Distillability and Positivity of Partial Transposes in General Quantum Field Systems

Verch, Rainer; Werner, R. F.

doi:10.1142/s0129055x05002364

Cited by 63 publications

(96 citation statements)

References 71 publications

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“…Later work in algebraic field theory showed that the vacuum state of the field is entangled provided that the theory satisfies certain assumptions [26][27][28][29][30][31][32][33]. This has prompted an interpretation by Reznik and his collaborators [29][30][31][32][33] in which effects similar to those of interest here (but for a scalar field) were assumed to be due to a transfer of pre-existing entanglement from the quantum vacuum to the atoms, with no requirement for any transfer of information outside of the light cone.…”

Section: Interpretation Of Resultsmentioning

confidence: 99%

“…An alternative interpretation has been suggested based on algebraic quantum field theory, where the quantum vacuum is considered to be an entangled state [21][22][23][24][25][26][27][28][29][30][31][32][33]. In that case, the effects of interest here could be interpreted instead as being due to the transfer of entanglement from the quantum vacuum to the atoms without the need for an exchange of particles or information outside of the forward light cone.…”

Section: Discussionmentioning

confidence: 99%

“…interpreted as being due to the propagation of virtual photons outside of the light cone. In a separate series of papers, Summers and Werner [21][22][23][24][25] used the more abstract techniques of algebraic quantum field theory [21][22][23][24][25][26][27][28] to show that Bell's inequality can be violated in the vacuum state of any quantum field theory that satisfies certain assumptions. In a similar manner, Reznik and his collaborators [29][30][31][32][33] have discussed the generation of entanglement outside of the light cone by scalar or Dirac fields, which they interpreted as being due to the transfer of pre-existing entanglement in the quantum vacuum to the atomic states.…”

Section: Introductionmentioning

confidence: 99%

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Generation of entanglement outside of the light cone

Franson

2008

Journal of Modern Optics

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The Feynman propagator has nonzero values outside of the forward light cone. That does not allow messages to be transmitted faster than the speed of light, but it is shown here that it does allow entanglement and mutual information to be generated at space-like separated points. These effects can be interpreted as being due to the propagation of virtual photons outside of the light cone or as a transfer of pre-existing entanglement from the quantum vacuum. The differences between these two interpretations are discussed.

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Section: Interpretation Of Resultsmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Generation of entanglement outside of the light cone

Franson

2008

Journal of Modern Optics

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“…This fact is borne out operationally by the ability to swap this entanglement to local quantum systems ('detectors') through local interactions [4]. Local hidden-variable models cannot account for the long-distance correlations due to this entanglement [4,5], which decrease at a rate slower than − L cT exp [ ( ) ] 3 , where L is the separation and T the duration of the detector-field coupling. Other types of vacuum correlations, such as true multi-region entanglement [6] and full nonlocality [7,8], are also possible.…”

Section: Introductionmentioning

confidence: 99%

Acceleration-assisted entanglement harvesting and rangefinding

2015

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We study entanglement harvested from a quantum field through local interaction with Unruh-DeWitt detectors undergoing linear acceleration. The interactions allow entanglement to be swapped locally from the field to the detectors. We find an enhancement in the entanglement harvesting by two detectors with anti-parallel acceleration over those with inertial motion. This enhancement is characterized by the presence of entanglement between two detectors that would otherwise maintain a separable state in the absence of relativistic motion (with the same distance of closest approach in both cases). We also find that entanglement harvesting is degraded for two detectors undergoing parallel acceleration in the same way as for two static, comoving detectors in a de Sitter universe. This degradation is known to be different from that of two inertial detectors in a thermal bath. We comment on the physical origin of the harvested entanglement and present three methods for determining distance between two detectors using properties of the harvested entanglement. Information about the separation is stored nonlocally in the joint state of the accelerated detectors after the interaction; a single detector alone contains none. We also find an example of entanglement sudden death exhibited in parameter space.

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“…It was shown that a local hidden-variable model cannot account for these correlations [1,2], and that as a function of the separation between the regions, L, and the duration of the coupling, T , the entanglement decreases at a slower rate than e −(L/cT ) 3 . It is, therefore, natural to ask whether the vacuum admits other types of these kinds of correlations, i.e.…”

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Many-region vacuum entanglement: Distilling aWstate

Silman

Reznik

2005

Phys. Rev. A

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We investigate the correlations between any number of arbitrarily far-apart regions of the vacuum of the free Klein-Gordon field by means of its finite duration coupling to an equal number of localized detectors. We show that the correlations between any N such regions enable us to distill an N -partite W state, and therefore exhibit true N -fold entanglement. Furthermore, we show that for N = 3, the correlations cannot be reproduced by a hybrid local-nonlocal hidden-variable model. For N ≥ 4 the issue remains open.In a recent paper [1], the nature of the correlations between two arbitrarily far-apart regions of the ground state of the free Klein-Gordon field was investigated by means of its finite duration coupling to a pair of localized detectors. It was shown that a local hidden-variable model cannot account for these correlations [1,2], and that as a function of the separation between the regions, L, and the duration of the coupling, T , the entanglement decreases at a slower rate than e −(L/cT ) 3 . It is, therefore, natural to ask whether the vacuum admits other types of these kinds of correlations, i.e. true many-region entanglement [3], and full nonlocality [4]. In this paper we will answer the first question affirmatively for any number of arbitrarily far-apart regions of the vacuum, N , while to the second question we will only be able to provide a positive answer for the case N = 3. We will follow the method developed in previous papers [1,5], and begin by investigating in detail the three-region case. We will then use results thus obtained to study the correlations between any number of regions.Our method consists of the finite duration coupling of the field we wish to investigate to any number of localized nonentangled detectors, such that all the detectors remain causally disconnected from one another throughout the interaction. Once the interaction is over, we trace over the field degrees of freedom to obtain the detectors' reduced density matrix. The crux of the method lies in the fact that since the detectors are initially nonentangled, any nonlocal correlations exhibited by the detectors' final reduced density matrix must have their origin in corresponding vacuum correlations. This enables us to apply recently developed tools from the field of quantum information theory to study the structure of the vacuum.Before we begin, let us first give the definitions of true multi-fold entanglement and full nonlocality. A multipartite mixed state is said to be truly multi-fold entangled iff it cannot be expressed as a convex sum of decomposable terms. In the tri-partite case this just means that the state cannot be written as a convex sum of terms of the form ρ i ⊗ ρ jk , where the subscripts denote any of the three subsystems. Examples of truly tri-fold entangled states are the GHZ [6] and W [7] states. Analogously, we can also distinguish between different types of nonlocality. A multi-partite state is fully nonlocal if there does not exist a decomposable hidden-variable dependent probability function t...

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Distillability and Positivity of Partial Transposes in General Quantum Field Systems

Cited by 63 publications

References 71 publications

Generation of entanglement outside of the light cone

Generation of entanglement outside of the light cone

Acceleration-assisted entanglement harvesting and rangefinding

Many-region vacuum entanglement: Distilling aWstate

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