Pith. sign in

REVIEW 3 minor 53 references

Nonlocal quantum correlations for fermions degrade monotonically with Hawking temperature in Einstein-Gauss-Bonnet black hole spacetime.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

T0 review · grok-4.3

2026-07-03 08:25 UTC pith:TEDQH2U7

load-bearing objection Standard Unruh-Hawking calculation applied to EGB; the usual degradation and NAQC-BN hierarchy survive the Gauss-Bonnet correction with no surprises.

arxiv 2607.02039 v1 pith:TEDQH2U7 submitted 2026-07-02 gr-qc

Nonlocal correlations of fermionic entanglement in the spacetime of Einstein-Gauss-Bonnet black hole

classification gr-qc
keywords nonlocal correlationsfermionic entanglementEinstein-Gauss-Bonnet black holeHawking temperaturequantum coherenceBell nonlocalityUnruh effectcurved spacetime
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

The paper examines how two measures of nonlocal correlations, the nonlocal advantage of quantum coherence and Bell nonlocality, behave for fermionic fields when one observer falls into an Einstein-Gauss-Bonnet black hole while the other accelerates outside. It shows that both quantities decrease steadily as the Hawking temperature rises, which is controlled by the Gauss-Bonnet coupling, dimension, and horizon radius. A key finding is that the hierarchical relation where nonlocal advantage exceeds Bell nonlocality continues to hold in this modified gravity setting. This work applies standard quantum information tools to a spacetime with higher-curvature corrections to see their effect on quantum resources near black holes.

Core claim

The authors find that for a maximally entangled fermionic Bell state shared between an inertial observer falling into the black hole and an accelerated observer outside, the mixed state after applying Bogoliubov transformations yields analytical expressions for NAQC and BN that both decrease with increasing Hawking temperature, while preserving the inequality NAQC greater than BN in d-dimensional EGB geometry.

What carries the argument

Bogoliubov transformations between Kruskal and Schwarzschild-like frames for fermionic modes in d-dimensional Einstein-Gauss-Bonnet spacetime.

Load-bearing premise

The Unruh-Hawking effect can be modeled accurately using Bogoliubov transformations for fermionic fields even when the spacetime includes Gauss-Bonnet corrections in higher dimensions.

What would settle it

An experiment or numerical simulation showing that NAQC or BN increases or stays constant with rising Hawking temperature in an EGB-like geometry would contradict the monotonic degradation claim.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • Quantum resources encoded in fermionic entanglement become less accessible as the black hole radiates more strongly.
  • The persistence of the NAQC-BN hierarchy suggests that certain ordering of correlation measures is robust against gravitational effects from higher curvature terms.
  • Analytical dependence on parameters alpha, d, and r_h allows direct computation of correlation strength for given black hole properties.
  • High curvature corrections in EGB spacetime influence the rate of degradation but do not eliminate the correlations entirely.

Where Pith is reading between the lines

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

  • This suggests that quantum communication protocols using fermions might need temperature-dependent error correction near such black holes.
  • Similar calculations could be extended to other modified gravity theories to test robustness of quantum correlations.
  • The results imply that Hawking radiation acts as a decohering environment whose strength is tunable by spacetime parameters.
  • If the hierarchy holds across more spacetimes, it may point to a general structural feature of fermionic correlations under acceleration.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

0 major / 3 minor

Summary. The paper studies nonlocal advantage of quantum coherence (NAQC) and Bell nonlocality (BN) for a fermionic Bell state shared between an inertial observer (Alice in Kruskal frame) and an accelerated observer (Rob in Schwarzschild-like frame) in d-dimensional Einstein-Gauss-Bonnet black hole spacetime. Using Bogoliubov transformations induced by the Unruh-Hawking effect, the authors derive the mixed bipartite density matrix and obtain analytical expressions for NAQC and BN that depend on the Hawking temperature T(α, d, r_h). They report that both quantities degrade monotonically with increasing T and that the NAQC > BN hierarchy persists.

Significance. If the central derivations hold, the work extends prior results on quantum correlations in black-hole spacetimes to the EGB family by showing that the qualitative features (monotonic degradation and algebraic hierarchy) survive the inclusion of the Gauss-Bonnet term, which enters only through a modified surface gravity. The explicit analytical dependence on α, d, and r_h is a concrete strength that permits direct comparison with the Schwarzschild limit.

minor comments (3)
  1. The abstract and introduction state that analytical expressions are derived, yet the main text should include the explicit form of the fermionic Bogoliubov coefficients (or at least the final density-matrix elements) before the NAQC and BN formulas, to allow verification that no additional d-dependent factors appear beyond the surface-gravity correction.
  2. Figure captions and axis labels should explicitly state the fixed values of d, α, and ω used when plotting versus T or r_h, so that the monotonicity claim can be reproduced from the plotted curves.
  3. A short paragraph comparing the EGB surface-gravity formula with the d-dimensional Schwarzschild case would clarify the precise manner in which the Gauss-Bonnet parameter modifies the temperature without altering the mode-mixing structure.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the positive assessment of our work on NAQC and BN in Einstein-Gauss-Bonnet spacetime and for recommending minor revision. No specific major comments appear in the report, so we have no points requiring point-by-point rebuttal. We will address any minor editorial or typographical suggestions in the revised version.

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The derivation applies standard Bogoliubov transformations between Kruskal and Schwarzschild-like frames to obtain the fermionic density matrix, then computes NAQC and BN analytically as functions of Hawking temperature T determined by the EGB metric parameters. The reported monotonic degradation and NAQC-BN hierarchy are direct algebraic consequences of the Fermi-Dirac form of the mixing coefficients and hold independently of the specific value of T or the EGB corrections to surface gravity. No parameters are fitted to data and then relabeled as predictions, no self-definitional loops appear in the mode transformations or correlation measures, and no load-bearing uniqueness theorems or ansatzes are imported via self-citation. The central results remain self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Only abstract available; ledger populated from stated modeling choices.

axioms (1)
  • domain assumption Bogoliubov transformations relate inertial Kruskal and accelerated Schwarzschild-like frames for fermions
    Invoked to obtain the mixed density matrix from the initial Bell state

pith-pipeline@v0.9.1-grok · 5737 in / 1053 out tokens · 27418 ms · 2026-07-03T08:25:52.692923+00:00 · methodology

0 comments
read the original abstract

The investigation of nonclassical correlations in curved spacetimes offers key insights into the intersection of quantum information theory and gravitational physics. This paper studies two nonlocal correlation measures, non local advantage of quantum coherence (NAQC) and Bell nonlocality (BN) in a $d$-dimensional spherically symmetric Einstein-Gauss-Bonnet (EGB) black hole spacetime. We consider two observers (Alice and Rob) initially sharing a maximally entangled Bell state: Alice freely falls into the black hole (inertial Kruskal frame), while Rob accelerates outside the horizon (non-inertial Schwarzschild-like frame). The Unruh-Hawking effect modifies Rob's field modes, requiring Bogoliubov transformations to relate the two frames. We derive the mixed bipartite density matrix for fermionic fields and analytical expressions for NAQC and BN, which depend on Hawking temperature (itself governed by $\alpha$, $d$, and $r_h$). Our results show both correlations degrade monotonically with increasing Hawking temperature, confirm the NAQC-BN hierarchical relationship persists in EGB spacetime, and highlighting the impact of high curvature corrections on quantum resources.

Figures

Figures reproduced from arXiv: 2607.02039 by Qi Xiao, Xiaolong Gong, Yanjun Chen, Yifei Xu.

Figure 1
Figure 1. Figure 1: Penrose diagram of metric in Eq. (3) spacetime of Gauss-Bonnet black hole, r∗ near the horizon can be expanded as r∗ ≈ Γ ln(r − rh) + G(r − rh), (7) where G(r−rh) is a nonsingular function at r∗. Comparing Γ with the analogous coefficient in the Schwarzschild spacetime, we infer that the Γ is the inverse of Hawking temperature of Gauss-Bonnet black hole,i.e., Γ−1 = T. T can be defined geometrically in term… view at source ↗
Figure 2
Figure 2. Figure 2: Bmax(ρA,I) characterizing Bell nonlocality for fermionic entanglement [PITH_FULL_IMAGE:figures/full_fig_p012_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Nl1 (ρA,I) characterizing the NAQC for fermionic entanglement (from Alice to Rob). 13 [PITH_FULL_IMAGE:figures/full_fig_p013_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Nl1 (ρI,A) characterizing the reversed NAQC (from Rob to Alice). 15 [PITH_FULL_IMAGE:figures/full_fig_p015_4.png] view at source ↗

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

53 extracted references · 1 canonical work pages · 1 internal anchor

  1. [1]

    Colloquium: Quantum coherence as a resource.Reviews of Modern Physics, 89(4):041003, 2017

    Alexander Streltsov, Gerardo Adesso, and Martin B Plenio. Colloquium: Quantum coherence as a resource.Reviews of Modern Physics, 89(4):041003, 2017

  2. [2]

    Quantum entanglement.Reviews of modern physics, 81(2):865–942, 2009

    Ryszard Horodecki, Pawe l Horodecki, Micha l Horodecki, and Karol Horodecki. Quantum entanglement.Reviews of modern physics, 81(2):865–942, 2009

  3. [3]

    Quantum steering

    Roope Uola, Ana CS Costa, H Chau Nguyen, and Otfried G¨ uhne. Quantum steering. Reviews of Modern Physics, 92(1):015001, 2020

  4. [4]

    Publisher’s note: Bell nonlocality [rev

    Nicolas Brunner, Daniel Cavalcanti, Stefano Pironio, Valerio Scarani, and Stephanie Wehner. Publisher’s note: Bell nonlocality [rev. mod. phys. 86, 419 (2014)].Reviews of Modern Physics, 86(2):839–840, 2014

  5. [5]

    Quantum teleportation.Scientific American, 282(4):50–59, 2000

    Anton Zeilinger. Quantum teleportation.Scientific American, 282(4):50–59, 2000

  6. [6]

    Quantum metrology.Phys- ical review letters, 96(1):010401, 2006

    Vittorio Giovannetti, Seth Lloyd, and Lorenzo Maccone. Quantum metrology.Phys- ical review letters, 96(1):010401, 2006

  7. [7]

    Quantum cryptography

    Charles H Bennett, Gilles Brassard, and Artur K Ekert. Quantum cryptography. Scientific American, 267(4):50–57, 1992

  8. [8]

    Dense coding in experimental quantum communication.Physical review letters, 76(25):4656, 1996

    Klaus Mattle, Harald Weinfurter, Paul G Kwiat, and Anton Zeilinger. Dense coding in experimental quantum communication.Physical review letters, 76(25):4656, 1996. 17

  9. [9]

    Experimental sharing of bell nonlocality with projective measurements.New Journal of Physics, 26(5):053019, 2024

    Ya Xiao, Yan Xin Rong, Shuo Wang, Xin Hong Han, Jin Shi Xu, and Yong Jian Gu. Experimental sharing of bell nonlocality with projective measurements.New Journal of Physics, 26(5):053019, 2024

  10. [10]

    Nonlocal advantage of quantum coherence.Physical Review A, 95(1):010301, 2017

    Debasis Mondal, Tanumoy Pramanik, and Arun Kumar Pati. Nonlocal advantage of quantum coherence.Physical Review A, 95(1):010301, 2017

  11. [11]

    Sharing of nonlocal advantage of quantum co- herence by sequential observers.Physical Review A, 98(4):042311, 2018

    Shounak Datta and AS Majumdar. Sharing of nonlocal advantage of quantum co- herence by sequential observers.Physical Review A, 98(4):042311, 2018

  12. [12]

    Complementarity Relations Between Quantum Steering Criteria

    Debasis Mondal and Dagomir Kaszlikowski. Complementarity relations between quantum steering criteria.arXiv preprint arXiv:1711.02612, 2017

  13. [13]

    Hierarchy of the nonlocal advantage of quantum coherence and bell nonlocality.Physical Review A, 98(3):032317, 2018

    Ming-Liang Hu, Xiao-Min Wang, and Heng Fan. Hierarchy of the nonlocal advantage of quantum coherence and bell nonlocality.Physical Review A, 98(3):032317, 2018

  14. [14]

    Nonlocal advantage of quantum coherence in high- dimensional states.Physical Review A, 98(2):022312, 2018

    Ming-Liang Hu and Heng Fan. Nonlocal advantage of quantum coherence in high- dimensional states.Physical Review A, 98(2):022312, 2018

  15. [15]

    Ex- perimental investigation of the nonlocal advantage of quantum coherence.Physical Review A, 100(2):022308, 2019

    Zhi-Yong Ding, Huan Yang, Hao Yuan, Dong Wang, Jie Yang, and Liu Ye. Ex- perimental investigation of the nonlocal advantage of quantum coherence.Physical Review A, 100(2):022308, 2019

  16. [16]

    Hierarchical relationship of nonlocal correlations in schwarzschild-de sitter spacetime.The European Physical Journal C, 85(1):59, 2025

    Huimin Yao, Li Zhang, Cuihong Wen, and Jieci Wang. Hierarchical relationship of nonlocal correlations in schwarzschild-de sitter spacetime.The European Physical Journal C, 85(1):59, 2025

  17. [17]

    Generation of genuine tripartite entanglement for continuous variables in de sitter space.Physics Letters B, 800:135109, 2020

    Jieci Wang, Cuihong Wen, Songbai Chen, and Jiliang Jing. Generation of genuine tripartite entanglement for continuous variables in de sitter space.Physics Letters B, 800:135109, 2020

  18. [18]

    The influence of Unruh effect on quantum steering for accelerated two-level detectors with different measurements

    Tonghua Liu, Jieci Wang, Jiliang Jing, and Heng Fan. The influence of Unruh effect on quantum steering for accelerated two-level detectors with different measurements. Annals of Physics, 390:334–344, March 2018

  19. [19]

    Quantum information and relativity theory.Re- views of Modern Physics, 76(1):93, 2004

    Asher Peres and Daniel R Terno. Quantum information and relativity theory.Re- views of Modern Physics, 76(1):93, 2004

  20. [20]

    Relativistic quantum information, 2012

    Robert B Mann and Timothy C Ralph. Relativistic quantum information, 2012

  21. [21]

    Accessible and inaccessible quantum coherence in relativistic quan- tum systems.Physical Review A, 105(5):052403, 2022

    Saveetha Harikrishnan, Segar Jambulingam, Peter P Rohde, and Chandrashekar Radhakrishnan. Accessible and inaccessible quantum coherence in relativistic quan- tum systems.Physical Review A, 105(5):052403, 2022. 18

  22. [22]

    Basis-independent quantum coherence and its distribution under relativistic motion.The European Physical Journal C, 84(8):838, 2024

    Ming-Ming Du, Hong-Wei Li, Zhen Tao, Shu-Ting Shen, Xiao-Jing Yan, Xi-Yun Li, Wei Zhong, Yu-Bo Sheng, and Lan Zhou. Basis-independent quantum coherence and its distribution under relativistic motion.The European Physical Journal C, 84(8):838, 2024

  23. [23]

    Huan Yang, Ling-Ling Xing, Min Kong, Gang Zhang, and Liu Ye. Investigating and controlling the quantum resources of bipartite-qubit detectors of scalar fields in the process of spacetime expansion.The European Physical Journal C, 83(10):966, 2023

  24. [24]

    Bosonic and fermionic coherence of n-partite states in the background of a dilaton black hole.Journal of High Energy Physics, 2024(9):1– 20, 2024

    Wen-Mei Li and Shu-Min Wu. Bosonic and fermionic coherence of n-partite states in the background of a dilaton black hole.Journal of High Energy Physics, 2024(9):1– 20, 2024

  25. [25]

    Gaussian quantum steering for continuous variables sharing in an expanding universe.The European Physical Journal C, 84(8):856, 2024

    Hengyu Wu, Xiaolong Gong, Tonghua Liu, and Shu-Min Wu. Gaussian quantum steering for continuous variables sharing in an expanding universe.The European Physical Journal C, 84(8):856, 2024

  26. [26]

    50 years of quantum chromodynamics: Introduction and review.The European Physical Journal C, 83(12):1125, 2023

    Franz Gross, Eberhard Klempt, Stanley J Brodsky, Andrzej J Buras, Volker D Burk- ert, Gudrun Heinrich, Karl Jakobs, Curtis A Meyer, Kostas Orginos, Michael Strick- land, et al. 50 years of quantum chromodynamics: Introduction and review.The European Physical Journal C, 83(12):1125, 2023

  27. [27]

    Can spacetime su- perposition alleviate gravitationally induced quantum decoherence?New Journal of Physics, 26(12):123012, 2024

    Changjing Zeng, Qianqian Liu, Cuihong Wen, and Jieci Wang. Can spacetime su- perposition alleviate gravitationally induced quantum decoherence?New Journal of Physics, 26(12):123012, 2024

  28. [28]

    Effects of Lorentz symmetry breaking on quantum coherence in an expanding universe.Physics Letters B, 872:140133, 2026

    Qi Xiao, Yanjun Chen, and Tonghua Liu. Effects of Lorentz symmetry breaking on quantum coherence in an expanding universe.Physics Letters B, 872:140133, 2026

  29. [29]

    Does relativistic mo- tion really freeze initially maximal entanglement?Journal of High Energy Physics, 03:218, 2026

    Si-Han Li, Hui-Chen Yang, Rui-Yang Xu, and Shu-Min Wu. Does relativistic mo- tion really freeze initially maximal entanglement?Journal of High Energy Physics, 03:218, 2026

  30. [30]

    Multiqubit coherence of mixed states near event horizon.Journal of Cosmology and Astroparticle Physics, 02:058, 2026

    Wen-Mei Li, Jianbo Lu, and Shu-Min Wu. Multiqubit coherence of mixed states near event horizon.Journal of Cosmology and Astroparticle Physics, 02:058, 2026

  31. [31]

    Quantum steering for different types of Bell-like states in gravitational background.Physics Letters B, 870:139895, 2025

    Si-Han Li, Si-Han Shang, and Shu-Min Wu. Quantum steering for different types of Bell-like states in gravitational background.Physics Letters B, 870:139895, 2025

  32. [32]

    Generated genuine tripartite steering and its monogamy in the background of a Kerr-Newman black hole.Chinese Physics C, 48(11):115106, 2024

    Xiaoli Huang, Haoyu Wu, and Shumin Wu. Generated genuine tripartite steering and its monogamy in the background of a Kerr-Newman black hole.Chinese Physics C, 48(11):115106, 2024. 19

  33. [33]

    Quantum steering of GHZ and W states in rela- tivistic motion.The European Physical Journal C, 85(7):790, 2025

    Si-Han Shang and Shu-Min Wu. Quantum steering of GHZ and W states in rela- tivistic motion.The European Physical Journal C, 85(7):790, 2025

  34. [34]

    Black hole explosions?Nature, 248(5443):30–31, 1974

    Stephen W Hawking. Black hole explosions?Nature, 248(5443):30–31, 1974

  35. [35]

    Particle creation by black holes.Communications in mathe- matical physics, 43(3):199–220, 1975

    Stephen W Hawking. Particle creation by black holes.Communications in mathe- matical physics, 43(3):199–220, 1975

  36. [36]

    Quantum black hole evap- oration.Physical Review D, 48(6):2670, 1993

    Kareljan Schoutens, Herman Verlinde, and Erik Verlinde. Quantum black hole evap- oration.Physical Review D, 48(6):2670, 1993

  37. [37]

    Black-hole thermodynamics.Physics Today, 33(1):24–31, 1980

    Jacob D Bekenstein. Black-hole thermodynamics.Physics Today, 33(1):24–31, 1980

  38. [38]

    Generation of quantum entan- glement in superposed diamond spacetime.The European Physical Journal C, 85(5):539, 2025

    Xiaofang Liu, Changjing Zeng, and Jieci Wang. Generation of quantum entan- glement in superposed diamond spacetime.The European Physical Journal C, 85(5):539, 2025

  39. [39]

    Gaussian tripartite steering in Schwarzschild black hole.Physics Letters B, 865:139493, 2025

    Shu-Min Wu, Hao-Yu Wu, Yu-Xuan Wang, and Jieci Wang. Gaussian tripartite steering in Schwarzschild black hole.Physics Letters B, 865:139493, 2025

  40. [40]

    Quantum nature of black hole and the superposition of fermionic field.The European Physical Journal C, 84(10):1113, 2024

    Jinshan An, Li Zhang, Lulu Xiao, and Jieci Wang. Quantum nature of black hole and the superposition of fermionic field.The European Physical Journal C, 84(10):1113, 2024

  41. [41]

    Gaussian quantum steering under the influence of a dilaton black hole.The European Physical Journal C, 81(10):925, 2021

    Biwei Hu, Cuihong Wen, Jieci Wang, and Jiliang Jing. Gaussian quantum steering under the influence of a dilaton black hole.The European Physical Journal C, 81(10):925, 2021

  42. [42]

    Irreversible degradation of quantum coherence under relativistic motion.Physical Review A, 93(6):062105, 2016

    Jieci Wang, Zehua Tian, Jiliang Jing, and Heng Fan. Irreversible degradation of quantum coherence under relativistic motion.Physical Review A, 93(6):062105, 2016

  43. [43]

    Characterization of quantum and clas- sical correlations in the Earth’s curved space-time.Scientific Reports, 10:14697, September 2020

    Tonghua Liu, Shuo Cao, and Shumin Wu. Characterization of quantum and clas- sical correlations in the Earth’s curved space-time.Scientific Reports, 10:14697, September 2020

  44. [44]

    Origin of the blackhole information paradox.Fortschritte der Physik, 62(3):255–265, 2014

    Ram Brustein. Origin of the blackhole information paradox.Fortschritte der Physik, 62(3):255–265, 2014

  45. [45]

    Genuinely accessible and inaccessible entanglement in schwarzschild black hole.Physics Letters B, 848:138334, 2024

    Shu-Min Wu, Xiao-Wei Teng, Jin-Xuan Li, Si-Han Li, Tong-Hua Liu, and Jie-Ci Wang. Genuinely accessible and inaccessible entanglement in schwarzschild black hole.Physics Letters B, 848:138334, 2024

  46. [46]

    Modes mismatch induced variation of quantum coherence for two-mode localized Gaussian states in accelerated frame.European Physical Journal Plus, 138(4):360, April 2023

    Xiaolong Gong, Yue Fang, Tonghua Liu, and Shuo Cao. Modes mismatch induced variation of quantum coherence for two-mode localized Gaussian states in accelerated frame.European Physical Journal Plus, 138(4):360, April 2023. 20

  47. [47]

    Superstring theory (cam- bridge.Press, Cambridge, 1987

    Michael B Green, John H Schwarz, and Edward Witten. Superstring theory (cam- bridge.Press, Cambridge, 1987

  48. [48]

    The einstein tensor and its generalizations.Journal of Mathematical Physics, 12(3):498–501, 1971

    David Lovelock. The einstein tensor and its generalizations.Journal of Mathematical Physics, 12(3):498–501, 1971

  49. [49]

    Asymptotically (anti)-de sitter solutions in gauss-bonnet gravity without a cosmological constant.Physical Review D, 70(6):064019, 2004

    MH Dehghani. Asymptotically (anti)-de sitter solutions in gauss-bonnet gravity without a cosmological constant.Physical Review D, 70(6):064019, 2004

  50. [50]

    Accelerated expansion of the universe in gauss-bonnet gravity.Phys- ical Review D, 70(6):064009, 2004

    MH Dehghani. Accelerated expansion of the universe in gauss-bonnet gravity.Phys- ical Review D, 70(6):064009, 2004

  51. [51]

    A laboratory analogue of the event horizon using slow light in an atomic medium.Nature, 415(6870):406–409, 2002

    Ulf Leonhardt. A laboratory analogue of the event horizon using slow light in an atomic medium.Nature, 415(6870):406–409, 2002

  52. [52]

    Quantum fields in curved space, cambridge university press, cambridge, uk

    ND Birrell and PCW Davies. Quantum fields in curved space, cambridge university press, cambridge, uk. 1982

  53. [53]

    Guaranteed violation of a bell inequality without aligned reference frames or calibrated devices.Scientific reports, 2(1):470, 2012

    Peter Shadbolt, Tam´ as V´ ertesi, Yeong-Cherng Liang, Cyril Branciard, Nicolas Brun- ner, and Jeremy L O’Brien. Guaranteed violation of a bell inequality without aligned reference frames or calibrated devices.Scientific reports, 2(1):470, 2012. 21