Cited by 217Quantum Information and CryptographyQuantum optics and atomic interactionsQuantum Mechanics and Applications

Entanglement of Trapped-Ion Qubits Separated by 230 Meters

Open access
Krutyanskiy, V., Galli, M., Krcmarsky, V., Baier, S., Fioretto, D. A., Pu, Y., Mazloom, A., Sekatski, P. +8 more·2023·Physical Review Letters

Abstract

We report on an elementary quantum network of two atomic ions separated by 230 m. The ions are trapped in different buildings and connected with 520(2) m of optical fiber. At each network node, the electronic state of an ion is entangled with the polarization state of a single cavity photon; subsequent to interference of the photons at a beam splitter, photon detection heralds entanglement between the two ions. Fidelities of up to (88.0+2.2-4.7)% are achieved with respect to a maximally entangled Bell state, with a success probability of 4×10^{-5}. We analyze the routes to improve these metrics, paving the way for long-distance networks of entangled quantum processors.

AI snapshot

Written from the paper’s full text.

TL;DR

Two trapped-ion nodes in separate buildings 230 m apart were entangled using cavity-generated photons sent through 520(2) m of optical fiber and interfered at a beam splitter. Bell-state fidelities reached up to about 88% for short coincidence windows, with a correspondingly low heralding success probability.

Key findings

  • The experiment entangled two single \(^{40}\mathrm{Ca}^+\) ions in different buildings separated by 230 m, connected by 520(2) m of fiber, with entanglement heralded by coincident detection of two 854 nm photons after beam-splitter interference.
  • For a coincidence window \(T=1\,\mu\mathrm{s}\), the reconstructed Bell-state fidelities were \(F_+ = (88.0^{+2.2}_{-4.7})\%\) and \(F_- = (83.3^{+3.3}_{-6.4})\%\), based on 555 coincidence events and a rate of 3.5 min\(^{-1}\). For \(T=17.5\,\mu\mathrm{s}\), fidelities fell to \(F_+ = (58.7^{+1.7}_{-2.1})\%\) and \(F_- = (58.0^{+2.0}_{-2.9})\%\).
  • Across 13,656,928 attempts, 4470 coincidences were recorded in the 5.5–23 \(\mu\mathrm{s}\) interval, giving a 0.033% success probability per attempt and a 0.49 s\(^{-1}\) entanglement rate; the high-fidelity \(T=1\,\mu\mathrm{s}\) subset corresponds to roughly \(4\times10^{-5}\) success probability.
  • Calibration measurements gave ion-photon entanglement fidelities of \((92.9^{+0.4}_{-0.5})\%\) at Node A and \((95.5^{+0.6}_{-0.9})\%\) at Node B, while two-photon interference visibility reached 101(6)% for \(T=0.25\,\mu\mathrm{s}\). Fidelity decreased with longer coincidence windows, which the models attribute to reduced photon indistinguishability, detector background, imperfect ion-photon entanglement, and technical noise.

Methods

  • Each node used a single \(^{40}\mathrm{Ca}^+\) ion in a linear Paul trap coupled to a 20 mm cavity; a bichromatic cavity-mediated Raman transition generated an ion-photon entangled state, and photons from the two nodes were overlapped on a balanced beam splitter for a photonic Bell-state measurement.
  • Data were acquired over seven hours, with up to 20 attempts per entanglement sequence, 0.3 ms initialization, a 50 \(\mu\mathrm{s}\) Raman pulse, and a 50 \(\mu\mathrm{s}\) detection window; the ion-ion state was reconstructed by quantum state tomography over nine Pauli basis combinations using maximum-likelihood estimation, with uncertainties from Monte Carlo resampling.
  • Two models were used: an empirical two-qubit density-matrix model incorporating photon distinguishability via Hong-Ou-Mandel visibility, detector background, and imperfect ion-photon entanglement; and a master-equation model for visibility including cavity frequency jitter, Raman-laser phase noise, and spontaneous emission.

Limitations

  • The paper has no dedicated limitations section. It states that fidelity and heralding efficiency trade off: longer coincidence windows lower fidelity because photon distinguishability increases, and spontaneous emission is identified as the most significant challenge. Technical noise from cavity jitter (60–100 kHz) and Raman-laser phase noise, plus temporal wave-packet mismatch, also limit visibility.
  • Evident from the text: only one ion per node was used, so register-based processing at network nodes was not demonstrated; the high-fidelity regime has a very low success probability, and the reported rates are 0.49 s\(^{-1}\) for the broader window and 3.5 min\(^{-1}\) for \(T=1\,\mu\mathrm{s}\).
  • The phase \(\phi\) was optimized from the data rather than determined independently from the node phases \(\theta_A\) and \(\theta_B\), which is an evident methodological limitation for full independent characterization.

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

Integrity signals

Registry

Crossref · 10.1103/physrevlett.130.050803

Cites

73 of 73 references verified0 citation errors · 0 not checkable

Statistics

Nothing to recompute.

Claims the paper makes

13 of 24 cited sources checked · 8 supported · 0 flagged · accuracy not yet measured

  • Study design and conductcitation

    The remote ion-ion state is characterized via quantum state tomography for all nine combinations of Pauli measurement bases.

    “The remote ion-ion state is characterized via quantum state tomography, for which the sequence is repeated for all nine combinations of the Pauli measurement bases for 2 ion qubits [52].”
    Quote in the paperSubstantial claim1 of 1 sources checked
    • cites [52] 52. D. F. V. James, P. G. Kwiat, W. J. Munro, and A. G. White, Measurement of qubits, Phys. Rev. A 64, 052312 (2001). source

      Section B, “Multiple beam Stokes parameters: multiple qubit tomography” (p. 4), supports tomography of two-qubit states and relates its measurement operators to Pauli operators. It describes a set of 16 measurements, however, not a sequence repeated for nine combinations of Pauli bases. The Introduction (p. 2) says its experiments use photon-polarization qubits, so it does not document the remote ion-ion procedure. (LLM, conf=0.85)

      Experimental — accuracy not yet measured
  • Interpretationcitation

    The probability for dephasing in the channel is parametrized by the HOM interference visibility.

    “The probability for dephasing in the channel is parametrized by the Hong-Ou-Mandel (HOM) interference visibility, which provides direct information about photon indistinguishability [58].”
    Quote in the paperSubstantial claim1 of 1 sources checked
    • cites [58] 58. G. Vittorini, D. Hucul, I. V. Inlek, C. Crocker, and C. Monroe, Entanglement of distinguishable quantum memo- ries, Phys. Rev. A 90, 040302(R) (2014). source

      The discussion on p. 1 links photon distinguishability and detection timing to decoherence, and p. 3 discusses fidelity loss from time-dependent phase shifts. Neither passage parametrizes a channel’s dephasing probability by Hong–Ou–Mandel interference visibility. Searches for HOM visibility and interference visibility found no passage establishing that relationship. (LLM, conf=0.72)

      Experimental — accuracy not yet measured
  • Interpretationcitation

    The success probabilities shown in Fig. 2(b) are comparable to those achieved over a few meters in Ref. [10].

    “It is notable that the success probabilities shown in Fig. 2(b) are comparable to those achieved over a few meters in Ref. [10]”
    Quote in the paperNot a substantial claim1 of 1 sources checked
    • cites [10] 10. L. J. Stephenson, D. P. Nadlinger, B. C. Nichol, S. An, P. Drmota, T. G. Ballance, K. Thirumalai, J. F. Goodwin, D. M. Lucas, and C. J. Ballance, High-Rate, High-Fidelity Entanglement of Qubits Across an Elementary Quantum Network, Phys. Rev. Lett. 124, 110501 (2020). source
  • Premisecitation

    Efficient, low-noise and entanglement-preserving telecom wavelength conversion of the 854 nm photons used in the present Letter has been achieved.

    “Furthermore, efficient, low-noise and entanglement-preserving telecom wavelength conversion of the 854 nm photons used in the present Letter has been achieved [25,26]”
    Quote in the paperSubstantial claim2 of 2 sources checked
    • cites [25] 25. M. Bock, P. Eich, S. Kucera, M. Kreis, A. Lenhard, C. Becher, and J. Eschner, High-fidelity entanglement between a trapped ion and a telecom photon via quantum frequency conversion, Nat. Commun. 9, 1998 (2018). source
    • cites [26] 26. V. Krutyanskiy, M. Meraner, J. Schupp, V. Krcmarsky, H. Hainzer, and B. P. Lanyon, Light-matter entanglement over 50 km of optical fibre, npj Quantum Inf. 5, 72 (2019). source
  • Findingnone given

    At each network node, the electronic state of an ion is entangled with the polarization state of a single cavity photon.

    “At each network node, the electronic state of an ion is entangled with the polarization state of a single cavity photon”
    Quote in the paperSubstantial claim
  • May combine two claims. 12
  • Classified as probably not a substantial claim. 8
  • May combine two claims.

    Premisecitation

    The photon generation method based on a cavity-mediated Raman process provides tunable entangled states and high efficiency, which are advantageous for establishing long-distance entanglement.

    “our photon generation method is based on a cavity-mediated Raman process providing tunable entangled states [34] and high efficiency [35], which are advantageous for establishing long-distance entanglement [36].”
    Quote in the paperSubstantial claim3 of 3 sources checked
    • cites [34] 34. A. Stute, B. Casabone, P. Schindler, T. Monz, P. O. Schmidt, B. Brandstätter, T. E. Northup, and R. Blatt, Tunable ion- photon entanglement in an optical cavity, Nature (London) 485, 482 (2012). source
    • cites [35] 35. J. Schupp, V. Krcmarsky, V. Krutyanskiy, M. Meraner, T. Northup, and B. Lanyon, Interface between trapped-ion qubits and traveling photons with close-to-optimal effi- ciency, PRX Quantum 2, 020331 (2021). source
    • cites [36] 36. N. Sangouard, R. Dubessy, and C. Simon, Quantum repeaters based on single trapped ions, Phys. Rev. A 79, 042340 (2009). source
  • Classified as probably not a substantial claim. May combine two claims.

    Premisecitation

    The trapped-ion platform has the capability for quantum-information processing with dozens of addressed qubits in a single trap and fidelities sufficient for fault-tolerant gate operations and error correction.

    “a particular strength of the trapped-ion platform is the capability for quantuminformation processing with dozens of addressed qubits in a single trap [22,23] and fidelities sufficient for faulttolerant gate operations and error correction [62,63].”
    Quote in the paperSubstantial claim2 of 4 sources checked
    • cites [22] 22. C. D. Bruzewicz, J. Chiaverini, R. McConnell, and J. M. Sage, Trapped-ion quantum computing: Progress and chal- lenges, Appl. Phys. Rev. 6, 021314 (2019). source

      The introduction (p. 2) says trapped-ion gates, preparation, and readout have achieved fidelities above those required by high-threshold fault-tolerant error-correction codes. But the DiVincenzo Criteria section (p. 3) reports only 20 ions in the largest fully controlled register, while Pros and Cons (p. 4) says larger chains with meaningful control and readout had not demonstrated entanglement between arbitrary ions. The copy therefore does not establish quantum-information processing with dozens of individually addressed qubits in one trap. (LLM, conf=0.86)

      Experimental — accuracy not yet measured
    • cites [23] 23. N. Friis, O. Marty, C. Maier, C. Hempel, M. Holzäpfel, P. Jurcevic, M. B. Plenio, M. Huber, C. Roos, R. Blatt, and B. Lanyon, Observation of Entangled States of a Fully Controlled 20-Qubit System, Phys. Rev. X 8, 021012 (2018). source
    • cites [62] 62. P. Kobel, M. Breyer, and M. Köhl, Deterministic spin- photon entanglement from a trapped ion in a fiber Fabry- Perot cavity, npj Quantum Inf. 7, 6 (2021). source
    • cites [63] 63. C. Ryan-Anderson, J. G. Bohnet, K. Lee, D. Gresh, A. Hankin, J. P. Gaebler, D. Francois, A. Chernoguzov, D. Lucchetti, N. C. Brown, T. M. Gatterman, S. K. Halit, K. Gilmore, J. A. Gerber, B. Neyenhuis, D. Hayes, and R. P. Stutz, Realization of Real-Time Fault-Tolerant Quantum Error Correction, Phys. Rev. X 11, 041058 (2021). source
  • Classified as probably not a substantial claim. May combine two claims.

    Premisecitation

    This capability provides a route to robust logical qubit encodings at network nodes, separate communication and information processing functionalities within each node, and quantum repeaters requiring Bell state measurements and either purification or error correction.

    “This capability provides a route to robust logical qubit encodings at network nodes [64], separate communication and information processing functionalities within each node [5,21], and quantum repeaters requiring Bell state measurements and either purification or error correction [65].”
    Quote in the paperSubstantial claim2 of 4 sources checked
    • cites [64] 64. L. Postler, S. Heußen, I. Pogorelov, M. Rispler, T. Feldker, M. Meth, C. D. Marciniak, R. Stricker, M. Ringbauer, R. Blatt, P. Schindler, M. Müller, and T. Monz, Demonstration of fault-tolerant universal quantum gate operations, Nature (London) 605, 675 (2022). source

      Split into 3 atoms — 0 confirmed, 1 partially supported, 0 disputed, 0 misattributed, 2 unverifiable. Expand the claim to see per-atom verdicts.

      Experimental — accuracy not yet measured
    • cites [5] 5. C. Monroe, R. Raussendorf, A. Ruthven, K. R. Brown, P. Maunz, L.-M. Duan, and J. Kim, Large-scale modular quantum-computer architecture with atomic memory and photonic interconnects, Phys. Rev. A 89, 022317 (2014). source

      Split into 3 atoms — 2 confirmed, 1 partially supported, 0 disputed, 0 misattributed, 0 unverifiable. Expand the claim to see per-atom verdicts.

      Experimental — accuracy not yet measured
    • cites [21] 21. L.-M. Duan and C. Monroe, Colloquium: Quantum networks with trapped ions, Rev. Mod. Phys. 82, 1209 (2010). source
    • cites [65] 65. M. Zwerger, B. P. Lanyon, T. E. Northup, C. A. Muschik, W. Dür, and N. Sangouard, Quantum repeaters based on trapped ions with decoherence-free subspace encoding, Quantum Sci. Technol. 2, 044001 (2017). source
  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Premisecitation

    In future long-distance networks limited by photon travel time, success probabilities will determine entanglement rates.

    “in future long-distance networks limited by photon travel time, it will be success probabilities that determine entanglement rates [36].”
    Quote in the paperNot a substantial claim1 of 1 sources checked
    • cites [36] 36. N. Sangouard, R. Dubessy, and C. Simon, Quantum repeaters based on single trapped ions, Phys. Rev. A 79, 042340 (2009). source
  • May combine two claims.

    Findingown data

    Fidelities of up to (88.0 +2.2 -4.7)% are achieved with respect to a maximally entangled Bell state, with a success probability of 4 × 10^-5.

    “Fidelities of up to ð88.0 þ 2.2 -4.7Þ% are achieved with respect to a maximally entangled Bell state, with a success probability of 4 × 10 -5 .”
    Quote in the paperSubstantial claim
  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Findingown data

    In total, 13 656 928 attempts were made to generate remote entanglement.

    “In total, 13 656 928 attempts were made to generate remote entanglement”
    Quote in the paperNot a substantial claim
  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Findingreasoning

    We optimize F ± over the phase φ, yielding φ = 82.2°.

    “We optimize F Æ over the phase ϕ in Eq. ( 1) because we did not determine θ A and θ B independently; this optimization yields ϕ ¼ 82.2°.”
    Quote in the paperNot a substantial claim
  • May combine two claims.

    Findingown data

    The fidelities of the reconstructed states at T = 17.5 μs are F+ = (58.7 +1.7 -2.1)% and F- = (58.0 +2.0 -2.9)%.

    “The fidelities of the reconstructed states are F þ ð17.5 μsÞ ¼ ð58.7 þ 1.7 -2.1Þ% and F -ð17.5 μsÞ ¼ ð58.0þ2.0-2.9Þ%”
    Quote in the paperSubstantial claim
  • May combine two claims.

    Findingown data

    The fidelities of the reconstructed states at T = 1 μs are F+ = (88.0 +2.2 -4.7)% and F- = (83.3 +3.3 -6.4)%.

    “The fidelities of the reconstructed states are F þ ð1 μsÞ ¼ ð88.0 þ 2.2 -4.7Þ% and F -ð1 μsÞ ¼ ð83.3 þ 3.3 -6.4Þ%.”
    Quote in the paperSubstantial claim
  • May combine two claims.

    Findingown data

    For T = 1 μs, 555 coincidence events were recorded, corresponding to a remote entanglement rate of 3.5 min^-1.

    “The density matrices shown in Fig. 2(c) correspond to T ¼ 1 μs, for which we recorded 555 coincidence events, that is, a remote entanglement rate of 3.5 min -1 .”
    Quote in the paperNot a substantial claim
  • May combine two claims.

    Findingown data

    Ion-photon entanglement fidelities at Nodes A and B are (92.9 +0.4 -0.5)% and (95.5 +0.6 -0.9)%, respectively.

    “Ion-photon entanglement was characterized in a calibration measurement at each node via quantum state tomography immediately prior to ion-ion entanglement, and fidelities of ð92.9 þ 0.4 -0.5Þ% and ð95.5 þ 0.6 -0.9Þ% with respect to a maximally entangled state were obtained at Nodes A and B, respectively.”
    Quote in the paperSubstantial claim
  • May combine two claims.

    Interpretationown data

    A detailed model is developed that captures the observed trade-off between the fidelity of remote entanglement and the heralding efficiency and shows how significant improvements can be made in the future.

    “A detailed model is developed that captures the observed trade-off between the fidelity of remote entanglement and the heralding efficiency and shows how significant improvements can be made in the future.”
    Quote in the paperSubstantial claim
  • Classified as probably not a substantial claim.

    Interpretationown data

    The empirical model is used to calculate theoretical fidelities, taking into account all three sources of infidelity.

    “The solid lines are calculated from the full model, taking into account all three sources of infidelity, while the dashed lines are calculated when photon distinguishability is excluded from the model.”
    Quote in the paperSubstantial claim
    • The authors state this as an assumption: For ion-photon entanglement, imperfections translate as a 2-qubit depolarizing channel on the ion-ion state.
  • May combine two claims.

    Study design and conductown data

    Spectral indistinguishability of the photons requires matching the resonant frequencies of the remote cavities, achieved via periodic calibration at 20 min intervals.

    “Spectral indistinguishability of the photons requires matching the resonant frequencies of the remote cavities.This is achieved via periodic calibration at 20 min intervals: 854 nm laser light that is resonant with the cavity at Node A is sent to Node B over a third fiber in the bundle, and the length of the Node B cavity is adjusted until it is resonant with this light.”
    Quote in the paperSubstantial claim
  • May combine two claims.

    Interpretationcitation

    Spontaneous emission during the Raman process provides information on which ion generated which cavity photon, introducing which-path information.

    “For example, spontaneous emission during the Raman process provides information on which ion generated which cavity photon [53][54][55], that is, scattering introduces which-path information.”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites [53][54][55]

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

  • May combine two claims.

    Study design and conductown data

    All parameter values used in the master-equation model are statistically consistent with independent estimates and determined via comparison of the model to measured single-photon wave packets.

    “All parameter values used in the model are statistically consistent with independent estimates and determined via comparison of the model to measured single-photon wave packets (see the Supplemental Material [40]).”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [40] 40. See Supplemental Material at http://link.aps.org/ supplemental/10.1103/PhysRevLett.130.050803 for details on the synchronization and stabilization procedures between the two nodes, a full description of our density-matrix model, an independent characterization of the noise sources, and the calculation of interference visibility, including Refs. [41-51].

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

    • The authors state this as an assumption: For ion-photon entanglement, imperfections translate as a 2-qubit depolarizing channel on the ion-ion state.
  • Classified as probably not a substantial claim.

    Study design and conductcitation

    Uncertainties for F ± (T) and for all quantities derived from the density matrices are obtained via Monte Carlo resampling.

    “Uncertainties for F Æ ðTÞ and for all quantities derived from the density matrices are obtained via Monte Carlo resampling (see the Supplemental Material [40]).”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites [40] 40. See Supplemental Material at http://link.aps.org/ supplemental/10.1103/PhysRevLett.130.050803 for details on the synchronization and stabilization procedures between the two nodes, a full description of our density-matrix model, an independent characterization of the noise sources, and the calculation of interference visibility, including Refs. [41-51].

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

  • Classified as probably not a substantial claim.

    Study design and conductcitation

    The polarization rotation of the fiber that carries single photons is characterized and corrected for at 20 min intervals.

    “Also at 20 min intervals, the polarization rotation of the fiber that carries single photons is characterized and corrected for (see the Supplemental Material [40]).”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites [40] 40. See Supplemental Material at http://link.aps.org/ supplemental/10.1103/PhysRevLett.130.050803 for details on the synchronization and stabilization procedures between the two nodes, a full description of our density-matrix model, an independent characterization of the noise sources, and the calculation of interference visibility, including Refs. [41-51].

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

18 of 18
  • The paper relies on this without support.

    Remote entanglement of trapped ions more than a few meters apart had not previously been reported.

    “Remote entanglement of trapped ions more than a few meters apart has not previously been reported.”
  • The authors state this as an assumption.

    For ion-photon entanglement, imperfections translate as a 2-qubit depolarizing channel on the ion-ion state.

    “For ion-photon entanglement, we assume that imperfections translate as a 2-qubit depolarizing channel on the ionion state (see the Supplemental Material [40]).”
2 of 2

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Authors
Krutyanskiy, V., Galli, M., Krcmarsky, V., Baier, S., Fioretto, D. A., Pu, Y., Mazloom, A., Sekatski, P., Canteri, M., Teller, M., Schupp, J., Bate, J., Meraner, M., Sangouard, N., Lanyon, B. P., & Northup, T. E.
Affiliations
  • Austrian Academy of Sciences (AT)
  • Universität Innsbruck (AT)
  • Georgetown University (US)
  • University of Geneva (CH)
  • Centre National de la Recherche Scientifique (FR)
Corresponding author
Lanyon, B. P.
Venue
Physical Review Letters
Published
2023-02-02
Volume
130
Issue
5
Pages
050803-050803
ISSN
  • 0031-9007 (ISSN-L)
  • 1079-7114
OpenAlex
W4294320751
Cited by
217
References
77
Citations by year
2026: 46 · 2025: 85 · 2024: 54 · 2023: 32
FWCI
20.49
Type
journal article
Language
en
Open access
Locations
  • Physical Review Letters (publishedVersion)
  • PubMed (publishedVersion)
  • HAL (submittedVersion)
  • arXiv (Cornell University) (submittedVersion)
  • Digital Library of the University of Innsbruck (University of Innsbruck) (submittedVersion)
  • arXiv (Cornell University)
Funders
  • Horizon 2020 Framework Programme (820445)
  • Austrian Science Fund (F 7109, Y 849, J 4229)
  • Army Research Office (W911NF-15-2-0060)
  • National Science Foundation (PHY-1915130)
  • Commissariat à l’Énergie Atomique et aux Énergies Alternatives
Topics
  • Physical Sciences › Computer Science › Artificial Intelligence › Quantum Information and Cryptography
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum optics and atomic interactions
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
Keywords
trapped-ion qubits, quantum networks, optical fiber links, cavity quantum electrodynamics, entanglement fidelity, quantum repeaters

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