Pith. sign in

REVIEW 1 major objections 4 minor 3 cited by

Entanglement of Dirac fields in non-inertial frames

T0 review · 1 major / 4 minor · reviewed 2026-08-28 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read Entanglement between two modes of a free Dirac field is degraded but not destroyed by the Unruh effect: in the infinite-acceleration limit the concurrence tends to $1/\sqrt{2}$, so the state always remains entangled.

desk verdict A clean, explicit calculation of Unruh-induced entanglement degradation for Dirac fields, with the striking nonvanishing limit in the infinite-acceleration case resting on the single-mode approximation the authors candidly acknowledge. read the letter →

arxiv quant-ph/0603269 v2 pith:DPQJZOCU submitted 2006-03-29 quant-ph gr-qchep-th

P.M. Alsing , I. Fuentes-Schuller , R.B. Mann , T.E. Tessier This is my paper · ORCID
classification quant-phgr-qchep-th PACS 03.67.Mn03.65.Vf03.65.Yz
keywords DiracfieldUnruheffectnon-inertialframesRindlermodesfermionicentanglementconcurrencesharingsingle-modeapproximation
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper asks how much of the entanglement between two modes of a free Dirac field survives when one observer is uniformly accelerated. It claims that the Unruh effect degrades the entanglement monotonically but that, unlike the scalar bosonic case, the entanglement never vanishes: in the infinite-acceleration limit the concurrence tends to $1/\sqrt{2}$, and the state remains usable as a quantum resource between accelerated partners. The difference comes from the Pauli principle, which gives each fermionic mode only two occupation levels, turning the Bogoliubov transformation between Minkowski and Rindler modes into a finite trigonometric mixing rather than an infinite hyperbolic one. The paper also accounts for where the lost entanglement goes, showing that acceleration redistributes it among bipartite correlations without creating any three-body entanglement.

What carries the argument

The load-bearing object is the single-mode Bogoliubov transformation $a_k = \cos r\, c_k^I - e^{-i\varphi}\sin r\, d_{-k}^{II\dagger}$, with $\tan r = \exp(-\pi\Omega)$ and $\Omega = \omega c/a$. It expresses a Minkowski particle mode as a superposition of a Rindler particle in region I and a Rindler antiparticle in region II, and its fermionic, trigonometric, finite-dimensional form is what keeps every density matrix finite-dimensional. The same transformation produces the Fermi-Dirac thermal state seen by Rob and, after tracing out region II, the two-qubit state $\rho_{A,I}$ whose concurrence is $\cos r$.

What would settle it

Compute the same setup without the single-mode approximation: expand the Minkowski annihilation operator as an integral over Unruh modes, give Rob's detector a finite response width around $\omega_R$, trace over region II, and recalculate $C(\rho_{A,I})$ as a function of acceleration. If the concurrence tends to zero as $a \to \infty$ for any nonzero bandwidth, the $1/\sqrt{2}$ floor is an artifact of the narrow-band assumption; if it remains nonzero, the paper's conclusion survives the approximation.

Watch

Extended reading notes

Core claim

The paper claims that for a free Dirac field, the entanglement between a Minkowski mode held by an inertial observer, Alice, and a Rindler mode held by a uniformly accelerated observer, Rob, decreases under the Unruh effect but never vanishes. In the single-mode approximation the reduced state $\rho_{A,I}$ has concurrence $C(\rho_{A,I}) = \cos r$, with $\tan r = \exp(-\pi\omega c/a)$, and as $r \to \pi/4$ (infinite acceleration) the concurrence tends to $1/\sqrt{2}$; the logarithmic negativity tends to $\log_2(3/2)$. Tracing over the causally disconnected Rindler region II acts like a finite-strength environment: entanglement is redistributed into the bipartitions A-II and I-II, but the residual three-tangle is zero for all $r$, so no genuinely tripartite entanglement is created. The paper concludes that a fermionic encoding preserves a usable entanglement resource between relatively accelerated parties, in contrast to the bosonic scalar case where the entanglement vanishes at infinite acceleration.

Load-bearing premise

The result rests on the single-mode approximation: Rob's detector is assumed to respond to one Rindler particle mode whose frequency is effectively the same as Alice's mode, collapsing the Minkowski operator to a single Unruh mode; if the detector has finite bandwidth or the frequencies are mismatched, the reduced density matrix and the nonzero entanglement floor do not follow as derived.

Editorial extensions

If this is right

  • Alice and Rob can in principle run entanglement-based tasks, such as teleportation, with nonzero fidelity at any acceleration, since the concurrence never drops below $1/\sqrt{2}$ in the single-mode regime.
  • In the black-hole analogue, with Alice falling in while Rob hovers just outside the horizon, the pair still shares a nonzero amount of entanglement, so horizon-induced information loss is partial rather than total for fermionic fields.
  • Because the partial transpose of $\rho_{A,I}$ has a negative eigenvalue for all $r$, the state is always distillable in principle, with logarithmic negativity $N = \log_2(1+\cos^2 r)$ bounding the distillable entanglement.
  • The residual three-tangle is zero at every acceleration, so no genuinely tripartite entanglement is generated; the Unruh effect only redistributes bipartite entanglement among the A-I, A-II, and I-II partitions.
  • If both parties accelerate with different accelerations $a_1$ and $a_2$, the entanglement degrades further but remains finite, with logarithmic negativity tending to $\log_2(5/4)$ at infinite acceleration.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Relaxing the single-mode approximation to a finite-bandwidth detector is the natural stress test: if the concurrence floor survives a wave-packet treatment, the value $1/\sqrt{2}$ becomes a quantitative benchmark for fermionic relativistic quantum communication, and if it does not, the floor should be read as an idealized narrow-band limit.
  • The same trigonometric Bogoliubov structure could be simulated in table-top two-level systems, where a 'horizon' operation is implemented as a partial trace; such a simulation would let experimenters watch the predicted redistribution of bipartite entanglement without access to actual Unruh radiation.
  • Zero residual tangle with nonzero bipartite tangles places the tripartite state in the W class, which is known to be robust against tracing out one party; this classification is implicit in the paper's numbers and gives a simple reason why the A-I entanglement floor is protected.
  • If fermionic channels are used in future relativistic quantum networks, the accelerated-party protocol described here suggests that the acceleration noise cannot completely destroy the resource, whereas bosonic channels would require full entanglement distillation to recover anything.
Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Request a human review

A listed scientist reviews the paper for a fee and the review publishes here regardless of verdict. See the reviewers or get listed.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

1 major / 4 minor

Summary. The paper analyzes the entanglement between two modes of a free Dirac field shared between an inertial observer Alice and a uniformly accelerated observer Rob. Starting from a maximally entangled Minkowski-mode Bell state, the authors use the standard Bogoliubov transformation between Minkowski and Rindler operators in the single-mode approximation to express Rob's Minkowski vacuum and one-particle states in terms of Rindler modes in regions I and II. After tracing out the causally inaccessible region II, they obtain a two-qubit density matrix and compute the concurrence, entanglement of formation, logarithmic negativity, and mutual information for the Alice–Rob partition and for the other two bipartitions. They also analyze entanglement sharing and complementarity relations, concluding that the tripartite state has no genuinely three-body entanglement. The central result is that, unlike the bosonic scalar-field case studied earlier, the fermionic entanglement is degraded by the Unruh effect but never vanishes: the concurrence C(ρ_{A,I}) = cos r approaches 1/√2 in the infinite-acceleration limit, and the logarithmic negativity approaches log2(3/2). The paper interprets this as showing that the state remains entangled and usable for quantum information tasks, and draws an analogy with a black-hole horizon.

Significance. Within the single-mode approximation, the paper's calculations are explicit, self-contained, and checkable: the eigenvalue computations for the partial transpose and the spin-flip matrices are straightforward and appear correct, and the closed-form expressions for concurrence, entanglement of formation, and negativity are a genuine strength. The qualitative contrast with the bosonic case—non-vanishing versus vanishing entanglement in the infinite-acceleration limit—is a clean and influential result, and the entanglement-sharing and complementarity analysis provides a useful interpretation of where the initial entanglement is distributed. The manuscript has no free parameters beyond the acceleration-to-frequency ratio, and all derivations are analytic. However, the journal-level significance depends on the breadth of the central claim: if the single-mode approximation is not valid for Minkowski plane-wave modes, the unqualified statement that 'the state always remains entangled to a degree' is not established for the setup introduced in Eq. (2).

major comments (1)
  1. [Sec. III, Eq. (8) and footnote [20]; Sec. IV, Eq. (22)] The nonvanishing concurrence C(ρ_{A,I}) = cos r → 1/√2 is derived under the single-mode approximation, in which a Minkowski annihilation operator is replaced by a single Unruh-mode operator. Footnote [20] itself states that a Minkowski mode is an integral over Unruh/Rindler frequencies and that the approximation assumes an extremely narrow-band detector and sharply peaked phase factors. The paper does not show that this truncation remains valid in the infinite-acceleration limit, where tan r = exp(−πΩ) saturates for every finite Ω and the Bogoliubov support still spreads over the continuum. In the full multimode picture, tracing out region II distributes Alice's correlations over infinitely many Rindler modes, and the monogamy bound used in Sec. V does not by itself prevent the A–I concurrence from falling below 1/√2 or even vanishing. Because the abstract and Sec. VII present 'always remains entangled to a degree' as a property of two Minkowski modes of a Dirac field, the central claim is broader than the derivation. The authors should either provide a multimode analysis (for example, for a Minkowski wavepacket and a finite-bandwidth Rindler detector) or explicitly restrict the abstract, Sec. I, and Sec. VII to the idealized single Unruh-mode model.
minor comments (4)
  1. [Sec. IV, definition before Eq. (23)] The definition of mutual information reads I = S(ρ_a) + S(ρ_a) − S(ρ_ab); the second term should be S(ρ_b). The subsequent calculations use the correct expression.
  2. [Sec. V.B, eigenvalues of ρ^T_{I,II}] The formula for the negative eigenvalue is written as λ_− = −¼[1 − sqrt(1+sin²2r)], which is positive; it should be λ_− = ¼[1 − sqrt(1+sin²2r)]. The surrounding text's conclusion that this eigenvalue is nonpositive is correct, but the displayed formula has a sign error.
  3. [Sec. I and Sec. VII] It is stated that the entanglement of formation reaches a minimum of 1/√2 at infinite acceleration. The quantity that approaches 1/√2 is the concurrence; using the formula for E_F in Sec. IV with sin r = 1/√2 gives E_F ≈ 0.60, not 1/√2.
  4. [Sec. III, after Eq. (8)] The single-mode approximation is announced in a parenthetical remark and then deferred to footnote [20]. Given that the entire quantitative conclusion depends on this approximation, the main text should state clearly at this point that all subsequent results are conditional on it.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the fermionic concurrence result follows from an explicit Bogoliubov calculation rather than from a fitted or assumed input.

full rationale

The derivation chain is self-contained. The input is an inertial Bell state (Eq. (2)) plus the standard Bogoliubov transformation (Eq. (8)) for a single Rindler mode. The coefficients cos r and sin r are fixed by the requirement that ak annihilates the Minkowski vacuum (Eqs. (12)-(15)) and by fermionic anticommutation; they are not fitted to the entanglement result. The reduced density matrix rho_A,I (Eq. (22)) is obtained by tracing the tripartite state over the inaccessible region II, and the concurrence C(rho_A,I)=cos r -> 1/sqrt(2) is computed from Wootters' formula rather than imposed. The nonvanishing asymptotic entanglement is an algebraic consequence of the two-dimensional fermionic Fock structure and of the particular off-diagonal coherence in Eq. (15), not an assumption renamed as a result. The self-citations ([3], [4], [7]) and footnotes [19],[20] supply the scalar-field analogue, the explicit single-mode idealization, and interpretational complementarity relations; none of these is the load-bearing proof of Eq. (22) or of the concurrence value. In particular, footnote [20] discloses that a Minkowski mode is an integral over Unruh/Rindler frequencies and that the single-mode approximation is an assumed narrow-band detector response; this is an honest scope limitation (relevant to physical applicability at large acceleration), not a circular step. No fitted input is called a prediction, no uniqueness theorem is imported from the authors, and no result is renamed in new coordinates. Therefore no circular step is exhibited.

Assumptions & free parameters 0 free parameters · 5 assumptions · 0 invented entities

The central claim rests on standard QFT in curved spacetime (Bogoliubov transformations from prior literature), a single-mode approximation that the authors acknowledge, and standard entanglement measures. No free parameters are fitted to data; the acceleration parameter r is a physical variable. No new physical entities are introduced; the anti-Rob observer is the standard Rindler region II counterpart.

assumptions (5)
  • domain assumption Bogoliubov transformation Eq. (8): a_k = cos r c^I_k - e^{-iφ} sin r d^{II†}_{-k}, mixing a particle in region I with an anti-particle in region II.
    Standard result for Dirac fields in Rindler space, referenced to [17,18,19]; the paper quotes it without derivation and it is essential to the vacuum decomposition.
  • domain assumption Single-mode approximation (footnote [20]): Rob's detector is sensitive to a single Rindler particle mode with ω_R approximately equal to Alice's frequency ω_A.
    Used to write the Minkowski operator as a single Bogoliubov transformation; the authors explicitly flag this as an approximation, and the quantitative results depend on it.
  • domain assumption Spin is aligned with the direction of acceleration, so no Thomas precession (footnote [13]).
    Used to keep the spin degrees of freedom trivial in the mode decomposition; without this assumption the spin would be a separate degree of freedom.
  • domain assumption The initial state is the maximally entangled Bell state of two Minkowski particle modes, Eq. (2).
    Defines the scenario studied; the specific result (finite entanglement at infinite acceleration) is derived for this class of initial states.
  • standard math Peres-Horodecki partial transpose criterion and Wootters concurrence formula are valid for two-qubit entanglement.
    Standard tools in quantum information, used to compute entanglement in Sec. IV; they are not derived in the paper.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Entanglement of Dirac fields in non-inertial frames." pith.science (2026). https://pith.science/paper/DPQJZOCU

@misc{pith2026quant-ph0603269,
  author       = {Pith},
  title        = {Pith review of: Entanglement of Dirac fields in non-inertial frames},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/DPQJZOCU}},
  note         = {Machine review of arXiv:quant-ph/0603269}
}
read the original abstract

We analyze the entanglement between two modes of a free Dirac field as seen by two relatively accelerated parties. The entanglement is degraded by the Unruh effect and asymptotically reaches a non-vanishing minimum value in the infinite acceleration limit. This means that the state always remains entangled to a degree and can be used in quantum information tasks, such as teleportation, between parties in relative uniform acceleration. We analyze our results from the point of view afforded by the phenomenon of entanglement sharing and in terms of recent results in the area of multi-qubit complementarity.

Figures

Figures reproduced from arXiv: quant-ph/0603269 by the authors.

Figure 1
Figure 1. FIG. 1: Rindler spacetime diagram: Lines of constant po [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2: (Color online) Bipartite pure state entanglement. [PITH_FULL_IMAGE:figures/full_fig_p009_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3: (Color online) The logarithmic negativity as a func [PITH_FULL_IMAGE:figures/full_fig_p011_3.png] view at source ↗
Figures from the paper (5 more)
Figure 4
Figure 4. Figure 4: FIG. 4: (Color online) Entanglement of formation as a func [PITH_FULL_IMAGE:figures/full_fig_p011_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5: (Color online) Mutual information as a function of [PITH_FULL_IMAGE:figures/full_fig_p011_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6: (Color online) Bipartite tangles as a function of [PITH_FULL_IMAGE:figures/full_fig_p012_6.png]
Figure 7
Figure 7. Figure 7: FIG. 7: (Color online) Separable uncertainties as a functio [PITH_FULL_IMAGE:figures/full_fig_p012_7.png]
Figure 8
Figure 8. Figure 8: FIG. 8: (Color online) Single qubit properties as a function [PITH_FULL_IMAGE:figures/full_fig_p013_8.png]

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Surviving correlations across a horizon: reflected entropy for bosonic fields in non-inertial frames and black hole spacetimes

    hep-th 2026-08 conditional novelty 6.0 of 10

    Bosonic Alice-Bob reflected entropy saturates at nonzero floors (1.757 bits for Bell, 0.315 for GHZ) at infinite acceleration, while the inter-wedge reflected entropy diverges linearly in the squeezing parameter.

  2. Enhancement and Suppression of Decay Rates in an Accelerated Fermionic Cavity Coupled to a Massive Field

    gr-qc 2025-10 reject novelty 6.0 of 10

    For a uniformly accelerated fermionic cavity coupled to a light massive field, the predicted decay-rate ratio is Γ_acc/Γ_in = al/ln(1+al), a geometric enhancement of up to tens of percent; heavy fields instead give ex...

  3. State of a particle pair produced by the Schwinger effect is not necessarily a maximally entangled Bell state

    hep-th 2019-08 conditional novelty 6.0 of 10

    Schwinger pair spin correlations depend on the momentum direction: transverse momentum produces spin states that are not maximally entangled Bell states.

Reference graph

Works this paper leans on

31 extracted references · 30 canonical work pages · cited by 3 Pith papers

  1. [20]

    J´ aureguei, M

    R. J´ aureguei, M. Torres and S. Hacyan, Phys. Rev. D 43, 3979 (1991)

    work page 1991

  2. [1]

    Bouwmeester, A

    The Physics of Quantum Information , Springer-Verlag 2000, D. Bouwmeester, A. Ekert, A. Zeilinger (Eds.)

    work page 2000

  3. [2]

    Minkowski mode for Al- ice

    = (φ 2,φ 1). The calculation of the Bogoliubov coefficients is straightforward, though lengthy and an exercise in spe- cial functions. Details can be found elsewhere [17, 18, 19]. For our purposes, the end result of such calculations yields a relationship between the Minkowski and Rindler creation and annihilation operators given by the Bogoli- ubov transfo...

    work page

  4. [3]

    Teleportation with a uniformly accelerated partner

    P.M. Alsing and G.J. Milburn, Phys. Rev. Lett. 91, 180404 (2003) and quant-ph/0302179; P.M. Alsing, D. McMahon and G.J. Milburn, J. Opt. B: Quantum Semi- class Opt. 6, S834 (2004)

    work page Pith review arXiv 2003

  5. [4]

    Czachor, Phys. Rev. A 55, 72 (1997); D.R. Terno and A. Peres, Rev. Mod. Phys. 76, 93 (2004); A. Peres, P.F. Scudo and D.R. Terno, Phys. Rev. Lett. 88, 230402 (2002); Czachor, Phys. Rev. Lett. 94, 078901 (2005); P.M. Alsing and G.J. Milburn, Quant. Inf. Comp. 2, 487 (2002); R.M. Gingrich and C. Adami, Phys. Rev. Lett. 89, 270402 (2002); J. Pachos and E. So...

    work page Pith review arXiv 1997

  6. [5]

    J. Ball, I. Fuentes-Schuller and F.P. Schuller, quant-ph/0506113

    work page Pith review arXiv

  7. [6]

    Fuentes-Schuller and R.B

    I. Fuentes-Schuller and R.B. Mann, Phys.Rev.Lett. 95 (2005) 120404

    work page 2005

  8. [7]

    T. E. Tessier, Found. Phys. Lett. 18(2), 107 (2005)

    work page 2005

Show all 31 references
  1. [8]

    We also estimate the total correlations (classical plus quantum) via the mutual information [10]

    and the logarithmic negativity [9]. We also estimate the total correlations (classical plus quantum) via the mutual information [10]. Our results show that the en- tanglement of formation does not vanish as it does in the bosonic case, but rather reaches a minimum of 1 / √ 2 i...

  2. [9]

    Coffman, J

    V. Coffman, J. Kundu, and W. K. Wootters, Phys. Rev. A 61, 052306 (2000)

    2000

  3. [10]

    W. K. Wootters, Phys. Rev. Lett. 80 2245 (1998)

    1998

  4. [11]

    Vidal and R

    G. Vidal and R. F. Werner Phys. Rev.A (65):032314, 2002; Plenio quant-ph/0505071, 2005

    2002 arXiv

  5. [12]

    R. S. Ingarden, A. Kossakowski and M. Ohya, Informa- tion Dynamics and Open Systems - Classical and Quan- tum Approach, (Kluwer Academic Publishers, Dordrecht, 1997). M.B

    1997

  6. [13]

    Mandl and G

    F. Mandl and G. Shaw, Quantum Field Theory , Wiley, N.Y. (1984)

    1984

  7. [14]

    1 one needs to switch cosh ↔ sinh in Eq

    To cover the Minkowski regions III and IV in Fig. 1 one needs to switch cosh ↔ sinh in Eq. (3), which changes the Rindler metric in these regions to the form ds2 = dt2 − dz2 −d2x⊥ = exp(2aζ)(d2ζ −d2τ) −d2x⊥. This makes τ a spacelike coordinate and ζ a timelike coordinate in re...

  8. [15]

    Since this motion is rectilinear, the succesive boost s into Rob’s instantaneous co-moving frame all commute

    In this work, we are implicitly assuming that the spin of each mode is along the direction of acceleration, the z- axis. Since this motion is rectilinear, the succesive boost s into Rob’s instantaneous co-moving frame all commute. Hence, the spin does not suffer any Thomas prec...

  9. [16]

    Birrel and P.C.W

    N.D. Birrel and P.C.W. Davies, Quantum fields in curved space, Cambridge Univ. Press, N.Y. (1982)

    1982

  10. [17]

    Carroll, Spacetime and Geometry , Addison and Wesley, p402-412 (2004)

    S.M. Carroll, Spacetime and Geometry , Addison and Wesley, p402-412 (2004)

    2004

  11. [18]

    In an arbitrary metric gµν (x) the Dirac inner product is given by ( φ (x),ϕ (x) ) Σ = ∫ dΣ µ ¯φ (x)γ µ (x)ϕ (x) where where dΣ µ =nµdS is a spacelike hypersurface with nor- malnµ and hyperspatial volume element dS, and ¯φ (x) = φ †(x)γ 0 M is the adjoint of the Dirac spinor w...

  12. [19]

    Takagi, Prog

    S. Takagi, Prog. Theor. Phys. Suppl. 88, 1-142 (1986)

    1986

  13. [21]

    McMahon, P.M

    D. McMahon, P.M. Alsing, P. Embid, The Dirac equation in Rindler space: a pedagogical introduction , gr-qc/0601010; W. Greiner, B. M¨ uller and J. Rafelski, Quantum Electrodynamics of Strong Fields , Springer Ver- lag, N,Y., p563-571, (1985); M. Soffel, B. M¨ uller and W. Grein...

    1985 arXiv

  14. [22]

    The Unruh modes analytically extend the Rindler region I modes to region II, and the region II modes to region I as discussed in the next paragraph

    The Minkowski annihilation operator for frequency ω A is related to the Rindler region I and region II opera- tors of frequency ω R more directly through an interme- diate set of modes called Unruh modes [14, 15, 23]. The Unruh modes analytically extend the Rindler region I mo...

  15. [23]

    Walls and G.J

    D.F. Walls and G.J. Milburn, Quantum Optics, Springer- Verlag, N.Y., (1994)

    1994

  16. [24]

    However, these opera- tors correspond to the mode −k, which we have ignored in the single mode approximation

    Similar relations exist for the operators cII −k and dI k namely, cII −k|0−k⟩+ II = 0, dI k|0k⟩− I = 0, cII † −k |0k⟩+ II = |1−k⟩+ II , and dI† k |0k⟩− I = |1k⟩− I . However, these opera- tors correspond to the mode −k, which we have ignored in the single mode approximation

  17. [25]

    Davies, J

    P.C.W. Davies, J. of Phys. A8, 609 (1975); W.G. Unruh, Phys. Rev. D14, 870 (1976)

    1975

  18. [26]

    Alsing and P.W

    P.M. Alsing and P.W. Milonni, Am. J. Phys 72, 1524 (2004); quant-ph/0401170

    2004 arXiv

  19. [27]

    Peres , Phys

    A. Peres , Phys. Rev. Lett. 77, 1413, (1996)

    1996

  20. [28]

    For a review on entanglement Dagmar Bruss J. Math. Phys., (43): 4237, 2002

    2002

  21. [29]

    Since entanglement is invariant under local unitaries, we can always rotate |ψ ⟩R to |0k⟩+, the Minkowski vacuum for mode k given in Eq

    Let the intial unaccelerated state between Alice and Ro b be the tensor product of Minkowski states ρA ⊗ |ψ ⟩R⟨ψ | whereρA is any state (possibly mixed) for Alice and ψ is any pure state for Rob. Since entanglement is invariant under local unitaries, we can always rotate |ψ ⟩R...

  22. [30]

    X. Peng, X. Zhu, D. Suter, J. Du, M. Liu, and K. Gao, Phys. Rev. A 72, 052109/1 (2005)

    2005

  23. [31]

    Adesso, F

    G. Adesso, F. Illuminati, and S. De Siena, Phys. Rev. A 68, 062318-1 (2003)

    2003

Pith tools

Reviewed August 28, 2026 · model on record in the stance chip above.