CoChat
Sign Up
Cited by 35Quantum Information and CryptographyQuantum Mechanics and ApplicationsQuantum optics and atomic interactions

Programmable entanglement oscillations in a non-Markovian channel

Open access
Cialdi, Simone, Brivio, Davide, Tesio, Enrico, Paris, Matteo G. A.·2011·Physical Review A
DOI 10.1103/physreva.83.042308
Open this paper in CoChat — free accountOpen PDF

Abstract

We suggest and demonstrate an all-optical experimental setup to observe and engineer entanglement oscillations of a pair of polarization qubits in an effective non-Markovian channel. We generate entangled photon pairs by spontaneous parametric down-conversion (SPDC), and then insert a programmable spatial light modulator in order to impose a polarization-dependent phase shift on the spatial domain of the SPDC output. This creates an effective programmable non-Markovian environment where modulation of the environment spectrum is obtained by inserting a spatial grating on the signal arm. In our experiment, programmable oscillations of entanglement are achieved, where the entangled state obtained at the maximum of the revival after sudden death violates Bell's inequality by $17$ standard deviations.

AI snapshot

Written from the paper’s full text.

TL;DR

The paper proposes and demonstrates an all-optical setup that uses spontaneous parametric down-conversion, a spatial light modulator, and a grating to create a programmable non-Markovian channel for polarization qubits, yielding entanglement revivals after sudden death. At the revival maximum, the measured state violates the CHSH-Bell inequality by 17 standard deviations.

Key findings

  • With the grating inserted, visibility oscillates with the evolution parameter \(a\): after purification \(V=0.881\pm0.004\), at the minimum \(a=0.23\) it falls to \(V=0.120\pm0.016\), and at the revival \(a=0.48\) it recovers to \(V=0.696\pm0.013\). Without the grating, no revival appears after entanglement degradation.
  • At the revival maximum, the Bell parameter is \(B=2.341\pm0.019\), violating the CHSH-Bell inequality by more than 17 standard deviations.
  • Narrowing the slit aperture from \(10\) mrad to \(4\) mrad reduces the coupled down-conversion spectrum from about \(200\) nm to \(60\) nm and increases visibility to \(V=0.963\pm0.005\).
  • The grating has period \(\delta x=2\) mm and transparent width \(0.4\delta x\), with the revival predicted at \(a_{\rm rev}=0.476\) rad/pixel.

Methods

  • Entangled photon pairs are generated by type-I SPDC in two BBO crystals pumped by a 406-nm cw diode; a half-wave plate balances the horizontal and vertical pairs, and an additional BBO crystal compensates temporal delay.
  • A programmable spatial light modulator imposes polarization- and position-dependent phases on signal and idler arms; a handmade grating on the signal arm provides amplitude modulation of the angular distribution.
  • The spatial degrees of freedom are traced out, leaving a polarization density matrix whose decoherence factor determines concurrence and visibility. Measurements include visibility with polarizers, full two-qubit polarization tomography with maximum-likelihood reconstruction, and Bell-parameter measurements.

Limitations

  • The paper states that low detector quantum efficiency (about 10%) forced a large angular acceptance of \(10\) mrad, coupling roughly \(200\) nm of the down-conversion spectrum and reducing the maximum visibility; a narrower \(4\) mrad aperture improved visibility but was not used for the main experiment.
  • The paper states that SLM pixel discretization limits the usable evolution parameter to \(a \le 2\pi/{\rm pixel}\), so high values of \(a\) were excluded from the analysis.
  • Evident from the text: the demonstration uses one specific all-optical configuration with a handmade grating and particular BBO/SPDC parameters, and no independent replication or alternative channel implementations are reported.

Model-written summary. Check it against the paper before relying on it.

Integrity signals

Registry

Crossref · 10.1103/physreva.83.042308

Cites

41 of 41 references verified0 citation errors · 0 not checkable

Statistics

Nothing to recompute.

Claims the paper makes

0 of 13 cited sources checked · 0 supported · 0 flagged

  • Findingown data

    The angular distributions g(θ) and g'(θ') are peaked at the central values θ = θ' = 0 with a width of 8.6 mrad.

    “Upon inspecting the distribution of Fig. 2 one sees that the angular distributions g(θ ), g (θ ) are peaked around the central values θ = θ = 0 value with a width of 8.6 mrad.”
    Quote in the paperNot a substantial claim
  • Findingown data

    When the grating is absent, no revival occurs after entanglement degradation.

    “Comparing the curve with the one obtained without the grating we see that in the latter case no revival occurs after the degradation of entanglement.”
    Quote in the paperSubstantial claim
  • Findingown data

    Programmable oscillations of entanglement were achieved in the experiment.

    “In our experiment, programmable oscillations of entanglement are achieved, where the entangled state obtained at the maximum of the revival after sudden death violates Bell's inequality by 17 standard deviations.”
    • Also stated in: § VI. CONCLUSIONS · plain
      “In our experiment, programmable oscillations of entanglement are achieved by varying the linear phase function imposed to the signal by the SLM and verified both by visibility measurements and full polarization state tomography.”
    Quote in the paperSubstantial claim
  • Findingown data

    The visibility after purification with the grating inserted is 0.881 ± 0.004.

    “The purification procedure with the grating inserted leads to a visibility V = 0.881 ± 0.004”
    • Also stated in: § V. STATE CHARACTERIZATION · plain
      “with visibility V = 0.881 ± 0.004.”
    Quote in the paperSubstantial claim
  • Findingown data

    A setup using only optical elements was demonstrated for observing and controlling oscillations of polarization-qubit entanglement in an effective non-Markovian channel.

    “We suggest and demonstrate an all-optical experimental setup to observe and engineer entanglement oscillations of a pair of polarization qubits in an effective non-Markovian channel.”
    • Also stated in: § VI. CONCLUSIONS · boosted
      “In conclusion, we have suggested and demonstrated an experimental setup to observe oscillations of polarization entanglement in a programmable way.”
    Quote in the paperSubstantial claim
  • May combine two claims. 13
  • Classified as probably not a substantial claim. 6

  • May combine two claims.

    Findingown data

    The measured coincidence count distribution agrees excellently with the product form computed from single-arm distributions, with a χ2 test P > 0.9.

    “The corresponding coincidence count distribution has then been compared with the one computed as”
    • Also stated in: § A. More details on the angular function · boosted
      “and an excellent agreement was found, also corroborated by a significant χ 2 test (P χ 2 >χ 2 0 0.9).”
    Quote in the paperSubstantial claim
    • The authors state this as an assumption: The angular function f(θ,θ') has the factorized form g(θ)g'(θ').

  • May combine two claims.

    Findingown data

    Narrowing the slit aperture to 4 mrad selects only 60 nm and increases the visibility to 0.963 ± 0.005.

    “By narrowing the slit aperture to = 4 mrad only 60 nm are selected, and the visibility is found to increase at V = 0.963 ± 0.005.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Findingreasoning

    A periodic angular distribution induces entanglement oscillations, whereas a nonperiodic angular distribution leads to entanglement decrease and then death.

    “from the expression of the visibility V (α), we see that a periodic structure of the angular distribution would induce oscillations, whereas entanglement decrease and then death may be expected for a nonperiodical angular distribution.”
    • Also stated in: § VI. CONCLUSIONS · boosted
      “This results in a periodic structure of the angular distribution, which corresponds to modulation of the enviroment spectrum, and induces oscillations of entanglement, whereas entanglement decrease and then death is observed for a nonperiodical angular distribution.”
    Quote in the paperSubstantial claim
    • The authors state this as an assumption: The angular function f(θ,θ') has the factorized form g(θ)g'(θ').

  • May combine two claims.

    Findingown data

    Varying the SLM-imposed linear phase on the signal produced programmable entanglement oscillations, confirmed by visibility measurements and full polarization-state tomography.

    “In our experiment, programmable oscillations of entanglement are achieved by varying the linear phase function imposed to the signal by the SLM and verified both by visibility measurements and full polarization state tomography.”
    Quote in the paperSubstantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

    Interpretationown data

    The angular distributions can be approximated by Gaussian curves, although the specific functional form is not relevant to the analysis.

    “They may be approximated by Gaussian curves, though the specific functional form is irrelevant for our analysis.”
    Quote in the paperNot a substantial claim
    • The authors state this as an assumption: The angular distribution is peaked at a central value with a finite width, for example a Gaussian shape.

  • May combine two claims.

    Interpretationreasoning

    The periodic structure implies that any two-point correlation function of the environment is not single peaked when spatial degrees of freedom are traced out, which indicates a non-Markovian channel.

    “Moreover, the periodic structure implies that in tracing out the spatial degrees of freedom any two-point correlation function of the environment is not single peaked and this is a sign of the non-Markovian character of the channel.”
    Quote in the paperSubstantial claim
    • The authors state this as an assumption: The angular function f(θ,θ') has the factorized form g(θ)g'(θ').

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Study design and conductreasoning

    Pixel discretization of the SLM imposes a step function with angular resolution ζ = 0.3 mrad to approximate the linear phase functions.

    “Because of the pixel discretization a step function with an angular resolution ζ = 0.3 mrad is physically inserted by the SLM in order to approximate the linear functions φ SLM (θ ),φ SLM (θ ).”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Interpretationreasoning

    The revival is expected at a_rev = 2π D δx / (h L), or in terms of the angular grating period δθ, α_rev = 2π/δθ.

    “The revival is expected at a rev = 2π D δx h L or, in terms of the angular grating period δθ , α rev = 2π δθ .”
    Quote in the paperSubstantial claim
    • The authors state this as an assumption: The angular function f(θ,θ') has the factorized form g(θ)g'(θ').

  • May combine two claims.

    Interpretationreasoning

    The decoherence factor ε equals the interferometric visibility V(α) = Re[ε], which also equals the concurrence C.

    “In turn, in this case, ε equals the interferometric visibility V (α) = Re[ε] which, in turn, coincides with the concurrence C.”
    Quote in the paperSubstantial claim
    • Rests on an assumption: The angular distribution g(θ) is symmetric.

  • Classified as probably not a substantial claim.

    Study design and conductreasoning

    Pixel discretization of the SLM imposes the condition a ≤ 2π/pixel, so high values of a must be neglected in the analysis.

    “Since the pixel discretization of the SLM imposes the condition a 2π/pixel, high values of a must be neglected in our analysis.”
    Quote in the paperSubstantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Study design and conductnone given

    The experiment used the larger aperture to compensate for the low quantum efficiency of the photodetectors.

    “The present experiment has been performed with the larger aperture to compensate for the low quantum efficiency of the photodetectors.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Interpretationreasoning

    Without purification, the off-diagonal elements of the polarization density matrix decrease exponentially and the state approaches the unentangled mixture m.

    “As a consequence, in the absence of any purification mechanism, the off-diagonal elements of the polarization density matrix decrease exponentially and the state is driven toward the unentangled mixture m .”
    Quote in the paperSubstantial claim
    • The authors state this as an assumption: The angular distribution is peaked at a central value with a finite width, for example a Gaussian shape.

  • May combine two claims.

    Premisecitation

    The angle-dependent phase shift causes decoherence of the polarization qubit and should be removed to obtain an effective entangled-pair source.

    “These angular-dependent terms are responsible for decoherence of the polarization qubit and should be removed in order to obtain an effective source of entangled pairs [25].”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites [25] 25. R. Rangarajan, M. Goggin, and P. Kwiat, Opt. Express 17, 18920 (2009).

      Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  • Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

    Premisecitation

    Entanglement oscillations are expected in continuous-variable systems, while collapses and revivals have been observed with polarization qubits.

    “In fact, entanglement oscillations are expected in continuous variable systems [18][19][20], whereas collapses and revivals of entanglement have been observed with polarization qubits [21].”
    Quote in the paperNot a substantial claim0 of 2 sources checked
    • cites [18][19][20]

      Couldn’t be matched to a paper in Crossref, so it can’t be checked.

    • cites [21] 21. J.-S. Xu, C.-F. Li, M. Gong, X.-B. Zou, C.-H. Shi, G. Chen, and G.-C. Guo, Phys. Rev. Lett. 104, 100502 (2010).

      Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  • May combine two claims.

    Interpretationown data

    The all-optical scheme can generate and detect entanglement and nonlocality revivals, which may enable control of decoherence for polarization qubits.

    “Our scheme is all-optical and allows us to generate and detect revivals of entanglement and nonlocality, thus paving the way for engineering of decoherence for polarization qubits.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Premisecitation

    For a Markovian interaction, entanglement decreases monotonically and may be destroyed in finite time.

    “If the interaction is Markovian, i.e., the loss of information is unidirectional, from the system to the environment, then entanglement monotonically decreases and may be also destroyed in a finite time [3][4][5][6][7].”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites [3][4][5][6][7]

      Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  • Classified as probably not a substantial claim.

    Premisecitation

    Entanglement of a bipartite system is usually degraded by interaction of each subsystem with the environment, inducing decoherence.

    “Entanglement of a bipartite system is usually degraded by the interaction of each subsystem with the environment, which induces decoherence, i.e., an irreversible loss of information from the system to the rest of the universe [1,2].”
    Quote in the paperSubstantial claim0 of 2 sources checked
    • cites [1] 1. W. H. Zurek, Rev. Mod. Phys. 75, 715 (2003).

      Couldn’t be matched to a paper in Crossref, so it can’t be checked.

    • cites [2] 2. M. Schlosshauer, Rev. Mod. Phys. 76, 1267 (2005).

      Couldn’t be matched to a paper in Crossref, so it can’t be checked.

17 of 17

  • The authors state this as an assumption.

    The angular function f(θ,θ') has the factorized form g(θ)g'(θ').

    “is assumed to have the factorized form g(θ )g (θ )”
    “This assumption has been experimentally verified by measuring the coincidence count distribution C = |f expt (θ,θ )| 2 , within a coincidence time window of 50 ns, as a function of the signal and idler slit positions θ and θ .”

  • The paper relies on this without support.

    The angular distribution g(θ) is symmetric.

    “Since the angular distribution g(θ ) is symmetric, ε is real and positive, and we may write”

  • The authors state this as an assumption.

    The angular distribution is peaked at a central value with a finite width, for example a Gaussian shape.

    “In general, the angular distribution may be assumed to be peaked at some central value with a finite width as, for example, the Gaussian shape we have discussed in the preceding section.”
3 of 3

Claims other papers make about this one

Each is checked against this paper’s own text: does it say what the citing paper says it does?

  • Quantum mutual information is another witness of non-Markovianity.

    “The total amount of correlations (as classical as quantum) as measured by the quantum mutual information is another witness of non-Markovianity [225].”

    From Quantum non-Markovianity: characterization, quantification and detection (2014) · cites this paper as [225]

    The Introduction (page unavailable) says non-Markovian interactions may produce nonmonotonic behavior of quantum correlations. The paper discusses entanglement and measures concurrence and a Bell parameter, but the passages found for “quantum mutual information” and “classical and quantum correlations” do not establish quantum mutual information as a witness or as a measure of total correlations. (LLM, conf=0.78)

    Experimental — accuracy not yet measured

Cites

Flagged first, then by citations

2 of the 43 references couldn’t be matched to a known paper.

Cited by

Sorted by citations

Related

Authors
Cialdi, S., Brivio, D., Tesio, E., & Paris, M. G. A.
Affiliations
University of Milan (IT)
ORCID
Venue
Physical Review A
Publisher
American Physical Society (APS)
Published
2011-04-08
Volume
83
Issue
4
ISSN
  • 0556-2791 (ISSN-L)
  • 1050-2947
  • 1094-1622
DOI
10.1103/physreva.83.042308
OpenAlex
W2015038284
Semantic Scholar
05f5bd2bee4ba1d46e6ff21308153592d244150c
Cited by
35
References
43
Citations by year
2026: 1 · 2025: 2 · 2024: 1 · 2022: 1 · 2021: 1 · 2020: 2 · 2019: 5 · 2018: 6 · 2017: 3 · 2016: 2 · 2015: 1 · 2014: 3 · 2013: 1 · 2012: 3
FWCI
2.94
Type
journal article
Language
en
Open access
Licence
link.aps.org/licenses/aps-default-license (vor)
Locations
  • Physical Review A (publishedVersion)
  • arXiv (Cornell University) (submittedVersion)
  • Archivio Istituzionale della Ricerca (Universita Degli Studi Di Milano) (submittedVersion, other-oa)
  • arXiv (Cornell University)
Topics
  • Physical Sciences › Computer Science › Artificial Intelligence › Quantum Information and Cryptography
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum optics and atomic interactions
Keywords
entanglement oscillations, non-Markovian dynamics, polarization qubits, spontaneous parametric down-conversion, spatial light modulator, entanglement revival, entanglement sudden death, Bell inequality violation

About these checks

Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.

Claims read by deepseek-v4.1-flash under definition version 3 (extract-v3) on 2026-10-07.

Classified by jev-1.13-20260917 (gold-guideline-v0.2) on 2026-10-07.

Statistics and arithmetic are recomputed, not judged.

Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.

What counts as a claim ›How we measure confidence ›How we check this ›

Are you an author, or do you see a problem with this page? Request a review