Pith. sign in

REVIEW 5 major objections 4 minor 1 cited by

Entanglement-Driven Energy Exchange in a Two-Qubit Quantum Battery

T0 review · 5 major / 4 minor · reviewed 2026-08-10 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read This paper claims that in a two-qubit quantum battery, stronger entanglement between the two qubits causes more efficient energy transfer from the charger-coupled cell to the other cell.

desk verdict The paper's central claim relies on a Lindblad system that fails to preserve trace and an undefined detuning parameter, so the numerical basis collapses; desk reject. read the letter →

arxiv 2412.19715 v1 pith:LCNGVTRZ submitted 2024-12-27 quant-ph

Ahmed A. Zahia , M.Y.Abd-Rabbou , Ahmed M. Megahed This is my paper · ORCID
classification quant-ph MSC 81P6881P4081P4581S22 PACS 03.65.Ud03.65.Yz03.67.-a
keywords quantumbatteryentanglement-drivenenergytransfertwo-qubitconcurrenceLindbladmasterequationfluctuationsanisotropicXYcouplingopensystems
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 studies a two-qubit quantum battery in which one qubit (the primary cell) is charged by a cavity field and passes energy to a second qubit (the secondary cell) through their mutual coupling. Using the Lindblad master equation (the standard equation for a quantum system that exchanges energy with its environment) and concurrence (a standard two-qubit entanglement measure, from 0 to 1), it claims that the stronger the entanglement between the two qubits, the more effectively energy is transferred to the secondary cell. It reports that larger coherent-state amplitudes, stronger inter-cell coupling, and anisotropic XY interactions raise both entanglement and stored energy but also enlarge energy fluctuations, while detuning and dissipation suppress both. The paper concludes that entanglement in this system is not merely correlated with energy transfer but is a mechanism that facilitates and optimizes it.

What carries the argument

The central object is the two-qubit density matrix $\hat{\rho}(t)$, evolved from the initial coherent-charger state $|gg,\alpha\rangle$ under the Lindblad master equation with cavity decay $\kappa$ and qubit decay $\gamma$. The paper writes the resulting ten differential equations for the density-matrix elements, Eq. (2-a), and uses them to evaluate three metrics for the secondary qubit: stored energy $E(t)=\mathrm{Tr}(\hat{\rho}(t)\hat{H}_{QB})-\mathrm{Tr}(\hat{\rho}(0)\hat{H}_{QB})$, energy fluctuation $\Sigma(t)$ defined through the Heisenberg-evolved $\hat{H}_{QB}$, and concurrence $C(\hat{\rho})$ from the Wootters formula. The load-bearing identities are the Lindblad dissipator $D[\hat{O}]=\hat{O}\hat{\rho}\hat{O}^\dagger-\tfrac12\{\hat{O}^\dagger\hat{O},\hat{\rho}\}$ and the concurrence formula, with the anisotropy parameter $\zeta$ in the XY inter-cell coupling acting as the directionality switch that most changes the entanglement-energy relation.

What would settle it

Directly integrate the full Lindblad master equation (2) for the same Hamiltonian and initial coherent state, without passing through the truncated ODE system (2-a), and check whether the secondary-qubit stored energy $E(t)/\omega_q$ and concurrence $C(\hat{\rho}(t))$ reproduce the curves in Fig. 2 and Fig. 4; if they do not, or if preparing a more entangled initial state does not increase transferred energy, the claimed entanglement-driven transfer would be falsified.

Watch

Extended reading notes

Core claim

The paper's central claim is that the degree of entanglement between the primary qubit and the secondary qubit directly controls how much energy flows from the charger-coupled cell to the other cell. In its model, the normalized stored energy in the secondary qubit, $E(t)/\omega_q$, and the concurrence $C(\hat{\rho}(t))$ rise together as the coherent-state amplitude $\alpha$, the inter-cell coupling $g$, or the anisotropy parameter $\zeta$ is increased; conversely, detuning $\Delta$ and dissipation rates $\kappa$ and $\gamma$ suppress both quantities simultaneously. The paper interprets these parallel behaviors as evidence that enhanced entanglement significantly facilitates energy transfer, with anisotropy acting as an amplifier that strengthens both the transfer and the associated energy fluctuations.

Load-bearing premise

The whole numerical study rests on the ten differential equations in Eq. (2-a) being the correct Lindblad equations for the Hamiltonian (1); if those equations are wrong or inconsistent, every energy and concurrence curve follows from an invalid model.

Editorial extensions

If this is right

  • If the claim holds, tuning $g$ and $\zeta$ upward is a practical way to charge the secondary qubit faster, but the accompanying growth of $\Sigma(t)$ sets a stability ceiling.
  • Resonance ($\Delta=0$) should be maintained, since detuning suppresses both stored energy and concurrence; anisotropy partially compensates but at the cost of larger fluctuations.
  • Reducing dissipation $\kappa$ and $\gamma$ is not just about retaining energy but also about preserving the entanglement that, according to the model, transfers it.
  • The parametric energy-versus-concurrence curves provide a design chart: for a target stored energy, one can read off the entanglement level required and the fluctuation penalty paid.

Reading between the lines

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

  • A direct test of the causal direction would prepare the two qubits in an entangled initial state rather than the product state $|gg\rangle$ and measure the secondary cell's stored energy; the paper does not report this run, but its causal claim predicts a higher transfer rate.
  • If the mechanism is general, a chain of $N$ qubits should show the same nearest-neighbor mediation, with pairwise concurrence acting as the transfer catalyst; this extension is not explored in the paper.
  • The trade-off between stored energy and fluctuations suggests defining a battery quality factor, such as peak stored energy divided by peak fluctuation, as a single figure of merit; the paper's data are sufficient to compute it but the paper stops at qualitative correlations.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

5 major / 4 minor

Summary. The manuscript studies a two-qubit quantum battery in which the first qubit (primary cell) is coupled to a cavity charger and interacts with the second qubit (secondary cell) through an anisotropic XX interaction. The authors model the open system with a Lindblad master equation, reduce it to a system of ordinary differential equations for the density-matrix elements, and then numerically solve these equations to compute the stored energy of the second qubit, its energy fluctuations, and the concurrence between the two qubits. They report that stronger entanglement between the two cells correlates with more efficient energy transfer, and they explore the effects of coherent-state amplitude, detuning, coupling strength, anisotropy, and dissipation on these quantities. The central claim is that enhanced entanglement significantly facilitates energy transfer between the two qubits.

Significance. If the central claim were supported by a correct calculation, the paper would provide a useful parametric study of a two-qubit quantum battery and would strengthen the case that entanglement can be a resource for energy-transfer efficiency. The manuscript has some virtues: it does not fit free parameters to a target curve, and stored energy and concurrence are defined independently, so there is no built-in circularity in the correlation plots. However, the numerical foundation is invalid as written: the master-equation reduction in Eq. (2-a) is not a valid Lindblad system, the detuning parameter Δ is never defined, and the treatment of the coherent initial state is incomplete. As a result, all energy and concurrence curves lack a well-defined dynamical basis, and the paper's potential significance is not realized in this version.

major comments (5)
  1. [§1, Eq. (2-a)] The ODE system (2-a) is not a valid Lindblad system and cannot serve as the basis for the numerical results. The diagonal elements ρ22 and ρ33 are real by Hermiticity, yet their equations contain the complex coefficient Δ2 = i g ζ − r0²κ/2 (and Δ3 for ρ33), so dρ22/dt would acquire an imaginary part unless g = 0 or ρ22 = 0. In addition, the system is not trace-preserving: summing the diagonal equations does not give zero even in the closed-system limit κ = γ = 0; residual terms such as i g ζ ρ22 − 2 i g ζ ρ23 and −i x0 ρ31 + i x1 ρ43 remain. Since every energy and concurrence curve in Figs. 2–6 is computed from this system, the central claim is unsupported.
  2. [§1, Eq. (1) and Figs. 2–6] The detuning parameter Δ is swept in Figs. 2(b), 3(b), 4(b), 5(b), and 6(b) but is nowhere defined in the Hamiltonian (1) or in the text. The only frequencies introduced are ωc and ωq, and the combinations θ0, θ1, θ2 are defined in terms of n, not of Δ. Without a definition of Δ, these parameter scans have no physical interpretation.
  3. [§1, Eqs. (2-a) and (3)] The initial state (3) is a coherent state with support on all Fock states, but the ODE coefficients x0, x1, r0, r1 in (2-a) are defined for a single Fock number n. The manuscript does not specify a Fock-space truncation or an average over the coherent-state distribution |c_n|². Consequently the plotted curves do not correspond to any well-defined density-matrix evolution.
  4. [§2.2, Eqs. (6)–(7)] The energy-fluctuation formula in Eq. (6) uses the Heisenberg operator H(t)_QB = e^{iHt} H_QB e^{-iHt} for the unitary evolution under the full Hamiltonian H. This is inconsistent with the dissipative dynamics governed by the Lindblad master equation (2): for κ, γ ≠ 0 the evolution is not unitary, and the correct Heisenberg-picture generator includes dissipative terms. Since Fig. 3(d) and Fig. 6(d) include κ = 0.6, γ = 0.4, those fluctuation results are not justified.
  5. [§4 and §5] The text repeatedly states that entanglement 'facilitates' or 'drives' energy transfer, for example 'quantum entanglement proved a crucial mechanism... facilitating but also optimizing inter-qubit energy flow' in §5. However, the analysis only shows parametric correlations between concurrence and stored energy; no causal mechanism or controlled intervention is demonstrated. The causal wording overreaches the evidence presented.
minor comments (4)
  1. [§1, Eq. (2-a)] The notation '= ρ∗_21' appended to several lines is ambiguous; it is unclear whether these are defining relations, constraints, or duplications, and it should be removed or explained.
  2. [§2.1, Fig. 2(d)] The sentence 'when ζ = 1, the directional interaction partially counteracts dissipation, enabling the system to retain more energy compared to the anisotropic case' appears to contain a typo; the comparison should likely be with the isotropic case (ζ = 0), given the following sentence.
  3. [Throughout] There are many missing spaces in the text (e.g., 'Wepositaquantumbatterymodelcomprisingtwocells'), which should be corrected.
  4. [References] Reference [22] has formatting errors in the author names ('Ju-YeonGyhmandUweRFischer'), and the introduction's roadmap omits Section 4, which nonetheless exists in the manuscript.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: stored energy and concurrence are independent functions of the same Lindblad solution; the causal wording is an overclaim, not a circular derivation.

full rationale

The paper's central relation is not constructed from its own output. Stored energy in the secondary cell is defined independently as E(t) = Tr(ρ(t)Ĥ_QB) − Tr(ρ(0)Ĥ_QB) with Ĥ_QB = (ω_q/2)σ_z^(2) (Eq. 5), and entanglement is defined by the Wootters concurrence C(ρ) (Eqs. 8–9). Both are evaluated on the same density-matrix solution of the Lindblad master equation, so their parametric correlation is a dynamical consequence rather than a fitted or tautological identity. No parameter is fitted to energy or concurrence targets; λ, g, κ, γ, ζ, and α are chosen inputs. The one self-citation [16] is an unrelated steering paper cited in a general list and is not load-bearing. The abstract's statement that enhanced entanglement 'facilitates' energy transfer is a causal interpretation of a computed correlation, which is an overclaim but not a circular reduction. The ODE system (2-a) has apparent structural errors (complex rates multiplying real diagonal elements and a trace that does not appear to vanish, even at κ=γ=0) and the detuning Δ used in Figs. 2–6 is not defined in Hamiltonian (1); however, these are correctness and reproducibility defects, not cases where the prediction is equivalent to its input by construction. Therefore the circularity score is low.

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

The central claim does not depend on fitted parameters, so the free-parameter list is empty. The load-bearing axioms are the validity of the Lindblad ODE system, the partial trace over the cavity, and the unitary fluctuation formula, none of which is demonstrated or checked. The paper introduces no new physical entities.

assumptions (5)
  • domain assumption The Lindblad master equation with Markovian and secular approximations describes the open system.
    Invoked in Eq (2) without deriving the Lindblad form or specifying the bath spectral densities.
  • domain assumption The reduced two-qubit dynamics is correctly captured by the ODE system Eq (2-a) at fixed photon number n.
    The paper never shows the partial trace over the cavity or the summation over coherent-state photon numbers; x0, x1, r0, r1 depend on n but the rho elements do not carry an index n.
  • domain assumption The initial coherent state can be treated by solving the master equation per Fock sector and recombining the results.
    Eq (3) expands the coherent state over Fock states, but the recombination rule is not stated.
  • ad hoc to paper Energy fluctuations are computed using unitary Heisenberg evolution of H_QB under the full Hamiltonian.
    Eq (7) ignores the Lindblad dissipator; in an open system the Heisenberg picture should use the adjoint generator.
  • domain assumption Concurrence is computed on the two-qubit reduced density matrix after tracing out the cavity.
    Wootters concurrence is standard, but the paper does not explicitly state that the cavity is traced out before applying Eq (8).

how reviews work

0 comments
Cite this review

Pith. "Pith review of Entanglement-Driven Energy Exchange in a Two-Qubit Quantum Battery." pith.science (2026). https://pith.science/paper/LCNGVTRZ

@misc{pith2026241219715,
  author       = {Pith},
  title        = {Pith review of: Entanglement-Driven Energy Exchange in a Two-Qubit Quantum Battery},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/LCNGVTRZ}},
  note         = {Machine review of arXiv:2412.19715}
}
read the original abstract

This study investigates the dynamics of quantum batteries (QBs), focusing on the pivotal role of quantum entanglement in mediating inter-cellular energy transfer within a two-cell configuration (two-qubit), wherein one cell is directly coupled to the charging source. Employing the Lindblad master equation to model the system's evolution, the influence of coherent state amplitudes, detuning, inter-cellular coupling strength, and dissipation rates on stored energy, energy fluctuations, concurrence-quantified entanglement, and their parametric interrelations is scrutinized. Our results indicate a direct correlation between the degree of entanglement and energy transfer efficiency between the qubits. Specifically, the stronger the entanglement between primary cell, which is connected to the charger, and secondary cell, the more effectively energy is transferred. This demonstrates that enhanced entanglement significantly facilitates energy transfer between the two qubits.

Figures

Figures reproduced from arXiv: 2412.19715 by the authors.

Figure 1
Figure 1. schematic diagram of a quantum battery system illustrating energy transfer between pri [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. The normalized stored energy E(t)/ωq as a function of the scaled time λt across isotropic interaction (solid-curve) and anisotropic interaction (dashed-curve), with system parameters: (a) α is varied, while ∆ = 0, g = 1, κ = γ = 0. (b) ∆ is varied, while g = 1, α = 2, κ = γ = 0. (c) g is varied, while ∆ = 0, α = 2, and κ = γ = 0. (d) κ, and γ are altered, while ∆ = 0, α = 1, and g = 1. as coupling strength (g), detu… view at source ↗
Figure 3
Figure 3. Energy fluctuations are a direct reflection of the inherent quantum mechanical uncertainty in [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figures from the paper (4 more)
Figure 3
Figure 3. Figure 3: The normalized energy fluctuation Σ(t)/ωq with respect to scaled time λt with the same parameters that are displayed in [PITH_FULL_IMAGE:figures/full_fig_p007_3.png]
Figure 4
Figure 4. Figure 4: The entanglement behaviour by the Concurrence [PITH_FULL_IMAGE:figures/full_fig_p008_4.png]
Figure 5
Figure 5. Figure 5: The Parametric relation between the normalized stored energy [PITH_FULL_IMAGE:figures/full_fig_p009_5.png]
Figure 6
Figure 6. Figure 6: The parametric relation between the normalized energy fluctuation [PITH_FULL_IMAGE:figures/full_fig_p011_6.png]

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Fluctuation in energy extraction from quantum batteries: How open should the system be to control it?

    quant-ph 2025-05 conditional novelty 5.0 of 10

    For fixed quantum batteries, random unitary, CPTP, and general quantum maps extract the same average energy, but fluctuations vanish only in a Cesàro limit over auxiliary dimensions; finite-ancilla scalings are 1/n (C...

Reference graph

Works this paper leans on

35 extracted references · 35 canonical work pages · cited by 1 Pith paper

  1. [1]

    Entanglement boost for extractable work from ensembles of quantum batteries

    Robert Alicki and Mark Fannes. Entanglement boost for extractable work from ensembles of quantum batteries. Phys. Rev. E , 87(4):042123, 2013

    work page 2013

  2. [2]

    High-power collective charging of a solid-state quantum battery

    Dario Ferraro, Michele Campisi, Gian Marcello Andolina, Vittorio Pellegrini, and Marco Polini. High-power collective charging of a solid-state quantum battery. Phys. Rev. Lett. , 120(11):117702, 2018

    work page 2018

  3. [3]

    Quantum batteries.Thermo- dynamics in the Quantum Regime: Fundamental Aspects and New Directions , pages 207–225, 2018

    Francesco Campaioli, Felix A Pollock, and Sai Vinjanampathy. Quantum batteries.Thermo- dynamics in the Quantum Regime: Fundamental Aspects and New Directions , pages 207–225, 2018

    work page 2018

  4. [4]

    Role of quantum coherence in the thermodynamics of energy transfer

    Ivan Henao and Roberto M Serra. Role of quantum coherence in the thermodynamics of energy transfer. Phys. Rev. E , 97(6):062105, 2018

    work page 2018

  5. [5]

    Quantum speed limits: from heisenberg’s uncertainty principle to optimal quantum control.J

    Sebastian Deffner and Steve Campbell. Quantum speed limits: from heisenberg’s uncertainty principle to optimal quantum control.J. Phys. A: Math. Theor. , 50(45):453001, 2017

    work page 2017

  6. [6]

    The role of entanglement in dynamical evolution

    Vittorio Giovannetti, Seth Lloyd, and Lorenzo Maccone. The role of entanglement in dynamical evolution. Europhys. Lett., 62(5):615, 2003

    work page 2003

  7. [7]

    Entangle- ment generation is not necessary for optimal work extraction.Phys

    Karen V Hovhannisyan, Martí Perarnau-Llobet, Marcus Huber, and Antonio Acín. Entangle- ment generation is not necessary for optimal work extraction.Phys. Rev. Lett., 111(24):240401, 2013

    work page 2013

  8. [8]

    Quantacell: powerful charg- ing of quantum batteries.New J

    Felix C Binder, Sai Vinjanampathy, Kavan Modi, and John Goold. Quantacell: powerful charg- ing of quantum batteries.New J. Phys. , 17(7):075015, 2015

    work page 2015

Show all 35 references
  1. [9]

    Enhancing the charging power of quantum batteries.Phys

    Francesco Campaioli, Felix A Pollock, Felix C Binder, Lucas Céleri, John Goold, Sai Vinjanam- pathy, and Kavan Modi. Enhancing the charging power of quantum batteries.Phys. Rev. Lett., 118(15):150601, 2017

    2017

  2. [10]

    Spin-chain model of a many-body quantum battery.Phys

    Thao P Le, Jesper Levinsen, Kavan Modi, Meera M Parish, and Felix A Pollock. Spin-chain model of a many-body quantum battery.Phys. Rev. A , 97(2):022106, 2018

    2018

  3. [11]

    Charger-mediated energy transfer in exactly solvable models for quantum batteries

    Gian Marcello Andolina, Donato Farina, Andrea Mari, Vittorio Pellegrini, Vittorio Giovannetti, and Marco Polini. Charger-mediated energy transfer in exactly solvable models for quantum batteries. Phys. Rev. B , 98(20):205423, 2018

    2018

  4. [12]

    Thermody- namical approach to quantifying quantum correlations.Phys

    Jonathan Oppenheim, Michał Horodecki, Paweł Horodecki, and Ryszard Horodecki. Thermody- namical approach to quantifying quantum correlations.Phys. Rev. Lett., 89(18):180402, 2002

    2002

  5. [13]

    Optimal work extraction and thermodynamics of quantum measurements and correlations.Phys

    Gonzalo Manzano, Francesco Plastina, and Roberta Zambrini. Optimal work extraction and thermodynamics of quantum measurements and correlations.Phys. Rev. Lett., 121(12):120602, 2018

    2018

  6. [14]

    Quantum entan- glement

    Horodecki Ryszard, Horodecki Pawel, Horodecki Michal, and Horodecki Karol. Quantum entan- glement. Rev. Mod. Phys, 81(2):865–942, 2009

    2009

  7. [15]

    Dynamics of quantum entanglement

    Karol Życzkowski, Paweł Horodecki, Michał Horodecki, and Ryszard Horodecki. Dynamics of quantum entanglement. Phys. Rev. A , 65(1):012101, 2001. 13

    2001

  8. [16]

    Bidirectional field- steering and atomic steering induced by a magnon mode in a qubit-photon system.Sci

    Ahmed A Zahia, MY Abd-Rabbou, Ahmed M Megahed, and A-SF Obada. Bidirectional field- steering and atomic steering induced by a magnon mode in a qubit-photon system.Sci. Rep., 13(1):14943, 2023

    2023

  9. [17]

    Substituting quantum entanglement for communication

    Richard Cleve and Harry Buhrman. Substituting quantum entanglement for communication. Phys. Rev. A , 56(2):1201, 1997

    1997

  10. [18]

    Williams

    Richard J Hughes and Colin P. Williams. Quantum computing: The final frontier?IEEE Intell. Syst. Their Appl , 15(5):10–18, 2000

    2000

  11. [19]

    Entanglement-based secure quantum cryptography over 1,120 kilometres.Nature, 582(7813):501–505, 2020

    Juan Yin, Yu-Huai Li, Sheng-Kai Liao, Meng Yang, Yuan Cao, Liang Zhang, Ji-Gang Ren, Wen- Qi Cai, Wei-Yue Liu, Shuang-Lin Li, et al. Entanglement-based secure quantum cryptography over 1,120 kilometres.Nature, 582(7813):501–505, 2020

    2020

  12. [20]

    Entanglement, coherence, and charging process of quantum batteries.Phys

    FH Kamin, FT Tabesh, S Salimi, and Alan C Santos. Entanglement, coherence, and charging process of quantum batteries.Phys. Rev. E , 102(5):052109, 2020

    2020

  13. [21]

    Entanglement, coherence, and extractable work in quantum batteries.Phys

    Hai-Long Shi, Shu Ding, Qing-Kun Wan, Xiao-Hui Wang, and Wen-Li Yang. Entanglement, coherence, and extractable work in quantum batteries.Phys. Rev. Lett., 129(13):130602, 2022

    2022

  14. [22]

    Beneficialanddetrimentalentanglementforquantumbattery charging

    Ju-YeonGyhmandUweRFischer. Beneficialanddetrimentalentanglementforquantumbattery charging. A VS Quantum Sci., 6(1), 2024

    2024

  15. [23]

    Dissipative dynamics of an open quantum battery.New J

    Matteo Carrega, Alba Crescente, Dario Ferraro, and Maura Sassetti. Dissipative dynamics of an open quantum battery.New J. Phys. , 22(8):083085, 2020

    2020

  16. [24]

    Enhancing the performance of an open quantum battery via environment engineering.Phys

    Kai Xu, Han-Jie Zhu, Guo-Feng Zhang, and Wu-Ming Liu. Enhancing the performance of an open quantum battery via environment engineering.Phys. Rev. E , 104(6):064143, 2021

    2021

  17. [25]

    Work fluctuations and entanglement in quantum batteries

    Satoya Imai, Otfried Gühne, and Stefan Nimmrichter. Work fluctuations and entanglement in quantum batteries. Phys. Rev. A , 107(2):022215, 2023

    2023

  18. [26]

    Oxford University Press, USA, 2002

    Heinz-Peter Breuer and Francesco Petruccione.The theory of open quantum systems . Oxford University Press, USA, 2002

    2002

  19. [27]

    Decoherence-free subspaces and subsystems

    Daniel A Lidar and K Birgitta Whaley. Decoherence-free subspaces and subsystems. InIrre- versible quantum dynamics , pages 83–120. Springer, 2003

    2003

  20. [28]

    Photon statistics on the extreme entanglement

    Yang Zhang, Jun Zhang, and Chang-shui Yu. Photon statistics on the extreme entanglement. Sci. Rep., 6(1):24098, 2016

    2016

  21. [29]

    Universal lindblad equation for open quantum systems

    Frederik Nathan and Mark S Rudner. Universal lindblad equation for open quantum systems. Phys. Rev. B , 102(11):115109, 2020

    2020

  22. [30]

    The promise and challenges of quantum computing for energy storage.Joule, 2(5):810–813, 2018

    Alan Ho, Jarrod McClean, and Shyue Ping Ong. The promise and challenges of quantum computing for energy storage.Joule, 2(5):810–813, 2018

    2018

  23. [31]

    A wide dynamic range diamond quantum sensor as an electric vehicle battery monitor

    YujiHatano, JunyaTanigawa, AkimichiNakazono, TakeharuSekiguchi, ShinobuOnoda, Takeshi Ohshima, Takayuki Iwasaki, and Mutsuko Hatano. A wide dynamic range diamond quantum sensor as an electric vehicle battery monitor. Philos. Trans. R. Soc., A , 382(2265):20220312, 2024. 14

    2024

  24. [32]

    Ultrafast charging in a two-photon dicke quantum battery.Phys

    Alba Crescente, Matteo Carrega, Maura Sassetti, and Dario Ferraro. Ultrafast charging in a two-photon dicke quantum battery.Phys. Rev. B , 102(24):245407, 2020

    2020

  25. [33]

    Charging and energy fluctuations of a driven quantum battery.New J

    A Crescente, M Carrega, M Sassetti, and D Ferraro. Charging and energy fluctuations of a driven quantum battery.New J. Phys. , 22(6):063057, 2020

    2020

  26. [34]

    Family of concurrence monotones and its applications.Phys

    Gilad Gour. Family of concurrence monotones and its applications.Phys. Rev. A: At., Mol., Opt. Phys., 71(1):012318, 2005

    2005

  27. [35]

    Entanglement of formation and concurrence

    William K Wootters. Entanglement of formation and concurrence. Quantum Inf. Comput. , 1(1):27–44, 2001. 15

    2001

Pith tools

Reviewed August 10, 2026 · model on record in the stance chip above.