Repulsive Gravitational Force as a Witness of the Quantum Nature of Gravity

Chiara Marletto; Pablo L. Saldanha; Vlatko Vedral

REVIEW 2 major objections 5 minor 20 references

A single superposed mass could make gravity repel, the paper argues—a quantum-only effect that would falsify classical gravity.

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2026-08-02 23:52 UTC pith:LKQIY4FM

load-bearing objection A genuinely new one-superposition witness for quantum gravity with a correct core, but the no-classical-repulsion claim is asserted rather than proved and the headline postselection probability is off by four orders of magnitude. the 2 major comments →

arxiv 2602.12266 v2 pith:LKQIY4FM submitted 2026-02-12 quant-ph gr-qc

Repulsive Gravitational Force as a Witness of the Quantum Nature of Gravity

Pablo L. Saldanha , Chiara Marletto , Vlatko Vedral This is my paper

classification quant-ph gr-qc

keywords quantum gravity witnessgravitationally induced entanglementquantum interference of forceweak valuespostselectionrepulsive gravitysuperposed source masstabletop experiment

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 proposes a tabletop experiment in which a single massive particle is placed in a spatial superposition and a second 'probe' mass is allowed to interact gravitationally. By postselecting the source particle on a particular superposition at the interferometer output, the probe's momentum wavefunction experiences a net shift opposite to the direction of gravitational attraction—an effective repulsive force. The authors argue that no classical gravitational field could produce this signed momentum transfer, because the effect relies on quantum interference between two distinct gravitational-field states. If observed, the repulsive kick would be direct laboratory evidence that gravity must be quantized and would contradict general relativity's always-attractive gravity. The scheme requires only one superposed mass and avoids measuring entanglement, simplifying earlier two-mass witnesses.

Core claim

Starting from a source in state α|A⟩+β|B⟩ and a probe with momentum wavefunction ψ(p), the authors show that after interaction time T the joint state is entangled, with the probe shifted by δ_A or δ_B depending on source location. Postselecting the source on (−e^{iφ_A}|A⟩+e^{iφ_B}|B⟩)/√2 yields a conditioned probe wavefunction proportional to βψ(p−δ_B)−αψ(p−δ_A). When β>α, this superposition subtracts more high-momentum than low-momentum components, producing a negative mean momentum: an effective repulsive momentum transfer δ_ef = δ_B − α(δ_A−δ_B)/(β−α). The same result follows from a weak-value calculation of the Heisenberg-picture momentum operator. The paper thus claims that this 'quantu

What carries the argument

The central object is the postselected interference of two gravitational momentum kicks, captured by Eq. (5): ψ_p.s.(p) ∝ βψ(p−δ_B)−αψ(p−δ_A), which can be approximated as a single displaced wavepacket ψ(p−δ_ef) with δ_ef = δ_B − (δ_A−δ_B)⟨Π̂_A⟩_W, where ⟨Π̂_A⟩_W is the weak value of the projector onto source path A. The weak value of the momentum transfer, ⟨∆p̂⟩_W = (βδ_B−αδ_A)/(β−α), provides the amplification mechanism: when the pre- and postselected source states are nearly orthogonal, the effective momentum shift can be orders of magnitude larger than the individual gravitational kicks.

Load-bearing premise

The witness claim assumes that no classical or semiclassical gravitational interaction can generate the entanglement that underlies the postselected interference; the paper relies on a previously proven theorem for entanglement generation, and if that theorem fails for gravity (e.g., because a classical field can mimic the conditioned momentum shift), the observation of repulsion would not prove quantum gravity.

What would settle it

If an experiment using the same postselection but with the source mass prepared in a classical statistical mixture of positions (no coherence between |A⟩ and |B⟩) still yields a negative momentum shift of the probe, the quantum-witness claim would be falsified. Alternatively, a semiclassical calculation that reproduces the conditioned probe momentum δ_ef from Eq. (5) without any quantum superposition of the gravitational field would falsify the claim.

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

If this is right

The same experiment can be run with only one mass in superposition, reducing the technical burden of previous two-superposition GIE schemes.
The anomalous momentum transfer scales with the weak-value amplification factor g=(α/(β−α))(δ_A/δ_B − 1), so the signal can be enhanced by choosing pre- and postselected states close to orthogonal, at the cost of lower postselection probability.
Detecting a negative momentum shift with the source in a coherent superposition would constitute evidence that gravity is quantized and would violate the classical prediction of always-attractive gravity.
The paper's parameter estimates suggest the effect could be observable with a 10^-14 kg superposed source and a heavier probe (10^-20 kg) over ~0.5 s, placing the test within reach of current quantum-interference technology.

Where Pith is reading between the lines

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

The same interference-of-force mechanism is not specific to gravity: the authors' earlier work showed an effective electrostatic attraction between like charges. A calibration experiment with charged particles could validate the postselection procedure before dedicating a gravity apparatus.
Because the sign and magnitude of δ_ef encode the ratio of gravitational accelerations at two nearby source positions, the scheme might double as a short-range probe of the gravitational force law, beyond its quantum-witness role.
A semiclassical gravity model—where the source generates a definite classical field for each branch but no coherence between branches—remains the main competitor; constructing such a model and checking whether it predicts any negative conditioned momentum would sharpen the witness claim.
The low postselection probability implies that the experiment requires a large flux of probe particles or a condensate; optimizing the trade-off between amplification and success probability (e.g., via biased interferometry) could be a practical route to a first test.

Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

A genuinely new one-superposition witness for quantum gravity with a correct core, but the no-classical-repulsion claim is asserted rather than proved and the headline postselection probability is off by four orders of magnitude.

read the letter

Dear Colleague,

This paper applies the quantum-interference-of-force effect to gravity and gets a genuinely simpler witness than the two-superposition GIE scheme: one superposed source mass, postselect the source, and look for a negative mean momentum transfer to a probe. The core calculation is sound. Eq. (4) correctly gives the postselected probe wavefunction, and Eq. (5) with the weak value in Eq. (10) are consistent. The weak-value amplification is a real practical twist that could make the effect testable with moderate masses. This is a legitimate application of a known effect, not a new framework, but it is new in this context.

The main soft spot is the claim that a classical gravitational field can never produce repulsion. The paper cites the GIE theorem for this, but the protocol doesn't measure entanglement directly — it measures a conditional momentum first moment. The negative mean comes from the off-diagonal coherence in the joint state, and it is plausible that the GIE theorem covers this. Still, the authors should either adapt the theorem explicitly to conditional momentum distributions or construct a classical-field model and show it fails. As written, the necessity direction is asserted, not demonstrated. That is an addressable gap, not a fatal one.

There is also a concrete numerical error. For beta = 1/sqrt(2) + 0.0003 and alpha = sqrt(1 - beta^2), the postselection probability ||^2 is about 1.8e-7, not 0.8e-3 as stated. The error is four orders of magnitude. Since the low postselection probability is the main experimental cost, the feasibility estimate needs to be redone.

The paper acknowledges the Casimir-Polder issue and the need for a detailed feasibility study, which is honest. The back-action of the probe on the source is neglected without much discussion; with a much lighter probe that is probably minor but should be quantified.

Overall: the central mechanism is correct, the simplification is real, and the gaps are fixable. This deserves thorough peer review.

Best.

Referee Report

2 major / 5 minor

Summary. The paper proposes a single-source protocol to witness the quantum nature of gravity. A massive 'source' particle is prepared in a spatial superposition of two positions A and B; a 'probe' wavepacket evolves under the gravitational potential and acquires a momentum shift conditioned on the source position, yielding an entangled source-probe state. After postselecting the source on the state (−|A⟩e^{iφ_A}+|B⟩e^{iφ_B})/√2, the probe's momentum wavefunction becomes a difference of two shifted wavepackets, whose mean momentum can be negative. The authors derive an effective momentum transfer δ_ef, relate it to a weak value of the projector on |A⟩, and describe weak-value amplification. They also give feasibility estimates for nanodiamond sources and atomic/BEC probes, and claim that observing the repulsive momentum transfer would witness quantum gravity and violate general relativity.

Significance. The proposal is attractive: it would avoid the two-superposition GIE setups and the need to measure inter-particle correlations, replacing them with a postselected probe momentum measurement. The Schrödinger-picture and weak-value calculations are transparent and internally consistent under the stated approximations, and the closed-form expressions for δ_ef together with the parameter estimates yield a falsifiable prediction. However, the central interpretative claim—that no classical gravitational field can produce the same conditioned momentum distribution—is not established within the manuscript; it relies on an imported theorem without adapting it to this observable. A numerical example also contains a large error in the postselection probability. The significance is therefore conditional on a rigorous no-classical-repulsion argument.

major comments (2)

[Abstract; §1–§2, Eqs. (4)–(6)] The central claim that a classical gravitational field can never produce the postselected repulsive momentum is asserted, not proved. The paper invokes refs. [2,3] for the GIE theorem, but that theorem concerns generation of entanglement by a classical mediator, whereas the present protocol measures a conditional first moment of the probe after source postselection, not entanglement. The statement that the anomalous momentum transfer is a direct consequence of the entanglement requires the converse direction: one must show that any model with a classical gravitational field yields a separable source-probe state and hence a positive (or zero) conditional mean momentum, or at least that the negative first moment is a rigorous entanglement witness. No such classical model is constructed, and no adaptation of the GIE theorem to this observable is given. Without this, the title claim and the
[§2, numerical example after Eq. (6)] The stated postselection probability is incorrect. For β=1/√2+0.0003 and α=√(1−β²), |⟨Ψ_f|Ψ_i⟩|² = (β−α)²/2 ≈ 1.8×10⁻⁷, not 0.8×10⁻³. The error is about four orders of magnitude and directly affects the event-rate estimate in the weak-value amplification example and the subsequent feasibility discussion. Please recalculate and correct the quoted probability and any derived estimates.

minor comments (5)

[Eq. (5)] The replacement of the exact postselected wavefunction by a single shifted wavepacket ψ(p−δ_ef) is a first-order Taylor approximation. For large amplification the exact state is better described as a derivative-like superposition of the two Gaussians, and δ_ef is an effective first-moment shift rather than a literal displacement of the whole wavepacket. Please state the validity conditions (e.g. small |δ_A−δ_B| relative to the momentum width) and avoid implying the full momentum distribution is simply shifted.
[Feasibility section] The back-action of the probe on the source is neglected without quantitative justification. The impulse approximation in Eq. (2) and the post-selection visibility require that the source's momentum kicks −δ_A, −δ_B do not disturb the spatial superposition during the interaction time. Please state and check the relevant inequalities (e.g. δ_j T/M small compared with the spatial separation and with the source momentum spread) for the proposed parameters.
[Abstract and §1] The phrase 'violation of Einstein's theory of general relativity' is stronger than the calculation supports. The effect is a postselected measurement anomaly (weak-value amplification), not a change in the classical field equation; the gravitational interaction remains attractive in each branch. Recommend rewording to avoid overstatement.
[Feasibility section] The authors acknowledge that an extended feasibility study is needed to separate the effect from competing backgrounds such as the Casimir-Polder interaction. This caveat should appear earlier and be reflected in the abstract, which currently promises a feasible table-top test.
[References] Reference [18] contains an apparent typo in the author name 'ATM. A. Rahman'; this should be corrected to the standard format.

Circularity Check

0 steps flagged

No significant circularity: the repulsion calculation follows from an explicitly assumed quantum Hamiltonian and is not fitted to data; the witness interpretation cites an external GIE theorem but does not reduce the derivation to it.

full rationale

The central result is a direct calculation under an explicitly stated quantum-superposition assumption. Starting from the separable state in Eq. (1), the paper assumes the gravitational interaction produces a branch-dependent momentum kick (Eq. (2)-(3)); postselecting the source on the state [-|A>e^{iφ_A}+|B>e^{iφ_B}]/√2 gives the probe wavefunction in Eq. (4). The negative effective momentum transfer δ_ef in Eq. (5) is obtained by a Taylor expansion, and the same quantity is re-derived in the Heisenberg picture via the weak value in Eq. (10), which the paper explicitly notes is identical to Eq. (5). This is a consistency check, not a fit or a circular reduction: no parameter is fitted to data, and the negative shift is a mathematical consequence of subtracting the two shifted probe wavepackets. The only potentially circular-looking element is the witness claim that observing this effect would demonstrate the quantum nature of gravity. That inference relies on the GIE theorem [2,3] that entanglement cannot be generated by classical interactions. That theorem is an external result, not a synonym for the postselected momentum shift, and the paper does not use it as a computational input; its authors overlap with the present paper but it is also supported by independent prior work. Two non-circular caveats are noted for the record: (i) the paper does not construct and rule out a classical/semiclassical field model that reproduces the conditioned momentum distribution, so the 'no classical repulsion' claim is under-supported; (ii) the stated postselection probability |⟨Ψ_f|Ψ_i⟩|^2 ≈ 0.8×10^-3 for the parameters β=1/√2+0.0003, α=√(1-β^2) is numerically inconsistent with (β-α)^2/2 ≈ 2.4×10^-7. These are correctness or completeness concerns, not circularity.

Axiom & Free-Parameter Ledger

1 free parameters · 5 axioms · 0 invented entities

The central derivation uses standard quantum mechanics plus the domain assumption of an operator Newtonian Hamiltonian for gravity. No new entities are introduced, and no numbers are fitted to data—only α, β and experimental geometries are chosen. The main unproven import is the GIE theorem excluding classical gravity.

free parameters (1)

postselection amplitudes α, β = Example: β=1/√2+0.0003, α=√(1−β²)
The sign of δ_ef and the weak-value amplification factor g are set by α and β; they are chosen state-preparation parameters, not fitted to data.

axioms (5)

domain assumption Gravitational interaction is described by the operator Newtonian Hamiltonian Ĥ = P²/2M + p²/2m − GmM/|X−x| (Eq. 7).
This is the starting point for the quantum superposition of forces in Eq. (2); if gravity is not described this way, the derivation does not apply.
domain assumption Classical gravity cannot generate the entanglement underlying the postselected interference (no-classical-repulsion theorem).
The witness claim depends on this theorem, imported from GIE refs. [2,3]; it is not derived in this paper.
domain assumption No environmental decoherence of the source superposition during the interaction time T.
Coherence between |A⟩ and |B⟩ is required for the postselected interference in Eq. (4).
domain assumption Momentum transfers δ_A and δ_B are much smaller than the probe's initial momentum uncertainty.
Needed for the Taylor expansion in Eq. (5) and for the weak-value approximation to be valid (stated after Eq. 10).
standard math Standard quantum mechanics: Born rule, superposition, postselection, weak values.
Used throughout to compute the postselected probe wavefunction and weak values.

pith-pipeline@v1.3.0-alltime-deepseek · 5939 in / 17136 out tokens · 157363 ms · 2026-08-02T23:52:40.256980+00:00 · methodology

0 comments

read the original abstract

We show that a single spatially superposed 'source' mass acting on a 'probe' matter wavepacket can reveal the quantum nature of the gravitational field. For this we use a specific state preparation and measurement of the superposed source mass, including a postselection, which altogether results in a repulsive gravitational force on the probe particle. A classical gravitational field can never lead to repulsion, as the effect requires quantum interference of two distinct states of gravity. The eventual observation of such an effect would be a violation of Einstein's theory of general relativity, where gravity is always attractive. We also present a calculation in the Heisenberg picture under the formalism of weak values that illustrates how repulsion is achieved. Finally, we estimate the range of parameters (masses and the spatio-temporal extent of interference) for which the experiment is feasible.

Figures

Figures reproduced from arXiv: 2602.12266 by Chiara Marletto, Pablo L. Saldanha, Vlatko Vedral.

discussion (0)

Reference graph

Works this paper leans on

20 extracted references · 1 linked inside Pith

[1]

Kiefer,Quantum Gravity, 2nd ed

C. Kiefer,Quantum Gravity, 2nd ed. (Oxford University Press, Oxford, 2007)

2007
[2]

Gravitationally induced en- tanglement between two massive particles is sufficient ev- idence of quantum effects in gravity,

C. Marletto and V. Vedral, “Gravitationally induced en- tanglement between two massive particles is sufficient ev- idence of quantum effects in gravity,” Phys. Rev. Lett. 119, 240402 (2017)

2017
[3]

Spin entanglement wit- ness for quantum gravity,

S. Bose, A. Mazumdar, G. W. Morley, H. Ulbricht, M. Toroˇ s, M. Paternostro, A. A. Geraci, P. F. Barker, M. S. Kim, and G. Milburn, “Spin entanglement wit- ness for quantum gravity,” Phys. Rev. Lett.119, 240401 (2017)

2017
[4]

Quantum- gravity effects could in principle be witnessed in neutrino- like oscillations,

C. Marletto, V. Vedral, and D. Deutsch, “Quantum- gravity effects could in principle be witnessed in neutrino- like oscillations,” New J. Phys.20, 083011 (2018)

2018
[5]

Observable quantum entanglement due to grav- ity,

T. Krisnanda, G. Y. Tham, M. Paternostro, and T. Pa- terek, “Observable quantum entanglement due to grav- ity,” Npj Quantum Inf.6, 12 (2020)

2020
[6]

Qudits for witnessing quantum-gravity-induced entan- glement of masses under decoherence,

J. Tilly, R. J. Marshman, A. Mazumdar, and S. Bose, “Qudits for witnessing quantum-gravity-induced entan- glement of masses under decoherence,” Phys. Rev. A 104, 052416 (2021)

2021
[7]

Improving resilience of quantum-gravity- induced entanglement of masses to decoherence using three superpositions,

M. Schut, J. Tilly, R. J. Marshman, S. Bose, and A. Mazumdar, “Improving resilience of quantum-gravity- induced entanglement of masses to decoherence using three superpositions,” Phys. Rev. A105, 032411 (2022)

2022
[8]

En- hancing gravitational interaction between quantum sys- tems by a massive mediator,

J. S. Pedernales, K. Streltsov, and M. B. Plenio, “En- hancing gravitational interaction between quantum sys- tems by a massive mediator,” Phys. Rev. Lett.128, 110401 (2022)

2022
[9]

Amplification of gravitation- ally induced entanglement,

T. Feng and V. Vedral, “Amplification of gravitation- ally induced entanglement,” Phys. Rev. D106, 066013 (2022)

2022
[10]

Table-top nanodiamond interferometer enabling quantum gravity tests,

M. Vicentini, E. Bernardi, E. Moreva, F. Piacentini, C. Napoli, I. P. Degiovanni, A. Manzin, and M. Gen- ovese, “Table-top nanodiamond interferometer enabling quantum gravity tests,” arXiv:2405.21029

arXiv
[11]

The Bose-Marletto-Vedral experiment with nanodiamond interferometers: an insight on entan- glement detection,

G. Di Pietra, F. Piacentini, E. Bernardi, E. Moreva, C. Napoli, I. P. Degiovanni, M. Genovese, V. Vedral, and C. Marletto, “The Bose-Marletto-Vedral experiment with nanodiamond interferometers: an insight on entan- glement detection,” arXiv:2410.19601

Pith/arXiv arXiv
[12]

Quantum-information meth- ods for quantum gravity laboratory-based tests,

C. Marletto and V. Vedral, “Quantum-information meth- ods for quantum gravity laboratory-based tests,” Rev. Mod. Phys.97, 015006 (2025)

2025
[13]

Quan- tum interference of force,

R. Corrˆ ea, M. F. B. Cenni, and P. L. Saldanha, “Quan- tum interference of force,” Quantum2, 112 (2018)

2018
[14]

Quantum inter- ference of force with entangled photons,

G. S. Militani, A. Matoso, D. F. ´Avila, R. Corrˆ ea, R. O. Vianna, P. L. Saldanha, and S. P´ adua, “Quantum inter- ference of force with entangled photons,” Phys. Rev. A 112, 012213 (2025)

2025
[15]

Ef- fective electrostatic attraction between electrons due to quantum interference,

M. F. B. Cenni, R. Corrˆ ea, and P. L. Saldanha, “Ef- fective electrostatic attraction between electrons due to quantum interference,” Phys. Rev. A100, 022101 (2019)

2019
[16]

How the result of a measurement of a component of the spin of a spin-1/2 particle can turn out to be 100,

Y. Aharonov, D. Z. Albert, and L. Vaidman, “How the result of a measurement of a component of the spin of a spin-1/2 particle can turn out to be 100,” Phys. Rev. Lett.60, 1351 (1988)

1988
[17]

Colloquium: Understanding quantum weak values: Basics and applications,

J. Dressel, M. Malik, F. M. Miatto, A. N. Jordan, and R. W. Boyd, “Colloquium: Understanding quantum weak values: Basics and applications,” Rev. Mod. Phys. 86, 307 (2014)

2014
[18]

Free nano-object Ramsey interferometry for large quantum superpositions,

C. Wan, M. Scala, G. W. Morley, ATM. A. Rahman, H. Ulbricht, J. Bateman, P. F. Barker, S. Bose, and M. S. Kim, “Free nano-object Ramsey interferometry for large quantum superpositions,” Phys. Rev. Lett.117, 143003 (2016)

2016
[19]

Cohen-Tannoudji, B

C. Cohen-Tannoudji, B. Diu, and F. Lalo¨ e,Quantum mechanics, Vol. 1 (Wiley, Paris, 1997)

1997
[20]

The influence of retar- dation on the London-van der Waals forces,

H. B. G. Casimir and D. Polder, “The influence of retar- dation on the London-van der Waals forces,” Phys. Rev. 73, 360–372 (1948)

1948

[1] [1]

Kiefer,Quantum Gravity, 2nd ed

C. Kiefer,Quantum Gravity, 2nd ed. (Oxford University Press, Oxford, 2007)

2007

[2] [2]

Gravitationally induced en- tanglement between two massive particles is sufficient ev- idence of quantum effects in gravity,

C. Marletto and V. Vedral, “Gravitationally induced en- tanglement between two massive particles is sufficient ev- idence of quantum effects in gravity,” Phys. Rev. Lett. 119, 240402 (2017)

2017

[3] [3]

Spin entanglement wit- ness for quantum gravity,

S. Bose, A. Mazumdar, G. W. Morley, H. Ulbricht, M. Toroˇ s, M. Paternostro, A. A. Geraci, P. F. Barker, M. S. Kim, and G. Milburn, “Spin entanglement wit- ness for quantum gravity,” Phys. Rev. Lett.119, 240401 (2017)

2017

[4] [4]

Quantum- gravity effects could in principle be witnessed in neutrino- like oscillations,

C. Marletto, V. Vedral, and D. Deutsch, “Quantum- gravity effects could in principle be witnessed in neutrino- like oscillations,” New J. Phys.20, 083011 (2018)

2018

[5] [5]

Observable quantum entanglement due to grav- ity,

T. Krisnanda, G. Y. Tham, M. Paternostro, and T. Pa- terek, “Observable quantum entanglement due to grav- ity,” Npj Quantum Inf.6, 12 (2020)

2020

[6] [6]

Qudits for witnessing quantum-gravity-induced entan- glement of masses under decoherence,

J. Tilly, R. J. Marshman, A. Mazumdar, and S. Bose, “Qudits for witnessing quantum-gravity-induced entan- glement of masses under decoherence,” Phys. Rev. A 104, 052416 (2021)

2021

[7] [7]

Improving resilience of quantum-gravity- induced entanglement of masses to decoherence using three superpositions,

M. Schut, J. Tilly, R. J. Marshman, S. Bose, and A. Mazumdar, “Improving resilience of quantum-gravity- induced entanglement of masses to decoherence using three superpositions,” Phys. Rev. A105, 032411 (2022)

2022

[8] [8]

En- hancing gravitational interaction between quantum sys- tems by a massive mediator,

J. S. Pedernales, K. Streltsov, and M. B. Plenio, “En- hancing gravitational interaction between quantum sys- tems by a massive mediator,” Phys. Rev. Lett.128, 110401 (2022)

2022

[9] [9]

Amplification of gravitation- ally induced entanglement,

T. Feng and V. Vedral, “Amplification of gravitation- ally induced entanglement,” Phys. Rev. D106, 066013 (2022)

2022

[10] [10]

Table-top nanodiamond interferometer enabling quantum gravity tests,

M. Vicentini, E. Bernardi, E. Moreva, F. Piacentini, C. Napoli, I. P. Degiovanni, A. Manzin, and M. Gen- ovese, “Table-top nanodiamond interferometer enabling quantum gravity tests,” arXiv:2405.21029

arXiv

[11] [11]

The Bose-Marletto-Vedral experiment with nanodiamond interferometers: an insight on entan- glement detection,

G. Di Pietra, F. Piacentini, E. Bernardi, E. Moreva, C. Napoli, I. P. Degiovanni, M. Genovese, V. Vedral, and C. Marletto, “The Bose-Marletto-Vedral experiment with nanodiamond interferometers: an insight on entan- glement detection,” arXiv:2410.19601

Pith/arXiv arXiv

[12] [12]

Quantum-information meth- ods for quantum gravity laboratory-based tests,

C. Marletto and V. Vedral, “Quantum-information meth- ods for quantum gravity laboratory-based tests,” Rev. Mod. Phys.97, 015006 (2025)

2025

[13] [13]

Quan- tum interference of force,

R. Corrˆ ea, M. F. B. Cenni, and P. L. Saldanha, “Quan- tum interference of force,” Quantum2, 112 (2018)

2018

[14] [14]

Quantum inter- ference of force with entangled photons,

G. S. Militani, A. Matoso, D. F. ´Avila, R. Corrˆ ea, R. O. Vianna, P. L. Saldanha, and S. P´ adua, “Quantum inter- ference of force with entangled photons,” Phys. Rev. A 112, 012213 (2025)

2025

[15] [15]

Ef- fective electrostatic attraction between electrons due to quantum interference,

M. F. B. Cenni, R. Corrˆ ea, and P. L. Saldanha, “Ef- fective electrostatic attraction between electrons due to quantum interference,” Phys. Rev. A100, 022101 (2019)

2019

[16] [16]

How the result of a measurement of a component of the spin of a spin-1/2 particle can turn out to be 100,

Y. Aharonov, D. Z. Albert, and L. Vaidman, “How the result of a measurement of a component of the spin of a spin-1/2 particle can turn out to be 100,” Phys. Rev. Lett.60, 1351 (1988)

1988

[17] [17]

Colloquium: Understanding quantum weak values: Basics and applications,

J. Dressel, M. Malik, F. M. Miatto, A. N. Jordan, and R. W. Boyd, “Colloquium: Understanding quantum weak values: Basics and applications,” Rev. Mod. Phys. 86, 307 (2014)

2014

[18] [18]

Free nano-object Ramsey interferometry for large quantum superpositions,

C. Wan, M. Scala, G. W. Morley, ATM. A. Rahman, H. Ulbricht, J. Bateman, P. F. Barker, S. Bose, and M. S. Kim, “Free nano-object Ramsey interferometry for large quantum superpositions,” Phys. Rev. Lett.117, 143003 (2016)

2016

[19] [19]

Cohen-Tannoudji, B

C. Cohen-Tannoudji, B. Diu, and F. Lalo¨ e,Quantum mechanics, Vol. 1 (Wiley, Paris, 1997)

1997

[20] [20]

The influence of retar- dation on the London-van der Waals forces,

H. B. G. Casimir and D. Polder, “The influence of retar- dation on the London-van der Waals forces,” Phys. Rev. 73, 360–372 (1948)

1948