can be applied to

different kinds of motions and fields beyond the example

we consider here. For a situation in which both observers

begin freely falling into a black hole with one observer

increasing acceleration to avoid this fate, the distillable

entanglement degrades to a finite value. The entanglement

degradation is due to the increase of entanglement

with the modes in the region causally undetectable by

the NUA observer. In curved spacetime, we expect in

general that entanglement is a time-dependent as well as

an observer-dependent concept."

Speeding up Entanglement Degradation

R.B. Mann† ‡ and V. M. Villalba†∗

† Department of Physics & Astronomy, University of Waterloo, Waterloo, Ontario Canada N2L 3G1 and

‡Perimeter Institute, 31 Caroline Street North Waterloo, Ontario Canada N2L 2Y5

"The ground state of a quantum field is an extremely structured state. This is true even if the field is non inter- acting. A first indication that this is the case is that the propagator between two spatially separated points never vanishes, no matter how far apart the points are. That is correlations in vacuum extend over an infinite range. More subtle is that these correlations are such that in vacuum two spatially separated regions are entangled. This was first exhibited in [1] by decomposing Minkowski space into two Rindler wedges, and quantizing the field in each wedge. It is also very closely related to phenomena like black hole evaporation or particle creation induced by cosmological expansion [2,3]. It was later shown that the ground state exhibits quantum non locality: it is in principle possible to violate Bell inequalities in the vacuum, both for free fields [4–6] and for interacting fields [7], and this property applies to almost any quantum state [8,9]. Recently B. Reznik considered a specific model in which two localized detectors are coupled to the vacuum in space like separated regions and showed that the detectors can get entangled [10]. In [11] it was shown that the correlations between the detectors could be used to violate a Bell inequality. These studies were later extended to the case of more than two localized detectors [12].

In the present work we pursue the study of how uniformly accelerated detectors in opposite Rindler wedges get entangled. Contrary to previous work [10] we shall study the case where the detectors are in equilibrium with the Unruh heat bath. Although both detectors have thermalized, we shall show that they get entangled for certain choices of parameters and for certain relative positions."

PHYSICAL REVIEW D 74, 085031 (2006)

Einstein-Podolsky-Rosen correlations between two uniformly accelerated oscillators

Serge Massar*

Laboratoire d’Information Quantique and Centre for Quantum Information and Communication, C.P. 165/59, Universite ? Libre de Bruxelles, Acade ?mie Wallonie-Bruxelles, Avenue F. D. Roosevelt 50, 1050 Bruxelles, Belgium

Philippe Spindel†

Me ?canique et Gravitation, Universite ? de Mons-Hainaut, Acade ?mie Wallonie-Bruxelles, Place du Parc 20, 7000 Mons, Belgium

(Received 21 June 2006; revised manuscript received 20 September 2006; published 31 October 2006)

Note that when Minkowski x is the SSS metric radial coordinate, then the light cone coordinates for Penrose-Newman null tetrads correspond to the Wheeler-Feynman phases in the advanced and retarded EM potentials.

On Dec 25, 2011, at 3:33 PM, JACK SARFATTI wrote:

"A remarkable phenomenon that appears naturally in

quantum field theory is that the ground state (vacuum) is

entangled and that observables in two separated regions

can be entangled. Recent studies in quantum information

theory have taught us that entanglement is a physical

property which can be exchanged between systems or

used in quantum processes such as quantum communication,

teleportation, and quantum cryptography [1]. This

suggests that vacuum entanglement as well could be detected

and used in quantum processes. There have been

several studies of vacuum entanglement in field theory

[2,3], as well as in other systems [4–6], but none have

proposed a way to observe vacuum entanglement in a

realistic experiment. The main purpose of this Letter is to

suggest a realistic physical implementation to observe this

phenomenon. ...

In the following, we propose and analyze the possibility

of observing vacuum entanglement with trapped ions

(Fig. 1). We consider a system of trapped ions that are

brought to equilibrium in a linear chain configuration. The

ground state (vacuum) of the system is an entangled state

of the different motional modes of the chain and manifests

entanglement between single ions or distant groups of ions.

In order to detect vacuum entanglement, we consider processes

wherein the external motional degrees of freedom

are mapped to the internal ions states, which are then used

for entanglement detection. The internal levels are well

isolated, they can be temporarily coupled ‘‘on demand’’ to

the phonon modes by sending finite duration laser pulses,

and finally can be measured with nearly perfect precision.

In analogy with the field-theoretical case, the interaction

must be limited to a duration shorter than the time it takes

for perturbations to propagate between the two (probe) ions

along the chain.We comment that in the case of ion chains,

this process is interesting on its own, because one can

entangle the internal levels of two ions without actually

doing gates [7]. The most spectacular manifestation of the

idea would involve a chain with many ions. However, a

proof of principle can be attained with just two trapped

ions and is feasible using current technology.

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PRL 94, 050504 (2005) PHYSICAL REVIEW LETTERS week ending

11 FEBRUARY 2005

Detecting Vacuum Entanglement in a Linear Ion Trap

A. Retzker,1 J. I. Cirac,2 and B. Reznik1

1School of Physics and Astronomy, Raymond and Beverly Sackler Faculty of Exact Sciences,

Tel-Aviv University, Tel-Aviv 69978, Israel

2Max-Planck-Institut fu¨r Quantenoptik, Hans-Kopfermann-Strasse 1, Garching, D-85748, Germany

(Received 8 August 2004; published 9 February 2005)

Category: MyBlog

Written by Jack Sarfatti

Published on Sunday, 25 December 2011 17:13

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