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arxiv: 1907.00442 · v1 · pith:JQIPT4XBnew · submitted 2019-06-30 · 🪐 quant-ph

Fisher information of accelerated two-qubit system in the presence of the color and white noise channels

F. Ebrahim , N. Metwally This is my paper

Pith reviewed 2026-05-25 12:09 UTC · model grok-4.3

classification 🪐 quant-ph
keywords fisher informationtwo-qubit systemcolor noisewhite noiseaccelerationconcurrenceentanglement
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The pith

The two-qubit form of Fisher information provides larger estimation accuracy for parameters of an accelerated two-qubit system under color and white noise than the single-qubit form.

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

The paper examines how white and color noise affect entanglement in an accelerated two-qubit system using different initial states. Entanglement survival is measured with concurrence, showing that color noise can increase entanglement even when initial purity is low, and higher white noise strength can also boost it. Initial parameters are estimated using Fisher information in both single-qubit and two-qubit versions, with the two-qubit version yielding better estimation precision.

Core claim

For an accelerated two-qubit system subject to color and white noise channels, the estimation of the system's initial parameters achieves a higher degree of accuracy when Fisher information is computed in the two-qubit form compared to the single-qubit form, while the noise channels modify the generated entanglement quantified by concurrence.

What carries the argument

Fisher information calculated separately in single-qubit and two-qubit forms to estimate initial parameters of the system.

If this is right

  • Color noise enhances the generated entanglement between the two particles even for small values of the initial purity.
  • Larger values of the white noise strength improve the generated entanglement.
  • The two-qubit form of Fisher information gives a larger estimation degree of the parameters than the single-qubit form.
  • Concurrence quantifies the survival amount of entanglement in the accelerated system under noise.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Two-qubit measurements may offer practical advantages for quantum parameter estimation in relativistic settings with environmental noise.
  • The differential impact of color versus white noise on entanglement suggests tailored noise management strategies for preserving quantum correlations during acceleration.
  • Extensions to multi-qubit systems could further improve estimation precision based on the observed scaling from one to two qubits.

Load-bearing premise

The chosen models for the color and white noise channels correctly describe the dynamics acting on the accelerated two-qubit system.

What would settle it

An experimental or numerical test showing that the Fisher information estimation accuracy is the same or lower in the two-qubit form compared to single-qubit for this system would falsify the central claim.

Figures

Figures reproduced from arXiv: 1907.00442 by F. Ebrahim, N. Metwally.

Figure 1
Figure 1. Figure 1: the concurrence Cw for the accelerated system in the presence of white noise, where the dot. solid, and dash lines for r = 0, 0.5 and 0.8, respectively and the system is initially prepared in (a) x = 0.2,(b)x = 0.4 and(c) x = √ 1 2 . where a1 = 5 + 6p − 11p 2 + 8q + 8p q + 3q 2 + 4p(1 + 31p − qx2 − 128p 2x 4 ), a2 = 16√ 2 p −p 2x 2 (−1 + x 2 (η1 + 4px2 cos2 r(3 + 5p + q − 8px2 + η2 cos 2r), a3 = η2(η1 + 4p… view at source ↗
Figure 2
Figure 2. Figure 2: the concurrence Cw for accelerated different initial state settings system in the presence of white noise, where the dot. solid, and dash lines for r = 0.0, 0.5 and 0.8, respectively, where (a) p = 0.4 and(b) p = 0.8. 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 q Cc q Cc q Cc [PITH_FULL_IMAGE:figures/full_f… view at source ↗
Figure 3
Figure 3. Figure 3: The same as Fig.(1), but in the presence of the color noise. [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: The same as Fig.(2), but in the presence of the color nosy, [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: The sane as Fig.(1) but in the presences of white-color nois [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: The same as Fig.(2), but in the presence of the white-color [PITH_FULL_IMAGE:figures/full_fig_p007_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: The effect of the acceleration same as Fig.(2), but in the pr [PITH_FULL_IMAGE:figures/full_fig_p008_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Estimating the Fisher information Fp for the accelerated system in the presence of white noise where the dot, solid, and dash lines for r = 0, 0.5 and 0.8, respectively and the system is initially prepared with x = 0.2 by using (a) Single -qubit and (b) Two-qubits. 0.0 0.2 0.4 <=> ?@A 1.0 0.0 0.2 0.4 BCD EFG 0.0 0.2 0.4 HIJ KLM 1.0 0 2 4 N O 10 12 14 x Fx x Fx [PITH_FULL_IMAGE:figures/full_fig_p011_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Estimating the Fisher information Fx for the accelerated system in the presence of white noise where the dot, solid, and dash lines for r = 0, 0.5 and 0.8, respectively and the system is initially prepared with p = 0.2 by using the form of a (a) single -qubit and (b) two-qubits. the acceleration are considered. The general behavior of Fp that displayed in Fig.(8a) and (8b) is similar. However, for Fp that … view at source ↗
Figure 10
Figure 10. Figure 10: Estimating the Fisher information Fr for the accelerated system in the presence of white noise where the dot, solid, and dash lines for x = 0.2, 0.4 and √ 1 2 , respectively and p = 0.2 ,by using the form of the (a) single -qubit and (b) the two￾qubits. 0.0 0.2 0.4 \]^ _`a 0 5 10 15 20 0.0 0.2 0.4 bcd efg 1.0 0 2 4 h i 10 0.0 0.2 0.4 jkl mno 0.0 0.5 1.0 1.5 2.0 2.5 p Fp p Fx p Fr [PITH_FULL_IMAGE:figures… view at source ↗
Figure 11
Figure 11. Figure 11: The same as Fig.(8), but for the color noise. [PITH_FULL_IMAGE:figures/full_fig_p012_11.png] view at source ↗
read the original abstract

In this manuscript, we investigate the effect of the white and color noise on a accelerated two-qubit system, where different initial state setting are considered. The behavior of the survival amount of entanglement is quantified for this accelerated system by means of the concurrence. We show that, the color noise enhances the generated entanglement between the two particles even for small values of the initial purity of the accelerated state. However, the larger values of the white noise strength improve the generated entanglement. The initial parameters that describe this system are estimated by using Fisher information, where two forms are considered, namely by using a single and two-qubit forms. It is shown that, by using the two-qubit form, the estimation degree of these parameters is larger than that displayed by using a single-qubit form.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 2 minor

Summary. The manuscript investigates the effects of color and white noise channels on an accelerated two-qubit system for various initial states. Entanglement survival is quantified via concurrence, with claims that color noise enhances generated entanglement even at small initial purity while larger white-noise strengths improve it. Initial parameters are estimated via Fisher information, with explicit comparison showing that the two-qubit form yields larger estimation values than the single-qubit reduction.

Significance. If the numerical comparisons hold, the work demonstrates a concrete advantage of retaining the full two-qubit density matrix for Fisher-information-based parameter estimation under combined acceleration and standard noise channels. This supplies a falsifiable, quantitative benchmark for relativistic quantum metrology and is grounded in conventional Kraus representations rather than ad-hoc models.

major comments (1)
  1. [Results on Fisher information] The central comparative claim (two-qubit Fisher information exceeds single-qubit) requires that both quantities be evaluated on the identical evolved state and the same set of parameters; the manuscript must state explicitly (in the section deriving the reduced single-qubit density matrix) how the reduction is performed and confirm that the parameter vector remains unchanged.
minor comments (2)
  1. [Abstract] The abstract uses the non-standard phrase 'estimation degree'; replace with a precise statement such as 'the value of the Fisher information' or 'the precision bound'.
  2. [Methods] Clarify whether the reported Fisher information is the quantum or classical version, and list the explicit parameters being estimated.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the constructive comment. We address the point raised below.

read point-by-point responses

  1. Referee: [Results on Fisher information] The central comparative claim (two-qubit Fisher information exceeds single-qubit) requires that both quantities be evaluated on the identical evolved state and the same set of parameters; the manuscript must state explicitly (in the section deriving the reduced single-qubit density matrix) how the reduction is performed and confirm that the parameter vector remains unchanged.

    Authors: We agree that an explicit statement is required to substantiate the comparison. In the revised manuscript we have added a paragraph in the section on the reduced single-qubit density matrix that (i) specifies the reduction is performed by taking the partial trace over one qubit of the evolved two-qubit state obtained after the combined acceleration and noise-channel evolution, and (ii) confirms that the identical parameter vector (acceleration parameter, noise strengths, and initial-state parameters) is used for both the two-qubit and single-qubit Fisher-information calculations. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivations rest on standard QI formulas

full rationale

The paper computes concurrence via the standard Wootters formula on the evolved two-qubit density matrix under Kraus channels for color and white noise, then evaluates classical/quantum Fisher information on the same state for parameter estimation. Both the single-qubit and two-qubit FI expressions are obtained by direct differentiation of the respective density-matrix elements; the comparison that two-qubit FI is larger is therefore a direct numerical consequence of the larger Hilbert-space dimension and is not obtained by fitting, renaming, or self-referential definition. No load-bearing step reduces to a prior self-citation or to an ansatz smuggled from the authors' earlier work. The derivation chain is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review yields no explicit free parameters, axioms, or invented entities; all modeling details are omitted.

pith-pipeline@v0.9.0 · 5663 in / 977 out tokens · 27124 ms · 2026-05-25T12:09:55.506461+00:00 · methodology

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Reference graph

Works this paper leans on

27 extracted references · 27 canonical work pages

  1. [1]

    Yu T., Eberly, J.H.: Finite-time disentanglement via spontaneous em ission. Phys. Rev. Lett. 93, 140404 (2004); Yu, T., Eberly, J.” Sudden Death of Entanglement : Classical Noise Effects”, Opt. Commun. 264, 393 (2006); Yu, T., Eb erly, ”Quan- tum Open System Theory: Bipartite Aspects”,J. Phys. Rev. Lett. 97, 140403 (2006)

    work page 2004

  2. [2]

    Yu and J

    T. Yu and J. H. Eberly,”Evolution from entanglement to decohere nce,” Quantum Inform. Comput. 7, pp. 459–468 (2007)

    work page 2007

  3. [3]

    Science 30, 598601 (2009)

    Yu, T., Eberly, J.H.: Sudden death of entanglement. Science 30, 598601 (2009)

    work page 2009

  4. [4]

    G. M. Palma, K. A. Suominen, and A. K. Ekert,” Quantum computer s and dissi- pation”, Proc. R. Soc. London A 452, 567 (1996)

    work page 1996

  5. [5]

    Prakash, N

    H. Prakash, N. Chandra, R. Prakash and Shivani, ”Effect of dec oherence on fidelity in teleportation using entangled coherent states”, J. Phys. B 40, 1613 (2007)

    work page 2007

  6. [6]

    Eleuch and I

    H. Eleuch and I. Rotter, Resonances in open quantum systems, Phys. Rev. A 95, 022117 (2017)

    work page 2017

  7. [7]

    Metwally,” Information Loss in Local dissipation environments” , Int

    N. Metwally,” Information Loss in Local dissipation environments” , Int. J. Theor. Phys. 49 1571 (2010)

    work page 2010

  8. [8]

    Metwally, ”Dynamics of encrypted information in superconduc ting qubits with the presence of imperfect operations”, J

    N. Metwally, ”Dynamics of encrypted information in superconduc ting qubits with the presence of imperfect operations”, J. Opt. Soc. Am. B, Vol. 2 9, No. 3 (2102)

    work page

  9. [9]

    P. M. Alsing, I. F. Schuller, R. B. Mann and T. E. Tessier, Phys. Re v. A 74 032326 (2006)

    work page 2006

  10. [10]

    Andre G. S. Landulfo, George E. A. Matsas, Phys. Rev. A 80, 032315, (2009); L. C. Celeri, A. G. S. Landulfo, R. M. Serra, G. E. A. Matsas, Phys. Rev. A 81, 062130 (2010)

    work page 2009

  11. [11]

    Metwally”Usefulness classes of travelling entangled channels in nonintertial frames” Int

    N. Metwally”Usefulness classes of travelling entangled channels in nonintertial frames” Int. J. Mod Phys. B, Vol. 27 No 28 1350155 (2013)

    work page 2013

  12. [12]

    Metwally” Teleportation of Accelerated Information” J

    N. Metwally” Teleportation of Accelerated Information” J. Opt . Soc. Am. B, Vol. 30, No. 1, 233-237 (2013)

    work page 2013

  13. [13]

    Metwally and A

    N. Metwally and A. Sagheer” Quantum coding in non-inertial fram es” Quantum Information processing, 13, 771-780 (2014)

    work page 2014

  14. [14]

    -Sagheer, H

    A. -Sagheer, H. Hamdoun and N. Metwally” Teleportation with mu ltiparties ac- celerated partners” , Comm. Theor. Phys. 63 287-194 (2015)

    work page 2015

  15. [15]

    Nielsen, I

    M. Nielsen, I. Chuang, Quantum Computation and Quantum Info rmation (Cam- bridge University Press, Cambridge, 2000) 14

    work page 2000

  16. [16]

    Ma, Y.-X

    J. Ma, Y.-X. Huang, X. Wang, C.P. Sun, Quantum Fisher informat ion of the GreenbergerHorneZeilinger state in decoherence channels. Phys . Rev. A 84, 022302 (2011)

    work page 2011

  17. [17]

    Giovannetti, S

    V. Giovannetti, S. Lloyd, L. Maccone, Quantum metrology. Phy s. Rev. Lett. 96, 010401 (2006)

    work page 2006

  18. [18]

    Zheng, Y

    Q. Zheng, Y. Uao, Y. Li, Optimal quantum channel estimation of two interacting qubit subject to decoherence. Eur. Phys. J. D 68, 170 (2014)

    work page 2014

  19. [19]

    Ozaydin, Quantum Fisher information of W States in Decohere n ce channels

    F. Ozaydin, Quantum Fisher information of W States in Decohere n ce channels. Phys. Lett. A 378, 3161 (2014)

    work page 2014

  20. [20]

    Metwally, Estimation of teleported and gained parameters in a non-inertial frame

    N. Metwally, Estimation of teleported and gained parameters in a non-inertial frame. Laser Phys. Lett. 14, 045202 (2017)

    work page 2017

  21. [21]

    D. E. Bruschi, J. Louko, E. Martn-Martnez, A. Dragan, and I . Fuentes,”Unruh effect in quantum information beyond the single-mode approximation ,” Phys. Rev. A 82 pp. 042332-042342 (2010)

    work page 2010

  22. [22]

    Cabello, A

    A. Cabello, A. Feito, and A.L.-Linares, ”Bell’s inequalities with realist ic noise for polarization-entangled photons” Phys. Rev. A 72, 052112

    work page

  23. [23]

    Dotsenko ,R

    S. Dotsenko ,R. Korobka ,” Entanglement Swapping in the Presen ce of White and Color Noise”, Communications in Theoretical Physics, 2018, 69(2): 143

    work page 2018

  24. [24]

    Aspachs, G

    M. Aspachs, G. Adesso, and I. Fuentes,”Optimal Quantum Est imation of the Unruh-Hawking Effect,” Phys. Rev. Lett. 105, pp. 151301–151303 (2010)

    work page 2010

  25. [25]

    Zhong, Wei and Sun, Zhe and Ma, Jian and Wang, Xiaoguang and N ori, Franc, ”Fisher information under decoherence in Bloch representation”, Phys. Rev. A 87 022337 (2013)

    work page 2013

  26. [26]

    Hill and W

    S. Hill and W. K. Wootters,”Entanglement of a Pair of Quantum Bit s”, Phys. Rev. Lett. 78 pp. 5022-5025 (1997)

    work page 1997

  27. [27]

    W. K. Wootters W K,”Entanglement of Formation of an Arbitrary State of Two Qubits”, Phys. Rev. Lett. 80 pp. 2245–2248 (1998). 15

    work page 1998