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.

We study the problem of charging a quantum battery in finite time. We demonstrate an analytical optimal protocol for the case of a single qubit. Extending this analysis to an array of N qubits, we demonstrate that an N-fold advantage in power per qubit can be achieved when global operations are permitted. The exemplary analytic argument for this quantum advantage in the charging power is backed up by numerical analysis using optimal control techniques. It is demonstrated that the quantum advantage for power holds when, with cyclic operation in mind, initial and final states are required to be separable.

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...

Genuinely quantum states of a harmonic oscillator may be distinguished from their classical counterparts by the Glauber-Sudarshan P-representation -a state lacking a positive P-function is said to be nonclassical. In this paper, we propose a general operational framework for studying nonclassicality as a resource in networks of passive linear elements and measurements with feed-forward. Within this setting, we define new measures of nonclassicality based on the quantum fluctuations of quadratures, as well as the quantum Fisher information of quadrature displacements. These lead to fundamental constraints on the manipulation of nonclassicality, especially its concentration into subsystems, that apply to generic multi-mode non-Gaussian states. Special cases of our framework include no-go results in the concentration of squeezing and a complete hierarchy of nonclassicality for single mode Gaussian states.

Accurately describing work extraction from a quantum system is a central objective for the extension of thermodynamics to individual quantum systems. The concepts of work and heat are surprisingly subtle when generalizations are made to arbitrary quantum states. We formulate an operational thermodynamics suitable for application to an open quantum system undergoing quantum evolution under a general quantum process by which we mean a completely-positive and trace-preserving map. We derive an operational first law of thermodynamics for such processes and show consistency with the second law. We show that heat, from the first law, is positive when the input state of the map majorises the output state. Moreover, the change in entropy is also positive for the same majorisation condition. This makes a strong connection between the two operational laws of thermodynamics.