Tightening Quantum Speed Limits for Almost All States

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.Comment: Updated and revised version; 5 pages, 2 figures, 1 page appendi

Hypersurfaces of Prescribed Gauss Curvature in Exterior Domains

We prove an existence theorem for convex hypersurfaces of prescribed Gauss curvature in the complement of a compact set in Euclidean space which are close to a cone.Comment: 15 pages, LaTeX (published version

Spectral Estimates and Non-Selfadjoint Perturbations of Spheroidal Wave Operators

We derive a spectral representation for the oblate spheroidal wave operator which is holomorphic in the aspherical parameter $\Omega$ in a neighborhood of the real line. For real $\Omega$, estimates are derived for all eigenvalue gaps uniformly in $\Omega$. The proof of the gap estimates is based on detailed estimates for complex solutions of the Riccati equation. The spectral representation for complex $\Omega$ is derived using the theory of slightly non-selfadjoint perturbations.Comment: 33 pages, LaTeX, 3 figures, typo in Lemma 4.1 corrected (published version

Enhancing the charging power of quantum batteries

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 \emph{quantum advantage} in charging power for two choices of constraints on the charging Hamiltonian. We then highlight the importance of entanglement by proving that the quantum advantage vanishes when the collective state of the batteries is restricted to be in the separable ball. Finally, we provide an upper bound to the achievable quantum advantage when the interaction order is restricted, i.e., at most $k$ batteries are interacting. Our result is a fundamental limit on the advantage offered by quantum technologies over their classical counterparts as far as energy deposition is concerned.Comment: In this new updated version Theorem 1 has been changed with Proposition 1. The paper has been published on PRL, and DOI included accordingl

The Pareto-Frontier in a simple Mirrleesian model of income taxation

We characterize the Pareto-frontier in a simple Mirrleesian model of income taxation. We show how the second-best frontier which incorporates incentive constraints due to private information on productive abilities relates to the first-best frontier which takes only resource constraints into account. In particular, we argue that the second-best frontier can be interpreted as a Laer-curve. We also use this second-best frontier for a comparative statics analysis of how optimal income tax rates vary with the degree of inequity aversion, and for a characterization of optimal public-good provision. We show that a more inequity averse policy maker chooses tax schedules that are more redistributive and involve higher marginal tax rates, but chooses a lower public-goods provision level.Optimal Income Taxation, Public-good provision, Laer-Curve

Simplicity-Expressiveness Tradeoffs in Mechanism Design

A fundamental result in mechanism design theory, the so-called revelation principle, asserts that for many questions concerning the existence of mechanisms with a given outcome one can restrict attention to truthful direct revelation-mechanisms. In practice, however, many mechanism use a restricted message space. This motivates the study of the tradeoffs involved in choosing simplified mechanisms, which can sometimes bring benefits in precluding bad or promoting good equilibria, and other times impose costs on welfare and revenue. We study the simplicity-expressiveness tradeoff in two representative settings, sponsored search auctions and combinatorial auctions, each being a canonical example for complete information and incomplete information analysis, respectively. We observe that the amount of information available to the agents plays an important role for the tradeoff between simplicity and expressiveness

Graded Lie algebras with finite polydepth

If A is a graded connected algebra then we define a new invariant, polydepth A, which is finite if $Ext_A^*(M,A) \neq 0$ for some A-module M of at most polynomial growth. Theorem 1: If f : X \to Y is a continuous map of finite category, and if the orbits of H_*(\Omega Y) acting in the homology of the homotopy fibre grow at most polynomially, then H_*(\Omega Y) has finite polydepth. Theorem 2: If L is a graded Lie algebra and polydepth UL is finite then either L is solvable and UL grows at most polynomially or else for some integer d and all r, $\sum_{i=k+1}^{k+d} {dim} L_i \geq k^r$, $k\geq$ some $k(r)$

CRACKING THE CODE: FACTORS THAT INFLUENCE ACADEMIC SUCCESS ON THE SOCIAL WORK DEGREE: A NEWLY QUALIFIED BLACK SOCIAL WORKER‟S PERSPECTIVE

This is a qualitative study of eleven newly qualified black social workers (NQBSW) and five social work educators. The study was carried out in a post-1992 millennium university in England between 2015 and 2018. The study findings have been skilfully interpreted through the lens of a number of Bourdieu‟s thinking tools, namely „Capital‟, „Habitus‟, „Field‟ and „Knowing the Game‟. Together, they suggest that black students know how to „crack the code‟ and „Play the Game‟. The landscape may be changing for black students who historically have not performed as well as their white counterparts. However, when identities are not in threat, this group appears to perform as well as, if not better, than their white peers. This ethically approved study aimed to identify factors that influence success on a university social work degree course. The objectives were to examine behavioural factors, differences in understandings and identify types of support embraced by NQBSW participants whilst undertaking the degree. The voices of black students and their educator‟s have been documented through semi-structured person-to-person and synchronised interviews. Using interpretive phenomenology and a constructivist approach, reading, self-directed learning groups, determination, the diversity of the student population and participation were found to be influential factors for success on the degree course. Moreover, the study found that ethnicity, social forces, cultural values and the university conditions all had a role to play in the navigation of student success on the degree course