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Abstract: Given a quantum heat engine that operates in a cycle that reaches maximal efficiency for a time-dependent Hamiltonian H(τ) of the working substance, with overall controllable driving H(τ) = g(τ) H, we study the deviation of the efficiency from the optimal value due to a generic time-independent perturbation in the Hamiltonian. We show that for a working substance consisting of two two-level systems, by suitably tuning the interaction, the deviation can be suppressed up to the third order in the perturbation parameter – and thus almost retaining the optimality of the engine. Graphical abstract: [Figure not available: see fulltext.].

The interaction between ultrashort light pulses and non-absorbing materials is dominated by impulsive stimulated Raman scattering (ISRS). The description of ISRS in the context of pump&probe experiments is based on effective classical models describing the interaction between the phonon and pulsed electromagnetic fields. Here we report a theoretical description of ISRS where we do not make any semi-classical approximation and we treat both photonic and phononic degrees of freedom at the quantum level. The results of the quantum model are compared with semiclassical results and validated by means of spectrally resolved pump&probe measurements on α-quartz.

I will review the possibility to retrieve nonlinear responses in complex materials by measuring noise correlations of classical and quantum nature.

We address an informational puzzle that appears with a non-Markovian open qubit dynamics: namely the fact that, while, according to the existing witnesses of information flows, a single qubit affected by that dissipative dynamics does not show information returning to it from its environment, instead two qubits do show such information when evolving independently under the same dynamics. We solve the puzzle by adding the so-called quasi-entropies to the possible witnesses of information flows.

I will review the possibility to retrieve nonlinear responses in complex materials by measuring noise correlations of classical and quantum nature.

We consider two qubits interacting with a common bosonic bath, but not directly between themselves. We derive the (bipartite) entanglement generation conditions for Gaussian non-Markovian dynamical maps and show that they are similar as in the Markovian regime. However, they depend on different physical coefficients and hold on different time scales. Indeed, for small times, in the non-Markovian regime entanglement is possibly generated on a shorter time scale (∝t2) than in the Markovian regime (∝t). Moreover, although the singular coupling limit of non-Markovian dynamics yields Markovian ones, we show that the same limit does not lead from non-Markovian entanglement generation conditions to Markovian ones. Also, entanglement generation conditions do not depend on the initial time for non-Markovian open dynamics resulting from couplings to bosonic Gaussian baths, while they may depend on time for open dynamics originated by couplings to classical, stochastic Gaussian environments.

Quantum detailed balance conditions and quantum fluctuation relations are two important concepts in the dynamics of open quantum systems: both concern how such systems behave when they thermalize because of interaction with an environment. We prove that for thermalizing quantum dynamics the quantum detailed balance conditions yield validity of a quantum fluctuation relation (where only forward-time dynamics is considered). This implies that to have such a quantum fluctuation relation (which in turn enables a precise formulation of the second law of thermodynamics for quantum systems) it suffices to fulfill the quantum detailed balance conditions. We, however, show that the converse is not necessarily true; indeed, there are cases of thermalizing dynamics which feature the quantum fluctuation relation without satisfying detailed balance. We illustrate our results with three examples.

Quantum-enhanced measurements exploit quantum mechanical effects for increasing the sensitivity of measurements of certain physical parameters and have great potential for both fundamental science and concrete applications. Most of the research has so far focused on using highly entangled states, which are, however, difficult to produce and to stabilize for a large number of constituents. In the following alternative mechanisms are reviewed, notably the use of more general quantum correlations such as quantum discord, identical particles, or nontrivial Hamiltonians; the estimation of thermodynamical parameters or parameters characterizing nonequilibrium states; and the use of quantum phase transitions. Both theoretically achievable enhancements and enhanced sensitivities not primarily based on entanglement that have already been demonstrated experimentally and indicate some possible future research directions are described.

We study the emergent dynamics resulting from the infinite volume limit of the mean-field dissipative dynamics of quantum spin chains with clustering, but not time-invariant states. We focus upon three algebras of spin operators: the commutative algebra of mean-field operators, the quasi-local algebra of microscopic, local operators and the collective algebra of fluctuation operators. In the infinite volume limit, mean-field operators behave as time-dependent, commuting scalar macroscopic averages while quasi-local operators, despite the dissipative underlying dynamics, evolve unitarily in a typical non-Markovian fashion. Instead, the algebra of collective fluctuations, which is of bosonic type with time-dependent canonical commutation relations, undergoes a time-evolution that retains the dissipative character of the underlying microscopic dynamics and exhibits non-linear features. These latter disappear by extending the time-evolution to a larger algebra where it is represented by a continuous one-parameter semigroup of completely positive maps. The corresponding generator is not of Lindblad form and displays mixed quantum-classical features, thus indicating that peculiar hybrid systems may naturally emerge at the level of quantum fluctuations in many-body quantum systems endowed with non time-invariant states.

Quantum-enhanced metrology is boosting interferometer sensitivities to extraordinary levels, up to the point where table-top experiments have been proposed to measure Planck-scale e®ects predicted by quantum gravity theories. In setups involving multiple photon interferometers, as those for measuring the so-called holographic °uctuations, entanglement provides substantial improvements in sensitivity. Entanglement is however a fragile resource and may be endangered by decoherence phenomena. We analyze how noisy e®ects arising either from the weak coupling to an external environment or from the modi¯cation of the canonical commutation relations in photon propagation may a®ect this entanglement-enhanced gain in sensitivity.

In the weak-coupling limit approach to open quantum systems, the presence of the bath is eliminated and accounted for by a master equation that introduces dissipative contributions to the system reduced dynamics: within this framework, there are no bath entropy contributions to the entropy balance. We show that, as a consequence, the entropy production fails to be positive for a class of physically legitimate, that is completely positive and trace preserving, non-Markovian dynamical maps. Moreover, in absence of the semigroup property, if the reduced dynamics has a thermal asymptotic state, this need not be stationary. Then even the integrated entropy production becomes negative. These observations imply that, when the conditions leading to reduced dynamics of semigroup type are relaxed, a consistent formulation of the second law of thermodynamics requires that the environment contribution to the entropy balance be explicitly taken into account.

Recent experimental results point to the existence of coherent quantum phenomena in systems made of a large number of particles, despite the fact that for many-body systems the presence of decoherence is hardly negligible and emerging classicality is expected. This behaviour hinges on collective observables, named quantum fluctuations, that retain a quantum character even in the thermodynamic limit: they provide useful tools for studying properties of many-body systems at the mesoscopic level, in-between the quantum microscopic scale and the classical macroscopic one. We herein present the general theory of quantum fluctuations in mesoscopic systems, and study their dynamics in a quantum open system setting, taking into account the unavoidable effects of dissipation and noise induced by the external environment. As in the case of microscopic systems, decoherence is not always the only dominating effect at the mesoscopic scale: certain types of environment can provide means for entangling collective fluctuations through a purely noisy mechanism.

We argue that in the case of identical particles the most natural identification of separability, that is of absence of non-classical correlations, is via the factorization of mean values of commuting observables. It thus follows that separability and entanglement depend both on the state and on the choice of observables and are not absolute notions. We compare this point of view with a recent novel approach to the entanglement of identical particles, which allows for the definition of an entanglement entropy from a suitably defined reduced particle density matrix, without the need of labelling the system constituents. We contrast this figure of merit with the aforementioned lack of an absolute notion of entanglement by considering few paradigmatic examples.

The semileptonic decay asymmetry AΔm is studied within the open quantum systems approach to the physics of the neutral meson B0–B0¯ system: this extended treatment takes into account possible non-standard, dissipative effects induced by the presence of an external environment. A bound on these effects is provided through the analysis of available experimental data from the Belle Collaboration.

We consider two chains, each made of N independent oscillators, immersed in a common thermal bath and study the dynamics of their mutual quantum correlations in the thermodynamic, large-N limit. We show that dissipation and noise due to the presence of the external environment are able to generate collective quantum correlations between the two chains at the mesoscopic level. The created collective quantum entanglement between the two many-body systems turns out to be rather robust, surviving for asymptotically long times even for non vanishing bath temperatures.

We study the relations between the recently proposed machine-independent quantum complexity of P. Gacs [1] and the entropy of classical and quantum systems. On one hand, by restricting Gacs complexity to ergodic classical dynamical systems, we retrieve the equality between the Kolmogorov complexity rate and the Shannon entropy rate derived by A. A. Brudno [2]. On the other hand, using the quantum Shannon-McMillan theorem [3], we show that such an equality holds densely in the case of ergodic quantum spin chains.

We propose a fully quantum treatment for pump and probe experiments applied to the study of phonon excitations in solids. To describe the interaction between photons and phonons, a single effective hamiltonian is used that is able to model both the excitation induced by pump laser pulses and the subsequent measuring process through probe pulses. As the photoexcited phonons interact with their surroundings, mainly electrons and impurities in the target material, they cannot be considered isolated: their dynamics needs to be described by a master equation that takes into account the dissipative and noisy effects due to the presence of the environment. In this formalism, the quantum dynamics of pump excited phonons can be analyzed through suitable probe photon observables; in particular, a clear signature of squeezed phonons can be obtained by looking simultaneously at the behavior of the scattered probe mean photon number and its variance.

The are several nonequivalent notions of Markovian quantum evolution. In this paper we show that the one based on the so-called CP divisibility of the corresponding dynamical map enjoys the following stability property: the dynamical map Λt is CP divisible if and only if the second tensor power Λt - Λt is CP divisible as well. Moreover, the P divisibility of the map Λt - Λt is equivalent to the CP divisibility of the map Λt. Interestingly, the latter property is no longer true if we replace the P divisibility of Λt - Λt by simple positivity and the CP divisibility of Λt by complete positivity. That is, unlike when Λt has a time-independent generator, positivity of Λt - Λt does not imply complete positivity of Λt.

Given two non-interacting 2-level systems weakly coupled to an environment and thus evolving according to a statistically mixing dissipative reduced dynamics, we provide necessary and sufficient conditions for the generator of the time-evolution to entangle the two systems.

Optical homodyne tomography consists in reconstructing the quantum state of an optical field from repeated measurements of its amplitude at different field phases (homodyne data). The experimental noise, which unavoidably affects the homodyne data, leads to a detection efficiency η < 1. The problem of reconstructing quantum states from noisy homodyne data sets prompted an intense scientific debate about the presence or absence of a lower homodyne efficiency bound (η > 0.5) below which quantum features, like quantum interferences, cannot be retrieved. Here, by numerical experiments, we demonstrate that quantum interferences can be effectively reconstructed also for low homodyne detection efficiency. In particular, we address the challenging case of a Schrödinger cat state and test the minimax and adaptive Wigner function reconstruction technique by processing homodyne data distributed according to the chosen state but with an efficiency η < 0.5. By numerically reproducing the Schrödinger’s cat interference pattern, we give evidence that quantum state reconstruction is actually possible in these conditions, and provide a guideline for handling optical tomography based on homodyne data collected by low efficiency detectors.