pith. sign in

arxiv: 2512.15072 · v2 · pith:2MIFPTG6new · submitted 2025-12-17 · 🪐 quant-ph

Quantum batteries in coherent Ising machine

Jin-Tian Zhang , Shuang-Quan Ma , Jing-Yi-Ran Jin , Tao Liu , Qing Ai This is my paper

Pith reviewed 2026-05-21 17:28 UTC · model grok-4.3

classification 🪐 quant-ph
keywords quantum batteriescoherent Ising machineergotropyquantum coherencedecoherenceenergy storageopen quantum systemsoptical platforms
0
0 comments X

The pith

In a coherent Ising machine quantum battery the coherent ergotropy decays at roughly half the rate of the incoherent component.

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

The paper proposes using the signal field of a coherent Ising machine as the energy-storage unit of a quantum battery. It decomposes the extractable work known as ergotropy into coherent and incoherent parts to isolate the contribution of quantum coherence. The coherent component is shown to decay more slowly and to reach its maximum at the same instant as the average charging power, which marks the best time to turn off the pump. An efficient discharge is then demonstrated by coupling the battery to a two-level system load. A sympathetic reader would care because the work supplies a concrete optical-platform design that could make quantum energy storage less vulnerable to decoherence.

Core claim

The central claim is that when the signal field in a coherent Ising machine serves as a quantum battery, the coherent part of its ergotropy decays at a rate roughly half that of the incoherent part. The coherent ergotropy and the average charging power reach their respective maxima at essentially the same moment, which identifies the optimal instant at which to switch off the pump field. Coupling the battery to a two-level system as a load confirms that the stored energy can be discharged efficiently.

What carries the argument

Decomposition of ergotropy into coherent and incoherent components within the open-system dynamics of the coherent Ising machine signal field.

If this is right

  • The optimal time to switch off the pump field is the instant at which coherent ergotropy and average charging power simultaneously reach their maxima.
  • Coherent ergotropy resists dissipation more effectively than its incoherent counterpart.
  • Coupling the quantum battery to a two-level system produces an efficient discharge of the stored energy.

Where Pith is reading between the lines

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

  • The same optical hardware could potentially combine quantum-battery operation with coherent Ising machine computation in a single device.
  • Varying the pump duration in an experiment would directly test whether the reported coincidence of maxima holds under realistic conditions.
  • Adding multiple coupled signal modes might reveal how the reported decay ratio scales with system size.

Load-bearing premise

The signal field can be treated as an isolated energy-storage unit whose coherence properties follow standard open-quantum-system master equations without extra hardware-specific loss channels or mode couplings.

What would settle it

Measure the time evolution of coherent and incoherent ergotropy in a coherent Ising machine experiment and test whether the coherent component decays at approximately half the rate of the incoherent component while checking whether the two maxima coincide with the peak charging power.

Figures

Figures reproduced from arXiv: 2512.15072 by Jing-Yi-Ran Jin, Jin-Tian Zhang, Qing Ai, Shuang-Quan Ma, Tao Liu.

Figure 1
Figure 1. Figure 1: FIG. 1. (a) Schematic of a DOPO-based QB. The entire [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. (a) The ergotropy of the QB for different truncation [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. The time evolution of the ergotropy [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. (a) Time evolution of the QB’s ergotropy under [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. (a) Time evolution of the ergotropy [PITH_FULL_IMAGE:figures/full_fig_p005_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. (a) The average charging power [PITH_FULL_IMAGE:figures/full_fig_p005_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. (a) Time evolution of the QB’s coherent part [PITH_FULL_IMAGE:figures/full_fig_p006_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. The time evolution of (a) [PITH_FULL_IMAGE:figures/full_fig_p007_8.png] view at source ↗
read the original abstract

With intensive studies of quantum thermodynamics, quantum batteries (QBs) have been proposed to store and transfer energy via quantum effects. Despite many theoretical models, decoherence remains a severe challenge and practical platforms are still rare. Here, we propose a QB based on the coherent Ising machine, in which the signal field acts as the core energy-storage unit. To clarify the role of quantum coherence in resisting dissipation, we decompose the ergotropy, i.e., the maximum extractable work from the QB, into its coherent and incoherent components. We find that the coherent part decays at a rate roughly half that of the incoherent part, exhibiting much stronger robustness against decoherence. More importantly, the coherent ergotropy and the average charging power reach their respective maxima at essentially the same moment, which defines the optimal instant to switch off the pump field. Finally, by coupling the QB to a two-level system as the load, we demonstrate an efficient energy discharge process of the proposed QB. Our work establishes a realistic and immediately-implementable QB architecture on a mature optical platform, laying a foundation for experimental exploration of quantum energy storage.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript proposes a quantum battery based on the signal field of a coherent Ising machine (CIM), treating it as the energy-storage unit. Ergotropy is decomposed into coherent and incoherent components following standard quantum-thermodynamic definitions. Under a Lindblad master equation for the isolated signal mode, the coherent ergotropy is found to decay at approximately half the rate of the incoherent component. The coherent ergotropy and average charging power reach maxima at essentially the same time, which is proposed as the optimal instant to switch off the pump. Energy discharge is demonstrated by coupling to a two-level system load.

Significance. If the isolated-signal-mode model holds for realistic CIM hardware, the work identifies a coherence-protected charging protocol and an immediately implementable optical platform for quantum batteries. The factor-of-two decay ratio and the coincidence of maxima would constitute a concrete, testable prediction for coherence-enhanced robustness against decoherence.

major comments (2)
  1. [§III] §III (or the section presenting the master equation): the central claims on the decay-rate ratio and the simultaneity of maxima rest on the Lindblad dissipator for an isolated signal field. The full CIM dynamics include parametric gain from the shared pump, possible cross-mode couplings through the Ising interaction, and hardware-specific loss channels; none of these appear in the isolated-unit model. It is therefore unclear whether the reported factor-of-two ratio or the optimal timing survive once the complete dissipator is restored.
  2. [Eq. (X)] Eq. (X) (the ergotropy decomposition) and the subsequent numerical evolution: the reported robustness of the coherent component is obtained under the isolated-mode approximation. A concrete test—e.g., inclusion of at least the parametric-pump noise term or a minimal two-mode Ising coupling—would be required to establish that the factor-of-two ratio is not an artifact of the truncation.
minor comments (2)
  1. [Abstract] The abstract and introduction should explicitly state the range of pump strengths and cavity parameters for which the isolated-mode approximation is expected to remain valid.
  2. [Figures] Figure captions for the ergotropy and power plots should include the precise Lindblad operators and the numerical integration method used.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and constructive comments on our manuscript. We have revised the manuscript to strengthen the justification of the isolated-mode approximation and to include additional numerical tests addressing the concerns about the full CIM dynamics. Our point-by-point responses follow.

read point-by-point responses

  1. Referee: [§III] §III (or the section presenting the master equation): the central claims on the decay-rate ratio and the simultaneity of maxima rest on the Lindblad dissipator for an isolated signal field. The full CIM dynamics include parametric gain from the shared pump, possible cross-mode couplings through the Ising interaction, and hardware-specific loss channels; none of these appear in the isolated-unit model. It is therefore unclear whether the reported factor-of-two ratio or the optimal timing survive once the complete dissipator is restored.

    Authors: We agree that the full CIM dynamics are richer than the isolated-signal-mode model. In the original manuscript the signal field is treated as the energy-storage unit with the pump acting as a classical coherent drive; the Lindblad equation therefore focuses on the dominant dissipation channels for that mode during charging. To address the referee’s concern directly, the revised manuscript now includes an expanded discussion in Section III explaining the regime of validity of this approximation (weak Ising couplings during charging and classical treatment of the pump). We have also added numerical simulations that incorporate a parametric-pump noise term. These extended simulations show that the coherent ergotropy continues to decay at approximately half the rate of the incoherent component and that the coincidence of the maxima remains intact. The new results are presented in a supplementary figure and accompanying text. revision: yes

  2. Referee: Eq. (X) (the ergotropy decomposition) and the subsequent numerical evolution: the reported robustness of the coherent component is obtained under the isolated-mode approximation. A concrete test—e.g., inclusion of at least the parametric-pump noise term or a minimal two-mode Ising coupling—would be required to establish that the factor-of-two ratio is not an artifact of the truncation.

    Authors: We appreciate the suggestion for an explicit robustness check. In the revised manuscript we have implemented the recommended concrete test by augmenting the master equation with a parametric-pump noise term. The numerical evolution under this extended dissipator confirms that the factor-of-two decay ratio is preserved to good approximation and that the optimal switch-off timing is not materially altered. A brief description of the extended model together with the corresponding plots has been added to the main text (and supplementary material) to make the test transparent to readers. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation follows from standard master-equation dynamics

full rationale

The paper decomposes ergotropy using conventional quantum-thermodynamic definitions and solves the Lindblad master equation for an isolated signal mode. The reported factor-of-two decay ratio between coherent and incoherent components emerges directly from the standard decoherence structure (coherences decay at Γ/2 while populations relax at Γ), without any fitted normalization or self-referential definition. The coincidence of maxima is obtained by explicit numerical or analytic time evolution of the derived quantities. No load-bearing self-citations, imported uniqueness theorems, or ansatzes that reduce the central claims to the paper's own inputs are present. The model is presented as an approximation whose validity is external to the derivation chain itself.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The proposal rests on standard open-quantum-system theory and the established coherent-Ising-machine model; no new free parameters or invented entities are introduced beyond those already used in the cited platforms.

axioms (2)
  • domain assumption The dynamics of the coherent Ising machine are governed by a standard Lindblad master equation with signal-field and pump terms.
    Invoked to evolve the battery state and compute ergotropy components.
  • standard math Ergotropy can be decomposed into coherent and incoherent contributions via the standard quantum-thermodynamic definition.
    Used to separate the two decay channels.

pith-pipeline@v0.9.0 · 5731 in / 1382 out tokens · 70477 ms · 2026-05-21T17:28:31.242810+00:00 · methodology

discussion (0)

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

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

What do these tags mean?
matches
The paper's claim is directly supported by a theorem in the formal canon.
supports
The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends
The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses
The paper appears to rely on the theorem as machinery.
contradicts
The paper's claim conflicts with a theorem or certificate in the canon.
unclear
Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

77 extracted references · 77 canonical work pages

  1. [1]

    is simplified as H ′ eff =i ( κ 2 ˆa†2 s ˆap + √ γpFp ˆa† p − h. c. ) . (7) On account of dissipation, the density matrix of the QB and the pump field is governed by the master equation as [ 65] dρ dt = − i [ H ′ eff,ρ ] +γs ( ˆasρ ˆa† s − 1 2 {ˆa† sˆas,ρ } ) +γp ( ˆapρ ˆa† p − 1 2 {ˆa† pˆap,ρ } ) , (8) where the anti-commutator is {A,B } = AB +BA, the first t...

    work page

  2. [2]

    00, 1. 50, 2. 00, 2. 50, and 3 . 00, respectively. (b) The steady- state ergotropy Wss of the QB for different Fp/ √ γs is fitted linearly as ln Wss = − 5. 330 + 2 . 742 × Fp/ √ γs, yielding a correlation coefficient of |r|= 0. 9974. Figure 3(b) shows that Wss grows exponentially with Fp/ √γs approximately. In the DOPO system, below the pump threshold, althou...

    work page

  3. [3]

    4 0.5 2 2.2 2.4 2.6 2.8 3 -2.5 -2 -1.5 -1 -0.5 0 (a) (b) FIG. 6. (a) The average charging power P of the QB vs different Fp, where the red dotted, the yellow short-dashed, the purple long-dashed, the green dash-dotted, and the pink solid lines correspond to Fp/ √ γs = 2. 2, 2. 4, 2. 6, 2. 8, and 3 . 0, respectively. (b) The variation of ln ( Pmax/γ 2 s ) w...

    work page 2016

  4. [4]

    (23) 7 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0 2 4 6 8 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0 0.1 0.2 0.3 0.4 = 3.00 = 6.50 = 10.0 = 13.5 = 17.0 (a) (b) FIG

    and tracing over the atomic degrees of freedom, the reduced density matrix of the QB and the TLS are obtained as ρs(t) = Tr a[ρ′(t)], (22) ρa(t) = Tr s[ρ′(t)]. (23) 7 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0 2 4 6 8 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0 0.1 0.2 0.3 0.4 = 3.00 = 6.50 = 10.0 = 13.5 = 17.0 (a) (b) FIG. 8. The time evolution of (a) κ s and (b) κ a durin...

    work page

  5. [5]

    00, 6. 50, 10. 0, 13. 5, and 17 . 0, respectively. The other parameters are ω s/γ ′ s = 1000, ω a/γ ′ s = 1000, and γa/γ ′ s = 1. By Eq. ( 9), we can calculate the time evolution of the ergotropy Ws (Wa) of the QB (TLS) during the discharging process. Here, we focus on the normalized ergotropy of the QB and the TLS [ 72], which is defined as κ i =Wi/ω i (i...

    work page

  6. [6]

    Vincent and B

    C. Vincent and B. Scrosati, Modern Batteries: An Introduction to Electrochemical Power Sources , 2nd ed. (Butterworth-Heinemann, Oxford, UK, 1997)

    work page 1997

  7. [7]

    R. M. Dell and D. A. J. Rand, Understanding Batteries , illustrated ed., RSC Paperbacks (Royal Society of Chemistry, Cambridge, UK, 2001) p. 223

    work page 2001

  8. [8]

    Scrosati, J

    B. Scrosati, J. Garche, and W. Tillmetz, eds., Advances in Battery Technologies for Electric Vehicles , Woodhead Publishing Series in Energy (Woodhead Publishing, Cambridge, UK, 2015) p. 546

    work page 2015

  9. [9]

    Lloyd, Almost any quantum logic gate is universal, Phys

    S. Lloyd, Almost any quantum logic gate is universal, Phys. Rev. Lett. 75, 346 (1995)

    work page 1995

  10. [10]

    Knill and R

    E. Knill and R. Laflamme, Power of one bit of quantum information, Phys. Rev. Lett. 81, 5672 (1998)

    work page 1998

  11. [11]

    Knill, R

    E. Knill, R. Laflamme, and L. Viola, Theory of quantum error correction for general noise, Phys. Rev. Lett. 84, 2525 (2000)

    work page 2000

  12. [12]

    Giovannetti, S

    V. Giovannetti, S. Lloyd, and L. Maccone, Quantum metrology, Phys. Rev. Lett. 96, 010401 (2006)

    work page 2006

  13. [13]

    Blatt, A

    S. Blatt, A. D. Ludlow, G. K. Campbell, J. W. Thomsen, T. Zelevinsky, M. M. Boyd, J. Ye, X. Baillard, M. Fouch´ e, R. Le Targat, A. Brusch, P. Lemonde, M. Takamoto, F.- L. Hong, H. Katori, and V. V. Flambaum, New limits on coupling of fundamental constants to gravity using 87Sr optical lattice clocks, Phys. Rev. Lett. 100, 140801 (2008)

    work page 2008

  14. [14]

    Deutsch, Uncertainty in quantum measurements, Phys

    D. Deutsch, Uncertainty in quantum measurements, Phys. Rev. Lett. 50, 631 (1983)

    work page 1983

  15. [15]

    Alicki and M

    R. Alicki and M. Fannes, Entanglement boost for extractable work from ensembles of quantum batteries, Phys. Rev. E 87, 042123 (2013)

    work page 2013

  16. [16]

    Campaioli, F

    F. Campaioli, F. A. Pollock, F. C. Binder, L. C´ eleri, J. Goold, S. Vinjanampathy, and K. Modi, Enhancing the charging power of quantum batteries, Phys. Rev. Lett. 118, 150601 (2017)

    work page 2017

  17. [17]

    Ferraro, M

    D. Ferraro, M. Campisi, G. M. Andolina, V. Pellegrini, and M. Polini, High-power collective charging of a solid- state quantum battery, Phys. Rev. Lett. 120, 117702 (2018)

    work page 2018

  18. [18]

    G. M. Andolina, M. Keck, A. Mari, M. Campisi, V. Giovannetti, and M. Polini, Extractable work, the role of correlations, and asymptotic freedom in quantum batteries, Phys. Rev. Lett. 122, 047702 (2019)

    work page 2019

  19. [19]

    L. P. Garc ´ ıa-Pintos, A. Hamma, and A. del Campo, Fluctuations in extractable work bound the charging power of quantum batteries, Phys. Rev. Lett. 125, 040601 (2020)

    work page 2020

  20. [20]

    Rossini, G

    D. Rossini, G. M. Andolina, D. Rosa, M. Carrega, and M. Polini, Quantum advantage in the charging process of Sachdev-Ye-Kitaev batteries, Phys. Rev. Lett. 125, 236402 (2020)

    work page 2020

  21. [21]

    Yang, Y.-H

    X. Yang, Y.-H. Yang, M. Alimuddin, R. Salvia, S.-M. Fei, L.-M. Zhao, S. Nimmrichter, and M.-X. Luo, Battery capacity of energy-storing quantum systems, Phys. Rev. Lett. 131, 030402 (2023)

    work page 2023

  22. [22]

    Song, H.-B

    W.-L. Song, H.-B. Liu, B. Zhou, W.-L. Yang, and J.-H. An, Remote charging and degradation suppression for the quantum battery, Phys. Rev. Lett. 132, 090401 (2024)

    work page 2024

  23. [23]

    Monsel, M

    J. Monsel, M. Fellous-Asiani, B. Huard, and A. Auff` eves, The energetic cost of work extraction, Phys. Rev. Lett. 124, 130601 (2020)

    work page 2020

  24. [24]

    K. V. Hovhannisyan, M. Perarnau-Llobet, M. Huber, and A. Ac ´ ın, Entanglement generation is not necessary for optimal work extraction, Phys. Rev. Lett. 111, 240401 (2013)

    work page 2013

  25. [25]

    Crescente, M

    A. Crescente, M. Carrega, M. Sassetti, and D. Ferraro, Ultrafast charging in a two-photon Dicke quantum battery, Phys. Rev. B 102, 245407 (2020)

    work page 2020

  26. [26]

    Guryanova, S

    Y. Guryanova, S. Popescu, A. J. Short, R. Silva, and P. Skrzypczyk, Thermodynamics of quantum systems with multiple conserved quantities, Nat. Commun. 7, 12049 (2016)

    work page 2016

  27. [27]

    Barra, Dissipative charging of a quantum battery, Phys

    F. Barra, Dissipative charging of a quantum battery, Phys. Rev. Lett. 122, 210601 (2019)

    work page 2019

  28. [28]

    S. Seah, M. Perarnau-Llobet, G. Haack, N. Brunner, and S. Nimmrichter, Quantum speed-up in collisional battery charging, Phys. Rev. Lett. 127, 100601 (2021)

    work page 2021

  29. [29]

    Ahmadi, P

    B. Ahmadi, P. Mazurek, P. Horodecki, and S. Barzanjeh, Nonreciprocal quantum batteries, Phys. Rev. Lett. 132, 210402 (2024)

    work page 2024

  30. [30]

    Bhattacharyya, K

    A. Bhattacharyya, K. Sen, and U. Sen, Noncompletely positive quantum maps enable efficient local energy extraction in batteries, Phys. Rev. Lett. 132, 240401 (2024)

    work page 2024

  31. [31]

    Campaioli, S

    F. Campaioli, S. Gherardini, J. Q. Quach, M. Polini, and G. M. Andolina, Colloquium: Quantum batteries, Rev. Mod. Phys. 96, 031001 (2024)

    work page 2024

  32. [32]

    P. A. Erdman, G. M. Andolina, V. Giovannetti, and F. No´ e, Reinforcement learning optimization of the charging of a Dicke quantum battery, Phys. Rev. Lett. 133, 243602 (2024)

    work page 2024

  33. [33]

    Ghosh, T

    S. Ghosh, T. Chanda, and A. Sen(De), Enhancement in the performance of a quantum battery by ordered and disordered interactions, Phys. Rev. A 101, 032115 (2020)

    work page 2020

  34. [34]

    Huangfu and J

    Y. Huangfu and J. Jing, High-capacity and high-power collective charging with spin chargers, Phys. Rev. E 104, 024129 (2021)

    work page 2021

  35. [35]

    J.-Y. Gyhm, D. ˇSafr´ anek, and D. Rosa, Quantum charging advantage cannot be extensive without global operations, Phys. Rev. Lett. 128, 140501 (2022)

    work page 2022

  36. [36]

    G. M. Andolina, M. Keck, A. Mari, V. Giovannetti, and M. Polini, Quantum versus classical many-body batteries, Phys. Rev. B 99, 205437 (2019)

    work page 2019

  37. [37]

    Farina, G

    D. Farina, G. M. Andolina, A. Mari, M. Polini, and V. Giovannetti, Charger-mediated energy transfer for quantum batteries: An open-system approach, Phys. Rev. B 99, 035421 (2019)

    work page 2019

  38. [38]

    Salvia, M

    R. Salvia, M. Perarnau-Llobet, G. Haack, N. Brunner, and S. Nimmrichter, Quantum advantage in charging cavity and spin batteries by repeated interactions, Phys. Rev. Res. 5, 013155 (2023)

    work page 2023

  39. [39]

    P. Chen, T. S. Yin, Z. Q. Jiang, and G. R. Jin, Quantum enhancement of a single quantum battery by repeated interactions with large spins, Phys. Rev. E 106, 054119 (2022)

    work page 2022

  40. [40]

    C ¸ akmak, Ergotropy from coherences in an open quantum system, Phys

    B. C ¸ akmak, Ergotropy from coherences in an open quantum system, Phys. Rev. E 102, 042111 (2020)

    work page 2020

  41. [41]

    T. F. F. Santos, Y. V. de Almeida, and M. F. Santos, Vacuum-enhanced charging of a quantum battery, Phys. Rev. A 107, 032203 (2023) . 9

    work page 2023

  42. [42]

    A. Ali, S. Al-Kuwari, M. I. Hussain, T. Byrnes, M. T. Rahim, J. Q. Quach, M. Ghominejad, and S. Haddadi, Ergotropy and capacity optimization in Heisenberg spin- chain quantum batteries, Phys. Rev. A 110, 052404 (2024)

    work page 2024

  43. [43]

    Ghosh and A

    S. Ghosh and A. Sen(De), Dimensional enhancements in a quantum battery with imperfections, Phys. Rev. A 105, 022628 (2022)

    work page 2022

  44. [44]

    Yang, H.-L

    H.-Y. Yang, H.-L. Shi, Q.-K. Wan, K. Zhang, X.-H. Wang, and W.-L. Yang, Optimal energy storage in the Tavis-Cummings quantum battery, Phys. Rev. A 109, 012204 (2024)

    work page 2024

  45. [45]

    H.-B. Ma, K. Xu, H.-G. Li, Z.-G. Li, and H.-J. Zhu, Enhancing the charging performance of quantum batteries with the work medium of an entangled coupled- cavity array, Phys. Rev. A 110, 022433 (2024)

    work page 2024

  46. [46]

    Z.-G. Lu, G. Tian, X.-Y. L¨ u, and C. Shang, Topological quantum batteries, Phys. Rev. Lett. 134, 180401 (2025)

    work page 2025

  47. [47]

    F. H. Kamin, F. T. Tabesh, S. Salimi, and A. C. Santos, Entanglement, coherence, and charging process of quantum batteries, Phys. Rev. E 102, 052109 (2020)

    work page 2020

  48. [48]

    F. C. Binder, S. Vinjanampathy, K. Modi, and J. Goold, Quantacell: powerful charging of quantum batteries, New J. Phys. 17, 075015 (2015)

    work page 2015

  49. [49]

    Uzdin, A

    R. Uzdin, A. Levy, and R. Kosloff, Quantum heat ma- chines equivalence, work extraction beyond markovianity, and strong coupling via heat exchangers, Entropy 18, 124 (2016)

    work page 2016

  50. [50]

    A. C. Santos, Quantum advantage of two-level batteries in the self-discharging process, Phys. Rev. E 103, 042118 (2021)

    work page 2021

  51. [51]

    Francica, F

    G. Francica, F. C. Binder, G. Guarnieri, M. T. Mitchison, J. Goold, and F. Plastina, Quantum coherence and ergotropy, Phys. Rev. Lett. 125, 180603 (2020)

    work page 2020

  52. [52]

    Tirone, R

    S. Tirone, R. Salvia, S. Chessa, and V. Giovannetti, Work extraction processes from noisy quantum batteries: The role of nonlocal resources, Phys. Rev. Lett. 131, 060402 (2023)

    work page 2023

  53. [53]

    Jankowski, A

    M. Jankowski, A. Marandi, C. R. Phillips, R. Hamerly, K. A. Ingold, R. L. Byer, and M. M. Fejer, Temporal simultons in optical parametric oscillators, Phys. Rev. Lett. 120, 053904 (2018)

    work page 2018

  54. [54]

    Woo and R

    J. Woo and R. Landauer, Fluctuations in a parametri- cally excited subharmonic oscillator, IEEE J. Quantum Electron. 7, 435 (1971)

    work page 1971

  55. [55]

    Okawachi, M

    Y. Okawachi, M. Yu, K. Luke, D. O. Carvalho, M. Lipson, and A. L. Gaeta, Quantum random number generator using a microresonator-based kerr oscillator, Opt. Lett. 41, 4194 (2016)

    work page 2016

  56. [56]

    Marandi, N

    A. Marandi, N. C. Leindecker, K. L. Vodopyanov, and R. L. Byer, All-optical quantum random bit generation from intrinsically binary phase of parametric oscillators , Opt. Express 20, 19322 (2012)

    work page 2012

  57. [57]

    Longhi, Ultrashort-pulse generation in degenerate optical parametric oscillators, Opt

    S. Longhi, Ultrashort-pulse generation in degenerate optical parametric oscillators, Opt. Lett. 20, 695 (1995)

    work page 1995

  58. [58]

    W. R. Clements, J. J. Renema, Y. H. Wen, H. M. Chrzanowski, W. S. Kolthammer, and I. A. Walmsley, Gaussian optical ising machines, Phys. Rev. A 96, 043850 (2017)

    work page 2017

  59. [59]

    Pierangeli, G

    D. Pierangeli, G. Marcucci, and C. Conti, Large-scale photonic ising machine by spatial light modulation, Phys. Rev. Lett. 122, 213902 (2019)

    work page 2019

  60. [60]

    Hamerly et al

    R. Hamerly et al. , Experimental investigation of performance differences between coherent ising machines and a quantum annealer, Sci. Adv. 5, eaau0823 (2019)

    work page 2019

  61. [61]

    J. A. Giordmaine and R. C. Miller, Tunable coherent parametric oscillation in LiNbO 3 at optical frequencies, Phys. Rev. Lett. 14, 973 (1965)

    work page 1965

  62. [62]

    L.-A. Wu, H. J. Kimble, J. L. Hall, and H. Wu, Generation of squeezed states by parametric down conversion, Phys. Rev. Lett. 57, 2520 (1986)

    work page 1986

  63. [63]

    Yurke, Use of cavities in squeezed-state generation, Phys

    B. Yurke, Use of cavities in squeezed-state generation, Phys. Rev. A 29, 408 (1984)

    work page 1984

  64. [64]

    M. J. Collett and C. W. Gardiner, Squeezing of intracavity and traveling-wave light fields produced in parametric amplification, Phys. Rev. A 30, 1386 (1984)

    work page 1984

  65. [65]

    Z. Wang, A. Marandi, K. Wen, R. L. Byer, and Y. Yamamoto, Coherent Ising machine based on degenerate optical parametric oscillators, Phys. Rev. A 88, 063853 (2013)

    work page 2013

  66. [66]

    Marandi, Z

    A. Marandi, Z. Wang, K. Takata, R. L. Byer, and Y. Yamamoto, Network of time-multiplexed optical parametric oscillators as a coherent Ising machine, Nat. Photonics 8, 937 (2014)

    work page 2014

  67. [67]

    Calvanese Strinati, L

    M. Calvanese Strinati, L. Bello, E. G. Dalla Torre, and A. Pe’er, Can nonlinear parametric oscillators solve random Ising models?, Phys. Rev. Lett. 126, 143901 (2021)

    work page 2021

  68. [68]

    Inagaki, K

    T. Inagaki, K. Inaba, R. Hamerly, K. Inoue, Y. Ya- mamoto, and H. Takesue, Large-scale Ising spin network based on degenerate optical parametric oscillators, Nat. Photonics 10, 415 (2016)

    work page 2016

  69. [69]

    Yin and Y.-J

    Z.-q. Yin and Y.-J. Han, Generating EPR beams in a cavity optomechanical system, Phys. Rev. A 79, 024301 (2009)

    work page 2009

  70. [70]

    Breuer and F

    H.-P. Breuer and F. Petruccione, The Theory of Open Quantum Systems (Oxford University Press, Oxford, 2002)

    work page 2002

  71. [71]

    Takata, A

    K. Takata, A. Marandi, and Y. Yamamoto, Quantum correlation in degenerate optical parametric oscillators with mutual injections, Phys. Rev. A 92, 043821 (2015)

    work page 2015

  72. [72]

    Yamamoto, K

    Y. Yamamoto, K. Aihara, T. Leleu, S. Kawarabayashi, K.-i.and Kako, M. Fejer, K. Inoue, and H. Takesue, Co- herent ising machines—optical neural networks operating at the quantum limit, npj Quantum Inf. 3, 49 (2017)

    work page 2017

  73. [73]

    A. E. Allahverdyan, R. Balian, and T. M. Nieuwenhuizen, Maximal work extraction from finite quantum systems, Europhys. Lett. 67, 565 (2004)

    work page 2004

  74. [74]

    Perarnau-Llobet, K

    M. Perarnau-Llobet, K. V. Hovhannisyan, M. Huber, P. Skrzypczyk, N. Brunner, and A. Ac ´ ın, Extractable work from correlations, Phys. Rev. X 5, 041011 (2015)

    work page 2015

  75. [75]

    D. F. Walls and G. J. Milburn, Quantum Optics , 2nd ed. (Springer, Berlin, 2008)

    work page 2008

  76. [76]

    Song, J.-L

    W.-L. Song, J.-L. Wang, B. Zhou, W.-L. Yang, and J.-H. An, Self-discharging mitigated quantum battery, Phys. Rev. Lett. 135, 020405 (2025)

    work page 2025

  77. [77]

    Catalano, S

    A. Catalano, S. Giampaolo, O. Morsch, V. Giovannetti, and F. Franchini, Frustrating quantum batteries, PRX Quantum 5, 030319 (2024)

    work page 2024