A New Lower Bound for the Distinct Distance Constant

The reciprocal sum of Zhang sequence is not equal to the Distinct Distance Constant. This note introduces a $B_2$-sequence with larger reciprocal sum, and provides a more precise estimation of the reciprocal sums of Mian-Chowla sequence and Zhang sequence.Comment: 4 pages, 3 ancillary table

Extracting work from correlated many-body quantum systems

The presence of correlations in the input state of a non-interacting many-body quantum system can lead to an increase in the amount of work we can extract from it under global unitary processes (ergotropy). The present work explore such effect on translationally invariant systems relaying on the Matrix Product Operator formalism to define a measure of how much they are correlated. We observe that in the thermodynamic limit of large number of sites, complete work extraction can be attained for relatively small correlation strength (a reduction of a 2 factor in dB unit). Most importantly such an effect appears not to be associated with the presence of quantum correlations (e.g. entanglement) in the input state (classical correlation sources), and to be attainable by only using incoherent ergotropy. As a byproduct of our analysis we also present a rigorous formulation of the heuristic typicality argument first formulated in [Alicki and Fannes, 2013], which gives the maximum work extractable for a set of many identical quantum systems in the asymptotic limit.Comment: 21 pages, 5 figure

Testing identity of collections of quantum states: sample complexity analysis

We study the problem of testing identity of a collection of unknown quantum states given sample access to this collection, each state appearing with some known probability. We show that for a collection of $d$-dimensional quantum states of cardinality $N$, the sample complexity is $O(\sqrt{N}d/\epsilon^2)$, which is optimal up to a constant. The test is obtained by estimating the mean squared Hilbert-Schmidt distance between the states, thanks to a suitable generalization of the estimator of the Hilbert-Schmidt distance between two unknown states by B\u{a}descu, O'Donnell, and Wright (https://dl.acm.org/doi/10.1145/3313276.3316344).Comment: 20+6 pages, 0 figures. Typos corrected, improved presentatio

Critical quantum metrology assisted by real-time feedback control

We investigate critical quantum metrology,that is the estimation of parameters in many-body systems close to a quantum critical point, through the lens of Bayesian inference theory. We first derive a no-go result stating that any non-adaptive measurement strategy will fail to exploit quantum critical enhancement (i.e. precision beyond the shot-noise limit) for a sufficiently large number of particles $N$ whenever our prior knowledge is limited. We then consider different adaptive strategies that can overcome this no-go result, and illustrate their performance in the estimation of (i) a magnetic field using a probe of 1D spin Ising chain and (ii) the coupling strength in a Bose-Hubbard square lattice. Our results show that adaptive strategies with real-time feedback control can achieve sub-shot noise scaling even with few measurements and substantial prior uncertainty.Comment: 6+5 pages, 3+5 figure

Optimal local work extraction from bipartite quantum systems in the presence of Hamiltonian couplings

We investigate the problem of finding the local analog of the ergotropy, which is the maximum work that can be extracted from a system if we can only apply local unitary transformation acting on a given subsystem. In particular, we provide a closed formula for the local ergotropy in the special case in which the local system has only two levels, and we give analytic lower bounds and semidefinite programming upper bounds for the general case. As nontrivial examples of application, we compute the local ergotropy for an atom in an electromagnetic cavity with Jaynes-Cummings coupling and the local ergotropy for a spin site in an XXZ Heisenberg chain, showing that the amount of work that can be extracted with a unitary operation on the coupled system can be greater than the work obtainable by quenching off the coupling with the environment before the unitary transformation

Work extraction processes from noisy quantum batteries: the role of non local resources

We demonstrate an asymmetry between the beneficial effects one can obtain using non-local operations and non-local states to mitigate the detrimental effects of environmental noise in the work extraction from quantum battery models. Specifically, we show that using non-local recovery operations after the noise action can in general increase the amount of work one can recover from the battery even with separable (i.e. non entangled) input states. On the contrary, employing entangled input states with local recovery operations will not generally improve the battery performances.Comment: 11 pages, 3 figures, it matches the journal versio

Quantum work extraction efficiency for noisy quantum batteries: the role of coherence

Quantum work capacitances and maximal asymptotic work/energy ratios are figures of merit characterizing the robustness against noise of work extraction processes in quantum batteries formed by collections of quantum systems. In this paper we establish a direct connection between these functionals and, exploiting this result, we analyze different types of noise models mimicking self-discharging, thermalization and dephasing effects. In this context we show that input quantum coherence can significantly improve the storage performance of noisy quantum batteries and that the maximum output ergotropy is not always achieved by the maximum available input energy.Comment: 16 pages, 8 figure