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REVIEW 3 major objections 3 minor 37 references

Generation of frequency entanglement by rotating Doppler effect

T0 review · 3 major / 3 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read Rotating q-plates can convert polarization-entangled photons into continuously tunable frequency-entangled pairs at room temperature.

desk verdict A cleanly derived but physically unsupported proposal: the rotating q-plate speeds required to create the claimed frequency entanglement are orders of magnitude beyond what transmissive optics can survive. read the letter →

arxiv 2506.09488 v1 pith:AQPFHXKD submitted 2025-06-11 quant-ph physics.optics

Bolong Yi , Ling Chen , Baocheng Zhang This is my paper · ORCID
classification quant-phphysics.optics
keywords frequencyentanglementrotationalDopplereffectq-plateorbitalangularmomentumspontaneousparametricdown-conversionHong-Ou-Mandelinterferencejointspectralamplitudetwo-photon
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 proposes a way to generate frequency-entangled photon pairs that does not rely on preselecting discrete frequency bins or on temperature tuning of a nonlinear crystal. Starting with the equal-frequency, polarization-entangled pairs emitted by type-II spontaneous parametric down-conversion, the authors send each photon through a rotating q-plate, which shifts one photon up by $l\Omega$ and the other down by $l\Omega$ through the rotational Doppler effect. After polarizers erase the polarization information, the surviving state is entangled in the combined orbital-angular-momentum and frequency degrees of freedom. The authors show that this state should produce a Hong-Ou-Mandel coincidence dip whose interior oscillates as $\cos(2l\Omega\tau)$, so the rotation speed and its changes are directly readable from the interference pattern. If the scheme works, frequency entanglement becomes continuously tunable at room temperature over a wide range.

What carries the argument

The load-bearing mechanism is the rotational Doppler effect in a rotating q-plate, a waveplate-like element that converts circular polarization into orbital angular momentum while flipping the spin. When the plate rotates at angular frequency $\Omega$, a photon passing through it gains or loses frequency by $l\Omega$ together with an OAM change of $\pm l$, through the spin-orbit coupling of light. The paper couples this to type-II SPDC, whose equal-frequency polarization-entangled output provides the two input photons, and uses polarizers to trace out polarization, leaving a hybrid OAM-frequency entangled state. The supporting mathematical machinery is the Gaussian joint spectral amplitude $F(\omega_1,\omega_2)=\Phi(\omega_1,\omega_2)\rho(\omega_1+\omega_2)$ with phase-matching parameters satisfying $A=-B$; shifting $\Phi$ to $\Phi(\omega_1+l\Omega,\omega_2-l\Omega)$ produces the two-peaked JSA, and the HOM coincidence integral yields the cosine-modulated dip.

What would settle it

Place the proposed apparatus after a type-II SPDC source and measure coincidence counts versus delay $\tau$; if the HOM dip does not show cosine oscillations at frequency $2l\Omega$ when $2l\Omega$ exceeds the pump bandwidth (for example with $\Omega=2$ Trad/s, $l=2$, and $\tau_c=1$ ps), the predicted entangled state is not being created.

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Extended reading notes

Core claim

The central claim is that the state $\frac{1}{\sqrt{2}}(|+l,\omega+l\Omega\rangle|{-}l,\omega-l\Omega\rangle + |{-}l,\omega-l\Omega\rangle|+l,\omega+l\Omega\rangle)$ can be produced by post-manipulation: type-II BBO SPDC gives polarization-entangled photons at a common frequency $\omega$; two quarter-wave plates convert H/V to left/right circular polarization; two synchronously rotating q-plates imprint opposite OAM and frequency shifts via the rotational Doppler effect; two more QWPs and polarizers discard the polarization tag. Because the spin-flip that creates the frequency shift is tied to the polarization, erasing polarization leaves the frequency and OAM degrees of freedom entangled. The paper's quantitative analysis uses a Gaussian joint spectral amplitude and Hong-Ou-Mandel interference to predict a coincidence probability $P_\tau = \frac{1}{2} - \frac{1}{2} \cos(2l\Omega\tau)e^{-\tau^2/(2\tau_c^2)}$, with distinct cosine oscillations when $2l\Omega$ exceeds the pump bandwidth. It also notes that the generated JSA consists of two separated peaks along the antidiagonal direction.

Load-bearing premise

The scheme works only if a transmissive q-plate can be spun at angular frequencies up to about $4$ Trad/s, and at least $0.2$ Trad/s with a 1 ps pump envelope, without destroying the optical mode; remove that assumption and the $\pm l\Omega$ frequency shifts vanish, so the predicted entangled state is never produced.

Editorial extensions

If this is right

  • If the scheme is correct, frequency-entangled photon pairs can be generated continuously at room temperature without discrete frequency-bin preselection or crystal temperature control.
  • The HOM dip's oscillation frequency $2l\Omega$ gives a direct, parameter-free readout of the q-plate rotation speed (or of the topological charge $l$) from coincidence counts.
  • The frequency splitting can be tuned continuously by changing either the rotation speed $\Omega$ or the topological charge $l$, which is useful for quantum metrology and quantum communication.
  • The predicted two-peaked joint spectral amplitude can be used to reconstruct a restricted frequency-space density matrix, as the authors point out.
  • Increasing the topological charge $l$ reduces the error caused by the finite SPDC bandwidth and allows observable HOM oscillations at lower rotation speeds.

Reading between the lines

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

  • An underexplored consequence is that the OAM degree of freedom is a bystander in the HOM calculation: the authors show the OAM does not affect the frequency-frequency correlations, so their scheme could in principle be operated with a spatial filter that removes the OAM label, leaving a purely frequency-entangled state.
  • The rotation-speed requirement points to a practical trade-off: if only GHz-rate mechanical rotation is available, the paper's own condition implies the pump linewidth must be narrowed to roughly MHz ($\tau_c \sim 1$ ns) for oscillations to appear, a concrete parameter regime a follow-up experiment could target.
  • A natural extension would be to replace the rotating plate with a time-varying electro-optic or acousto-optic phase modulation to generate the same anti-correlated frequency shifts; the HOM cosine signature would then serve as a diagnosis of the modulation rate.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 3 minor

Summary. The paper proposes generating OAM-frequency entangled photon pairs by sending frequency-degenerate polarization-entangled photons from type-II SPDC through two synchronously rotating q-plates, then eliminating polarization with polarizers. The resulting state is written as Eq. (4), and the paper derives a joint spectral amplitude and a Hong-Ou-Mandel coincidence probability P_tau = 1/2 - 1/2 cos(2 l Omega tau) exp(-tau^2/(2 tau_c^2)). The authors claim this provides a room-temperature, continuously tunable source of frequency entanglement, with numerical JSA and HOM curves for rotation frequencies up to 4 Trad/s.

Significance. If the proposal were physically realizable, the HOM beating formula and the joint-spectrum treatment of Doppler-shifted SPDC photons would be a useful, if incremental, contribution to frequency-bin entanglement, with continuous tunability of the splitting 2 l Omega. The analytic derivations are internally consistent under the assumed Gaussian phase-matching model, and the simplifications are explicitly stated. However, the significance is strongly limited by the absence of any plausible mechanical platform for the required rotation speeds, and by the gap between the abstract's promised density-matrix reconstruction and the content of the body. The central experimental claim is therefore unsupported as it stands.

major comments (3)
  1. [Section III, Eq. (9) and Figs. 4-5] The proposed observable HOM beating requires rotation speeds Omega = 1-4 Trad/s when tau_c = 1 ps, and the text's own lower bound is 0.2 Trad/s. No transmissive optical element has been demonstrated at such angular velocities; the only speed citation, Ref. [37], is an optically levitated nanodumbbell, not a q-plate in an optical beam. A standard centripetal-stress estimate for fused silica (sigma_t ~ 50 MPa, rho ~ 2200 kg/m^3) gives Omega_max ~ 2 x 10^5 rad/s for a 1 mm radius disk and ~ 2 x 10^7 rad/s for a 10 micron radius disk, i.e., four to six orders of magnitude below 0.2 Trad/s. Since the state of Eq. (4) is created only through the Doppler shifts +/- l Omega, the central experimental regime is mechanically inaccessible and the main feasibility claim is unsupported.
  2. [Abstract and Section III] The abstract states that the combined joint-spectrum and HOM calculation can be used to reconstruct a restricted density matrix in the frequency space, but no density-matrix reconstruction, no explicit density matrix, and no tomography procedure appears anywhere in Sections III or IV. This advertised deliverable is therefore missing from the manuscript.
  3. [Section II, Eq. (4), and Section III] The state produced by the proposed polarizer step is an OAM-frequency entangled state, not a purely frequency-entangled state. Tracing out the OAM degree of freedom leaves rho_freq = 1/2 (|omega_1, omega_2><omega_1, omega_2| + |omega_2, omega_1><omega_2, omega_1|), which is classically correlated and separable. To obtain genuine frequency entanglement, the OAM must be erased or post-selected (for example, by coupling into a single-mode fiber that projects all OAM onto a common spatial mode); the paper neither specifies such a step nor justifies the assertion that the OAM degree of freedom does not affect the frequency-frequency entanglement. This weakens the title and abstract claims even in the ideal, lossless case.
minor comments (3)
  1. [Figure 5 caption] The figure caption lists rotation frequencies such as 0.4 Trad/s but the axes of the HOM plots are not labeled, which makes quantitative comparison of the curves unnecessarily difficult.
  2. [Section III, Eqs. (5)-(9)] The relation between the pump spectral width sigma used in the JSA and the envelope time tau_c used in Eqs. (7) and (9) is not stated; the text defines tau_c through Delta omega_FWHM but does not connect it to sigma, leaving the parameter mapping incomplete.
  3. [Section II, Eq. (3)] The assignment of omega_1 = omega + l Omega to the sigma_-, +l OAM component is asserted from angular momentum conservation, but the derivation is not shown and the q-plate conversion efficiency, losses, and mode distortion are not modeled; a more complete transfer-matrix treatment would strengthen the proposal.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the derivation is a self-contained calculation from standard SPDC states and the known rotational Doppler shift, with no fitted parameters and no load-bearing self-citation.

full rationale

The paper's derivation chain is a straightforward theoretical calculation. It starts from a standard polarization-entangled SPDC state (Eq. (1)), applies the well-known rotational Doppler frequency shift ±lΩ produced by a rotating q-plate, and obtains the hybrid OAM-frequency state (Eq. (4)). The JSA and HOM coincidence probability (Eq. (9)) are then computed from this assumed state using standard quantum-optics formulas. No parameter is fitted to data, no experimental result is used as input, and the output is not renamed as an independent prediction of the same input. The HOM result is a mathematical consequence of the assumed shifted-frequency state, which is ordinary theoretical derivation rather than circularity. The only self-citation, reference [30] in the phrase "RDE which has been widely investigated in q-plate, rough surface and particles [26,27,30–32]", appears in a general literature list and is not load-bearing. The main weakness of the paper is experimental feasibility — the required rotation speeds (0.2–4 Trad/s) may be mechanically unachievable for a transmissive q-plate — but that is a physical assumption, not a circular argument. The abstract also promises a restricted density-matrix reconstruction that is not presented, but that omitted deliverable is a completeness issue, not circularity. Therefore no significant circularity is present.

Assumptions & free parameters 4 free parameters · 5 assumptions · 0 invented entities

The central model depends on the standard rotational Doppler shift, an idealized degenerate SPDC source, independent manipulation of the two arms, and an unphysical rotation speed assumption. The free parameters (Omega, l, sigma/tau_c, gamma/A/B) are hand-chosen simulation inputs, not fitted to data, but Omega and l are the load-bearing ones for the claimed effect. No new physical entities are introduced.

free parameters (4)
  • Rotational angular frequency Omega = 1, 2, 4 Trad/s in Fig. 4; 0.2 Trad/s threshold; 1 Mrad/s in Fig. 5b
    Introduced by hand to produce visible HOM oscillations; not derived from any physical constraint on rotating optics.
  • Topological charge l = 2 in main plots; up to 100 suggested
    Sets the frequency shift l Omega and is chosen to make oscillations observable; larger l reduces the required rotation speed in principle.
  • Pump spectral width sigma and envelope time tau_c = sigma = 10^12, tau_c = 1 ps; also 1 us and 2 us in Fig. 5b
    Chosen Gaussian parameters that define the pump bandwidth; tau_c directly controls the required Omega through the visibility condition.
  • Phase-matching Gaussian parameters gamma, A, B = gamma = 0.1, A = -B = 0.7/(sigma sqrt(2 gamma))
    Ad hoc Gaussian phase-matching profile chosen 'only to simplify the calculation' per Section III; not derived from crystal parameters.
assumptions (5)
  • standard math Rotational Doppler effect shifts the frequency of each photon by +/- l Omega when passing through a rotating q-plate.
    This is the established result cited in [17-19] and [33]; the paper applies it without re-deriving it.
  • domain assumption Type-II SPDC from a BBO crystal at the cone intersection produces polarization-entangled photons with the same frequency omega.
    This is an idealized degenerate phase-matching assumption; the paper omits residual spectral correlations and phase mismatch in Eq. (1).
  • domain assumption The two photons can be manipulated independently by identical QWPs and rotating q-plates so that one photon receives +l Omega and the other receives -l Omega.
    Requires spatial separation of signal and idler modes and identical components; no experimental alignment analysis is provided.
  • ad hoc to paper A rotating q-plate can reach angular frequencies of order 1-4 Trad/s while maintaining optical quality.
    No mechanism or prior demonstration supports rotating a transmissive waveplate at ~10^11-10^12 rad/s; the cited GHz rotor [37] is a nanoscale levitated object, not a q-plate.
  • ad hoc to paper Gaussian phase-matching with A = -B captures the joint spectral amplitude of the SPDC photons.
    The authors explicitly say this is chosen to simplify the calculation without influencing the main entanglement analysis.

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Cite this review

Pith. "Pith review of Generation of frequency entanglement by rotating Doppler effect." pith.science (2026). https://pith.science/paper/AQPFHXKD

@misc{pith2026250609488,
  author       = {Pith},
  title        = {Pith review of: Generation of frequency entanglement by rotating Doppler effect},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/AQPFHXKD}},
  note         = {Machine review of arXiv:2506.09488}
}
read the original abstract

We propose a method to generate the frequency entanglement, allowing a continuous generation of entangled two-photon states in a hybrid degree of freedom by post-manipulation. Our method is based on type-II spontaneous parametric down-conversion in a nonlinear crystal and the rotation Doppler effect by rotating the q-plates, without preset discrete frequency entanglement. This allows the arbitrary modification of frequency entangled photons in a wide frequency range at room temperature, offering enhanced flexibility for quantum information tasks and quantum metrology. We also analyze the entanglement state by a combined calculation for the joint spectrum and Hong-Ou-Mandel interference of the two photons, which can be used to reconstruct a restricted density matrix in the frequency space.

Figures

Figures reproduced from arXiv: 2506.09488 by the authors.

Figure 1
Figure 1. FIG. 1: (Color online) Schematic diagram of the experimenta [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2: (Color online) From left to right, we simulated the re [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3: (Color online) (a) Joint spectral amplitudes as a fun [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figures from the paper (2 more)
Figure 4
Figure 4. Figure 4: FIG. 4: (Color online) Joint spectral amplitudes (a,c) and H [PITH_FULL_IMAGE:figures/full_fig_p008_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5: (Color online) HOM coincidence patterns for frequen [PITH_FULL_IMAGE:figures/full_fig_p010_5.png]

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Works this paper leans on

37 extracted references · 37 canonical work pages

  1. [37]

    J. Ahn, Z. Xu, J. Bang, et al. Optically Levitated Nanodu mbbell Torsion Balance and GHz Nanomechanical Rotor, Phys. Rev. Lett. 121, 033601 (2018). 14

    work page 2018

  2. [1]

    Horodecki, P

    R. Horodecki, P. Horodecki, M. Horodecki, and K. Horodec ki, Quantum entanglement, Rev. Mod. Phys. 81, 865 (2009)

    work page 2009

  3. [2]

    C. H. Bennett, G. Brassard, C. Cr´ epeau, R. Jozsa, A. Pere s, and William K. Wootters, Tele- porting an unknown quantum state via dual classical and Eins tein-Podolsky-Rosen channels, Phys. Rev. Lett. 70, 1895 (1993)

    work page 1993

  4. [3]

    I. A. Walmsley, Quantum optics: Science and technology i n a new light, Science 348, 525 (2015)

    work page 2015

  5. [4]

    Flamini, N

    F. Flamini, N. Spagnolo, F. Sciarrino, Photonic quantum information processing: a review, Rep. Prog. Phys. 82, 016001 (2018)

    work page 2018

  6. [5]

    Mastrovich, K

    M. Mastrovich, K. J. Resch, J. M. Donohue, Spectrally Eng ineering Photonic Entanglement with a Time Lens, Phys. Rev. Lett. 117, 243602 (2016)

    work page 2016

  7. [6]

    J. M. Donohue, K. J. Resch, and J. W. MacLean, Direct Chara cterization of Ultrafast Energy- Time Entangled Photon Pairs, Phys. Rev. Lett. 120, 053601 (2 018)

    work page

  8. [7]

    Ansari, J

    V. Ansari, J. M. Donohue, B. Brecht, et al. Tailoring nonl inear processes for quantum optics with pulsed temporal-mode encodings, Optica 5, 534 (2018)

    work page 2018

Show all 37 references
  1. [8]

    Cussey, A

    J. Cussey, A. T. Nguyen, P. Emplit, et al. Frequency-bin e ntangled photons, Phys. Rev. A 82, 013804 (2010)

    2010

  2. [9]

    M. Kues, C. Reimer, J. M. Lukens, et al. Quantum optical mi crocombs, Nat. Photon. 13, 170 (2019)

    2019

  3. [10]

    Kwiat, K

    P. Kwiat, K. Mattle, H. Weinfurter, et al. New High-Inte nsity Source of Polarization-Entangled Photon Pairs, Phys. Rev. Lett. 75, 4337 (1995)

    1995

  4. [11]

    Hensen, H

    B. Hensen, H. Bernien, A. E. Dr´ eau, et al. Loophole-free Bell inequality violation using electron spins separated by 1.3 kilometres, Nature 526, 682 (2015). 12

    2015

  5. [12]

    Bienfait, K

    A. Bienfait, K. J. Satzinger, Y. P. Zhong, et al. Phonon- mediated quantum state transfer and remote qubit entanglement, Science 364, 368 (2019)

    2019

  6. [13]

    Brecht, D

    B. Brecht, D. V. Reddy, C. Silberhorn, et al. Photon Temp oral Modes: A Complete Framework for Quantum Information Science, Phys. Rev. X 5, 041017 (201 5)

  7. [14]

    J. M. Lukens, P. Lougovski, Frequency-encoded photoni c qubits for scalable quantum infor- mation processing, Optica 4, 8 (2017)

    2017

  8. [15]

    Peˇ rina, Z

    J. Peˇ rina, Z. Hradil, and B. Jurˇ co, Quantum Optics and Fundamentals of Physics (Kluwer, Boston, 1994), chaps. 7 and 8

    1994

  9. [16]

    Mandel and E

    L. Mandel and E. Wolf, Optical Coherence and Quantum Opt ics (Cambridge Univ. Press, Cambridge, 1995), chap. 22

    1995

  10. [17]

    B. A. Garetz, Angular Doppler effect, J. Opt. Soc. Am. 71, 6 09 (1981)

    1981

  11. [18]

    Bialynicki-Birula and Z

    I. Bialynicki-Birula and Z. Bialynicka-Birula, Rotat ional Frequency Shift, Phys. Rev. Lett. 78, 2539 (1997)

    1997

  12. [19]

    Courtial, D

    J. Courtial, D. A. Robertson, K. Dholakia, L. Allen, and M. J. Padgett, Rotational Frequency Shift of a Light Beam, Phys. Rev. Lett. 81, 4828 (1998)

    1998

  13. [20]

    P. J. Allen, A radiation torque experiment, Am. J. Phys. 34, 1185 (1966)

    1966

  14. [21]

    B. A. Garetz, S. Arnold, Variable frequency shifting of circularly polarized laser radiation via a rotating half-wave retardation plate, Opt. Commun. 31, 1 ( 1979)

    1979

  15. [22]

    C. K. Hong, Z. Y. Ou, L. Mandel, Measurement of subpicose cond time intervals between two photons by interference, Phys. Rev. Lett. 59, 2044 (1987)

    1987

  16. [23]

    Francesconi, A

    S. Francesconi, A. Raymond, R. Duhamel, et al, On-chip g eneration of hybrid polarization- frequency entangled biphoton states, Photonics Res. 11, 27 0 (2023)

    2023

  17. [24]

    Z. Chen, C. Lu, H. Weinfurter, et al. Multiphoton entang lement and interferometry, Rev. Mod. Phys. 84, 777 (2012)

    2012

  18. [25]

    Franke-Arnold, L

    S. Franke-Arnold, L. Allen, M. Padgett, Advances in opt ical angular momentum, Laser & Photon. Rev. 2, 299 (2010)

    2010

  19. [26]

    T. Stav, A. Faerman, E. Maguid, et al. Quantum entanglem ent of the spin and orbital angular momentum of photons using metamaterials, Science 361, 1101 (2018)

    2018

  20. [27]

    Yabushita, T

    A. Yabushita, T. Kobayashi, Spectroscopy by frequency entangled photon pairs. Phys. Rev. A 69, 013806 (2003)

    2003

  21. [28]

    Ramelow, L

    S. Ramelow, L. Ratschbacher, A. Fedrizzi, et al. Discre te Tunable Color Entanglement, Phys. 13 Rev. Lett. 103, 253601 (2009)

    2009

  22. [29]

    S. C. Zhuang, B. Li, M. Y. Zheng, et al. Ultrabright-enta nglement-based quantum key distri- bution over a 404-km-long optical fiber, arXiv:2408.04361 ( 2024)

    2024 arXiv

  23. [30]

    S. Quan, L. Chen, S. Wu, and B. Zhang, Vectorial Doppler c omplex spectrum and its appli- cation to the rotational detection, Appl. Phys. Express 16, 042002 (2023)

    2023

  24. [31]

    Leach, B

    J. Leach, B. Jack, J. Romero, et al. Quantum Correlation s in Optical Angle-Orbital Angular Momentum Variables, Science 329, 662 (2010)

    2010

  25. [32]

    D. S. Simon, A. V. Sergienko, High Capacity Quantum Key D istribution via Hyper-Entangled Degrees of Freedom, New J. Phys. 16, 063052 (2013)

    2013

  26. [33]

    Georgi, C

    P. Georgi, C. Schlickriede, G. Li, S. Zhang, and T. Zentg raf, Rotational Doppler shift induced by spin-orbit coupling of light at spinning metasurfaces, O ptica 4, 1000, (2017)

    2017

  27. [34]

    W. P. Grice and I. A. Walmsley, Spectral information and distinguishability in type-II down- conversion with a broadband pump, Phys. Rev. A 56, 1627 (1997 )

    1997

  28. [35]

    P. B. Dixon, J. H. Shapiro, and F. N. C. Wong, Spectral eng ineering by Gaussian phase- matching for quantum photonics, Opt. Express 21, 5879 (2013 )

    2013

  29. [36]

    Dosseva, L

    A. Dosseva, L. Cincio, and A. M. Bra´ nczyk, Shaping the j oint spectrum of down-converted photons through optimized custom poling, Phys. Rev. A 93, 01 3801 (2016)

    2016

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