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Enhancing the Charging Power of Quantum Batteries
Open accessAbstract
Can collective quantum effects make a difference in a meaningful thermodynamic operation? Focusing on energy storage and batteries, we demonstrate that quantum mechanics can lead to an enhancement in the amount of work deposited per unit time, i.e., the charging power, when N batteries are charged collectively. We first derive analytic upper bounds for the collective quantum advantage in charging power for two choices of constraints on the charging Hamiltonian. We then demonstrate that even in the absence of quantum entanglement this advantage can be extensive. For our main result, we provide an upper bound to the achievable quantum advantage when the interaction order is restricted; i.e., at most k batteries are interacting. This constitutes a fundamental limit on the advantage offered by quantum technologies over their classical counterparts.
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TL;DR
The paper defines a collective quantum advantage for charging power when N quantum batteries are charged jointly rather than in parallel, and derives upper bounds on this advantage under energetic constraints. It shows that an extensive advantage is possible even without entanglement, but for physically realisable at-most-k-body interactions the advantage cannot scale with N and is bounded by a function quadratic in k.
Key findings
- For two constraints on the collective charging Hamiltonian, the quantum advantage is upper bounded as Γ_C1 ≤ √N and Γ_C2 ≤ N, with β = T‖/T_QSL^(1) quantifying inability to saturate the quantum speed limit in parallel charging.
- An extensive advantage can occur even for highly mixed states inside the separable ball: for N two-level thermal batteries, Γ_C1 = √N, Γ_C2 = N, and Γ_C0 = N, while the joint state need not be entangled during charging.
- For circuit-based charging with interaction order at most k, Theorem 2 gives Γ_C0 < γk, where γ does not scale with N; for ground-to-maximally-excited states γ = π/2.
- For generic time-dependent charging with interaction order k and maximum participation number m, Theorem 3 gives Γ_C0 < γ(k²(m−1)+k). Achievable comparisons are Γ_C1 = √k and Γ_C2 = k when N/k is an integer, and Γ_C0 = k in that same situation.
Methods
- Theoretical study of unitary charging of N quantum batteries, defining the quantum advantage as Γ = P♯/P‖ = T‖/T♯, where P♯ is collective charging power and P‖ is parallel charging power.
- Analytic derivation using the quantum speed limit, Bures angle L_N, Uhlmann fidelity, and three constraints C0, C1, and C2 on the collective Hamiltonian’s energy, standard deviation, or operator norm.
- Supplementary proofs use a piecewise unitary circuit model, Trotter-Suzuki decomposition, and a numerical search over Haar-random charging Hamiltonians with sample size ν = 10⁵ for (N,k) = (3,2), (4,2), (4,3), and (6,2).
Limitations
- The paper states that its bounds are not tight; Theorem 2’s strict inequality is only different by a constant factor from an achievable bound in a special case.
- Conjecture 4, extending Theorem 2 to any time-dependent k-body interaction Hamiltonian, is not proven; the numerical search found no counterexamples but “does not represent a proof,” and measure-zero counterexamples cannot be excluded.
- The paper states that k-body interactions are hard to engineer and that higher interaction orders are generally difficult; the exact radius of the separable ball is not known, though it has been bounded.
- Evident from the text: the work is theoretical and numerical, with no experimental demonstration of the predicted charging advantage.
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25 Own interpretation · 18 No basis given · 10 Not checked yet · 7 Own result
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“In contrast, the joint charging of N batteries is achieved in T ♯ = T ‖ /α ♯ using the global Hamiltonian H ♯ = α ♯ H ⊗ N , where the positive constant α ♯ is introduced to satisfy the chosen constraint.”
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“Proposition 1 An extensive quantum advantage can be attained even for highly mixed states, including those confined to the separable ball throughout the charging procedure.”
- Also stated in: § Enhancing the charging power of quantum batteries · p. 3 · plain
“no matter how mixed the battery is a quantum advantage that scales with the number of batteries involved is always achievable.”
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“We then go on to analytically prove that, for charging fields with finite interaction order, i.e. , involving at most k -body interaction terms, the quantum advantage is upper bounded by a quadratic function of k and cannot scale with the total number of batteries.”
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“The Hamiltonian used in the example above, and in Ref. [15], to saturate the bound for quantum advantage involves N -body interactions.”
What the sources say
- Not checked yetcites [15] F. Binder, S. Vinjanampathy, K. Modi, and J. Goold, New J. Phys. 17 , 075015 (2015). source
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“Theorem 2 For a circuit based charging procedure with interaction order of at most k , the achievable quantum advantage is upper bounded as Γ C0 < γk , where γ is a constant that does not scale with the number N of batteries.”
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“The optimal local charging scheme is achieved in time T ‖ = π/ 2 by applying Hamiltonian H = | E 0 〉〈 E 1 | + | E 1 〉〈 E 0 | to each battery.”
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“We then demonstrate that even in the absence of quantum entanglement this advantage can be extensive.”
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“In the important case where ρ and σ are the ground and maximally excited states respectively, γ = π/ 2 .”
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“In this sense, it is a stricter constraint than C1 or C2.”
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“We first derive analytic upper bounds for the collective quantum advantage in charging power for two choices of constraints on the charging Hamiltonian.”
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“The quantum advantage is tight for orthogonal initial and final states, due to the example given in Ref. [15].”
What the sources say
- Not checked yetcites [15] F. Binder, S. Vinjanampathy, K. Modi, and J. Goold, New J. Phys. 17 , 075015 (2015). source
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“We then go on to analytically prove that, for charging fields with finite interaction order, i.e. , involving at most k -body interaction terms, the quantum advantage is upper bounded by a quadratic function of k and cannot scale with the total number of batteries.”
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“this advantage - upper bounded by a quantity that depends at most quadratically on k - cannot scale with the number N of batteries that compose the system.”
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“In the same situation, using constraint C0 we obtain Γ C0 = k”
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“With a sample size ν = 10 5 we ran the simulation for ( N,k ) equal to (3 , 2) , (4 , 2) , (4 , 3) and (6 , 2) . Not a single instance of P > 1 was recorded.”
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“Theorem 3 For a generic time-dependent charging procedure, the achievable quantum advantage is upper bounded as Γ C0 < γ ( k 2 ( m -1) + k ) , where k is the interaction order and m is the maximum participation number.”
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“While we cannot exclude measure zero cases, a large sample of charging Hamiltonians (generated from Haar-random unitary operations), with ( N,k ) = (3 , 2) , (4 , 2) , (4 , 3) and (6 , 2) , has failed to produce any counterexamples.”
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“Our result is a fundamental limit on how large power can be for physically realisable charging schemes, where the achievable interaction order is typically constrained.”
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“This constitutes a fundamental limit on the advantage offered by quantum technologies over their classical counterparts.”
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“For N quantum systems of d-dimensions, there exists a ball of radius R ( N,d ) , centred on the maximally mixed state, containing only separable states [35].”
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- Not checked yetcites [35] source
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“Next, we show that attaining a quantum advantage requires entangling operations, but not entanglement itself.”
- Also stated in: § Enhancing the charging power of quantum batteries · p. 3 · plain
“Proposition 1 implies that, while a quantum advantage requires entangling operations, the joint state of N -batteries does not have to be entangled during the charging process.”
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“this advantage - upper bounded by a quantity that depends at most quadratically on k - cannot scale with the number N of batteries that compose the system.”
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“By construction, the bound on the quantum advantage is not tight.”
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“The trade-off of using highly mixed states is that the charging power suffers as ϵ becomes smaller and smaller.”
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“we demonstrate that quantum mechanics can lead to an enhancement in the amount of work deposited per unit time, i.e. , the charging power, when N batteries are charged collectively.”
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“A striking consequence of our results, which hold in general for mixed states, is that an enhanced charging power is available even for arbitrarily mixed states, in remarkable analogy to the case of quantum metrology.”
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“Theorem 2 can be extended to more general cases, where k -body time-dependent interactions can occur between overlapping sets of batteries, with the restriction that each battery is simultaneously interacting with at most m others.”
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“Nevertheless, a quantum advantage that grows with the interaction order k can be achieved.”
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“In this particular case, such a speed-up can be obtained for pure states using the time-independent Hamiltonian H = √ s ∑ s µ =1 h µ , with h µ = | 1 〉 ⊗ k 〈 d | ⊗ k + h.c. , assuming that each h µ acts on a completely different set of k batteries, i.e. , [ h µ , h µ ′ ] = 0 ∀ µ, µ ′ .”
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“suggesting that the strict inequality in Theorem 2 is only different by a constant factor from an achievable bound.”
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“it is more likely that the quantum advantage is tightly limited by k”
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“Exceptions to this include the Dicke model [40] where collective coherence leads to superradiance, the Lipkin-Meshkov-Glick model [41], where all particles interact with each other, and the Mølmer-Sørensen interaction [42], in which an ensemble of ions are effectively coupled by a spatially uniform electromagnetic field.”
What the sources say
- Not checked yetcites [40] R. H. Dicke, Phys. Rev. 93 , 99 (1954). http://dx.doi.org/10.1103/PhysRev.93.99 source
- Not checked yetcites [41] H. Lipkin, N. Meshkov, and A. Glick, Nuclear Physics 62 , 188 (1965). source
- Not checked yetcites [42] K. Mølmer and A. Sørensen, Phys. Rev. Lett. 82 , 1835 (1999). source
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“Thus, if the time-averaged operator norm of the Hamiltonian is bounded, ∆ E ♯ and E ♯ are also bounded.”
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“while a scaling of the power P ♯ with the number of batteries N is surely not feasible in the context of k -body interactions”
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“The unitary evolution U generated by this time-dependent Hamiltonian can always be approximated, using the Trotter-Suzuki decomposition [47], by the following product of unitary tranformations:”
What the sources say
- Not checked yetcites [47] D. Poulin, A. Qarry, R. Somma, and F. Verstraete, Phys. Rev. Lett. 106 , 170501 (2011).
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“We have also shown analytically that a quantum advantage that grows with the number of batteries is not achievable with any physically reasonable Hamiltonian ( i.e. , one with at most k -body interactions).”
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“Our results directly complement a previous strain of research into quantum speed limits, by deriving a concrete upper bound on the ratio between the maximum speed of interacting and non-interacting driving between separable states.”
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“Since we have an upper bound, from Theorem 2, on the quantum advantage for circuit model Hamiltonians, and the power for a more general Hamiltonian is at most M times greater, it must be that Γ C0 < Mγk in this case.”
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“Firstly, for orthogonal pure initial and final states, the QSL can be saturated and β = 1 .”
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“In both cases (local and global) the deposited work is identical; thus, the quantum advantage is simply the ratio of T ‖ to T ♯ : Γ = α ♯ , which can be evaluated for the choice of constraint.”
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“Constraint C0 guarantees that both the time-averaged standard deviation and the time-averaged energy are bounded from above, as shown in Sec. A of SM.”
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“The two bounds in Eq. (4) are independent from each other, and constraint C1 is stronger than C2, as it leads to a stricter bound on the quantum advantage.”
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“The two bounds in Eq. (4) are independent from each other, and constraint C1 is stronger than C2, as it leads to a stricter bound on the quantum advantage.”
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“There, we show that E ♯ upper bounds both E ♯ / 2 and ∆ E ♯ .”
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“We find Γ C1 = √ N and Γ C2 = N (also Γ C0 = N for C0 given in Eq. (5)).”
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“Remarkably, neither T ‖ nor T ♯ depend on ϵ , while the total work done does.”
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- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“Here we show that ∆ E ♯ ≤ E ♯ and E ♯ ≤ 2 E ♯ by direct computation.”
boosted- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: unclear — It is unclear whether the paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“We have proven two fundamental upper bounds for the quantum advantage, each corresponding to a different constraint on the charging Hamiltonian.”
boostedcorrelational- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Next, we show that attaining a quantum advantage requires entangling operations, but not entanglement itself.”
- Also stated in: § Enhancing the charging power of quantum batteries · p. 3 · plain
“Proposition 1 implies that, while a quantum advantage requires entangling operations, the joint state of N -batteries does not have to be entangled during the charging process.”
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
- Also stated in: § Enhancing the charging power of quantum batteries · p. 3 · plain
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Since the distance from the maximally mixed state cannot change under unitary evolution, for a small enough choice of ϵ , the joint state of N batteries will lie within this ball throughout the evolution; yet, the quantum advantage remains extensive.”
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Though the quantum advantage for power could be larger in other cases, including where the battery states are mixed [26], the improvement cannot grow with the number of batteries; i.e. , β is a constant function of N .”
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
None of the sources cited for this claim have been checked yet.
In the paper
“For comparison, it has been shown elsewhere that Γ C1 = √ k and Γ C2 = k are achievable if the total number of batteries N can be divided by k , i.e. , if N/k = s ∈ N [15, 36].”
What the sources say
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it. It may state two separate claims as one.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“This numerical evidence does not represent a proof of our conjecture since there could be a measure zero set of Hamiltonians for which P > 1 .”
hedged- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it.
In the paper
“The quantum advantage has been interpreted as the result of rapid evolution through the space of high-dimensional quantum states, typically obtained by means of global operations [15].”
What the sources say
- Not checked yetcites [15] F. Binder, S. Vinjanampathy, K. Modi, and J. Goold, New J. Phys. 17 , 075015 (2015). source
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Note that these bounds are not tight”
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it.
In the paper
“There, an enhancement in sensing is still available for highly mixed states lying inside the separable ball [43].”
What the sources say
- Not checked yetcites [43] K. Modi, H. Cable, M. Williamson, and V. Vedral, Phys. Rev. X 1 , 021022 (2011). source
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“While, in the case of pure states, entanglement is a necessary consequence of these global operations, a fully separable evolution is still accessible for those states that live in the separable ball.”
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Since each of the M terms at each time step must be implemented sequentially, U Trot takes M times longer to run than U , with a corresponding drop in power P ♯ = MP Trot .”
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“This Letter demonstrates that thermodynamic processes can indeed benefit from collective effects when time enters the picture, though physical limitations on the interaction order prevent us from utilising them.”
boosteddirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
None of the sources cited for this claim have been checked yet.
In the paper
“For many physical systems, both k and m are limited: 2 or 3-body interactions are the norm for fundamental processes, and higher interaction orders are generally hard to engineer here [37-39].”
What the sources say
- Not checked yetcites [37] H. P. B¨ uchler, A. Micheli, and P. Zoller, Nat. Phys. 3 , 726 (2007). source
- Not checked yetcites [38] S. Boixo, S. T. Flammia, C. M. Caves, and J. Geremia, Phys. Rev. Lett. 98 , 090401 (2007). source
- Not checked yetcites [39] M. Napolitano, M. Koschorreck, B. Dubost, N. Behbood, R. Sewell, and M. W. Mitchell, Nature 471 , 486 (2011). source
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
The authors state this as an assumption.
Each hµ acts on a completely different set of k batteries, i.e., [hµ, hµ'] = 0 for all µ, µ'.
“assuming that each h µ acts on a completely different set of k batteries, i.e. , [ h µ , h µ ′ ] = 0 ∀ µ, µ ′ .”
The authors state this as an assumption.
The reach of the interaction should be limited.
“This restriction is motivated by the idea that the reach of the interaction should be limited.”
The paper relies on this without support.
The effective participation number m tends to be constrained by the spatial arrangement of systems and the fact that interaction strength often drops off with distance.
“The effective participation number, or reach, m tends to be constrained by the spatial arrangement of systems and the fact that interaction strength often drops off with distance.”
The paper relies on this without support.
Collective behaviour has been demonstrated to provide an advantage in performing many information theoretic tasks, but such distinctions from classical behaviour are few and far between in thermodynamics.
“While collective behaviour has been demonstrated to provide an advantage in performing many information theoretic tasks, such distinctions from classical behaviour are few and far between in thermodynamics.”
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?
In the citing paper
“In addition, similar techniques have been employed to optimally charge a quantum battery [110,111].”
From Quantum speed limits: from Heisenberg’s uncertainty principle to optimal quantum control (2017) · cites this paper as [111]
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
Each contradiction between two passages listed here was confirmed by an independent check.
Rated minor: it would not touch a result — a value no result rests on, a p-value that stays on the same side of the significance level, or a conflict that is clerical, resolved elsewhere in the paper, or outside its own findings.
In the paper
§ Appendix C: Proof of Theorem 3 · p. 7
“( k = 3 , m = 2) Now the first 3-partition (1 , 2 , 3) is followed by (1 , 4 , 5) , (2 , 4 , 6) and (3 , 5 , 6) .”
§ Enhancing the charging power of quantum batteries · p. 4
“each battery is simultaneously interacting with at most m others.”
Citations
Cites
Coherence in Spontaneous Radiation Processes
Dicke, R. H. (1954) · Physical Review · doi:10.1103/physrev.93.99 · Cited by 7,445
Validity of many-body approximation methods for a solvable model
Lipkin, H. J., Meshkov, N., & Glick, A. J. (1965) · Nuclear Physics · doi:10.1016/0029-5582(65)90862-x · Cited by 1,504
Multiparticle Entanglement of Hot Trapped Ions
Mølmer, K., & Sørensen, A. S. (1999) · Physical Review Letters · doi:10.1103/physrevlett.82.1835 · Cited by 1,024
The role of quantum information in thermodynamics—a topical review
Goold, J., Huber, M., Riera, A., del Rio, L., & Skrzypczyk, P. (2016) · Journal of Physics A Mathematical and Theoretical · doi:10.1088/1751-8113/49/14/143001 · Cited by 973
Self-citationVinjanampathy, S., & Anders, J. (2016) · Contemporary Physics · doi:10.1080/00107514.2016.1201896 · Cited by 940
Self-citationThe maximum speed of dynamical evolution
Margolus, N., & Levitin, L. B. (1998) · Physica D: Nonlinear Phenomena · doi:10.1016/s0167-2789(98)00054-2 · Cited by 887
Quantum metrology from a quantum information science perspective
Tóth, G., & Apellaniz, I. (2014) · Journal of Physics A Mathematical and Theoretical · doi:10.1088/1751-8113/47/42/424006 · Cited by 862
The quantum open system as a model of the heat engine
Alicki, R. (1979) · Journal of Physics A: Mathematical and General · doi:10.1088/0305-4470/12/5/007 · Cited by 765
Extracting Work from a Single Heat Bath via Vanishing Quantum Coherence
Scully, M. O., Zubairy, M. S., Agarwal, G. S., & WALTHER, H. (2003) · Science · doi:10.1126/science.1078955 · Cited by 751
Quantum metrology from a quantum information science perspective
Tóth, G., & Apellaniz, I. (2014) · Repository of the Academy's Library (Library of the Hungarian Academy of Sciences) · Cited by 672
Research works printed but not linked: 1
- L. Mandelstam, 1945, J. Phys. (Moscow), 9, 1
Cited by
Sorted by citations
Quantum speed limits: from Heisenberg’s uncertainty principle to optimal quantum control
Deffner, S., & Campbell, S. (2017) · Journal of Physics A: Mathematical and Theoretical · doi:10.1088/1751-8121/aa86c6 · Cited by 585
High-Power Collective Charging of a Solid-State Quantum Battery
Ferraro, D., Campisi, M., Andolina, G. M., Pellegrini, V., & Polini, M. (2018) · Physical Review Letters · doi:10.1103/physrevlett.120.117702 · Cited by 543
Quantum speed limits: from Heisenberg's uncertainty principle to optimal quantum control
Deffner, S., & Campbell, S. (2017) · Maryland Shared Open Access Repository (USMAI Consortium) · doi:10.13016/m2heya-i4ys · Cited by 485
Extractable Work, the Role of Correlations, and Asymptotic Freedom in Quantum Batteries
Andolina, G. M., Keck, M., Mari, A., Campisi, M., Giovannetti, V., & Polini, M. (2019) · Physical Review Letters · doi:10.1103/physrevlett.122.047702 · Cited by 369
Spin-chain model of a many-body quantum battery
Le, T. P., Levinsen, J., Modi, K. K., Parish, M. M., & Pollock, F. A. (2018) · Physical Review A · doi:10.1103/physreva.97.022106 · Cited by 337
Self-citation
Metadata
- Authors
- Campaioli, F., Pollock, F. A., Binder, F. C., Céleri, L., Goold, J., Vinjanampathy, S., & Modi, K.
- Affiliations
- Monash University (AU)
- Nanyang Technological University (SG)
- Universidade Federal de Goiás (BR)
- The Abdus Salam International Centre for Theoretical Physics (ICTP) (IT)
- Centre for Quantum Technologies (SG)
- ORCID
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 2017-04-12
- Volume
- 118
- Issue
- 15
- Pages
- 150601-150601
- ISSN
- 0031-9007 (ISSN-L)
- 1079-7114
- OpenAlex
- W2561264561
- Cited by
- 531
- References
- 50
- Citations by year
- 2026: 108 · 2025: 107 · 2024: 77 · 2023: 51 · 2022: 51 · 2021: 43 · 2020: 39 · 2019: 30 · 2018: 23 · 2017: 2
- FWCI
- 13.30
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical Review Letters (publishedVersion)
- arXiv (Cornell University) (publishedVersion)
- PubMed (publishedVersion)
- RMIT Research Repository (RMIT University Library) (submittedVersion)
- DR-NTU (Nanyang Technological University) (submittedVersion)
- DSpace (IIT Bombay) (submittedVersion)
- Figshare (submittedVersion)
- arXiv (Cornell University)
- Funders
- National Research Foundation Singapore (NRF-CRP14-2014-02, NRF-NRFF2016-02)
- European Cooperation in Science and Technology (MP1209)
- Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq: 401230/2014-7, CNPq: 305086/2013-8, CNPq: 445516/2014-3)
- IITB-IRCC (16IRCCSG019)
- Topics
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Advanced Thermodynamics and Statistical Mechanics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Information and Cryptography
- Physical Sciences › Engineering › Mechanical Engineering › Advanced Thermodynamic Systems and Engines
- Keywords
- quantum batteries, charging power, quantum advantage, energy storage, work rate, upper bounds, quantum entanglement, interaction order, quantum thermodynamics
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.
A language model drew the claims from the paper on 2026-10-06, under version 3 of the claim definition (model deepseek-v4.1-flash, prompt extract-v3).
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