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.
Conventional quantum speed limits perform poorly for mixed quantum states: They are generally not tight and often significantly underestimate the fastest possible evolution speed. To remedy this, for unitary driving, we derive two quantum speed limits that outperform the traditional bounds for almost all quantum states. Moreover, our bounds are significantly simpler to compute as well as experimentally more accessible. Our bounds have a clear geometric interpretation; they arise from the evaluation of the angle between generalized Bloch vectors.Quantum speed limits (QSLs) set fundamental bounds on the shortest time required to evolve between two quantum states [1][2][3]. The earliest derivation of minimal time of evolution was in 1945 by Mandelstam and Tamm [4] with the aim of operationalising the famous (but oft misunderstood) timeenergy uncertainty relations [5-9] ∆t ≥ /∆E, relating the standard deviation of energy with the time it takes to go from one state to another. QSLs were originally derived for the unitary evolution of pure states [10][11][12]; since then they have been generalized to the case of mixed states [13][14][15][16], nonunitary evolution [17][18][19], and multi-partite systems [20][21][22][23][24].Extending their original scope, their significance has evolved from fundamental physics to practical relevance, defining the limits of the rate of information transfer [25] and processing [26], entropy production [27], precision in quantum metrology [28] and time-scale of quantum optimal control [29]. For example, in [30], the authors use QSLs to calculate the maximal rate of information transfer along a spin chain; similarly, Reich et al. show that optimization algorithms and QSLs can be used together to achieve quantum control over a large class of physical systems [31]. In Refs. [32][33][34] QSLs are used to bound the charging power of non-degenerate multi-partite systems, which are treated as batteries. The latter results imply a significant speed advantage for entangling over local unitary driving of quantum systems, given the same external constraints.Combining the Mandelstam-Tamm result with the results by Margolus and Levitin, along with elements of quantum state space geometry [35], leads to a unified QSL [36]. It bounds the shortest time required to evolve a (mixed) state ρ to another state σ by means of a unitary operator U t generated by some time-dependent Hamiltonian H twhere L(ρ, σ) = arccos(F(ρ, σ)) is the Bures angle, a measure of the distance between states ρ and σ, F(ρ, σ) = tr[ √ ρσ √ ρ] is the Uhlmann root fidelity [37,38]; For pure states ρ = |ψ ψ| and σ = |φ φ|, the Bures angle reduces to the Fubini-Study distance d(|ψ , |φ ) = arccos | ψ|φ | [35,39,40]. Under this condition Eq. (1) is provably tight [36]. An insightful geometric interpretation of QSLs for pure states (in a Hilbert space of any dimension) is that the geodesic connecting initial and final states lives on a complex projective line CP 1 (isomorphic to a 2-sphere S 2 ), defined by the linear combinations of |ψ an...
Starting from a geometric perspective, we derive a quantum speed limit for arbitrary open quantum evolution, which could be Markovian or non-Markovian, providing a fundamental bound on the time taken for the most general quantum dynamics. Our methods rely on measuring angles and distances between (mixed) states represented as generalized Bloch vectors. We study the properties of our bound and present its form for closed and open evolution, with the latter in both Lindblad form and in terms of a memory kernel. Our speed limit is provably robust under composition and mixing, features that largely improve the effectiveness of quantum speed limits for open evolution of mixed states. We also demonstrate that our bound is easier to compute and measure than other quantum speed limits for open evolution, and that it is tighter than the previous bounds for almost all open processes. Finally, we discuss the usefulness of quantum speed limits and their impact in current research, giving particular attention to quantum optimal control. arXiv:1806.08742v4 [quant-ph]
This chapter is a survey of the published literature on quantum batteries -ensembles of nondegenerate quantum systems on which energy can be deposited, and from which work can be extracted. A pedagogical approach is used to familiarize the reader with the main results obtained in this field, starting from simple examples and proceeding with in-depth analysis. An outlook for the field and future developments are discussed at the end of the chapter.
A quantum battery is a work reservoir that stores energy in quantum degrees of freedom. When immersed in an environment an open quantum battery needs to be stabilized against free energy leakage into the environment. For this purpose we here propose a simple protocol that relies on projective measurement and obeys a secondlaw like inequality for the battery entropy production rate. PACS numbers: 03.65. Yz, 05.70.Ln, 42.50.Lc Among recent research in quantum thermodynamics [1][2][3][4][5], the design of quantum energy storage-devices, called quantum batteries [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20], is of increasing interest. So far the main focus has lied on multipartite speed-up effects in charging [7,[9][10][11][12][15][16][17], fluctuations in charging precision [8,13,17,19], and mitigating imprecise unitary control pulses [20]. However, as of yet no attention has been paid to efficiently stabilizing charged quantum states, even if contributions in the area of control theory [21,22] touch upon this question both in classical [23] and in quantum settings [24,25].
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