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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.

We provide a characterization of energy in the form of exchanged heat and work between two interacting constituents of a closed, bipartite, correlated quantum system. By defining a binding energy we derive a consistent quantum formulation of the first law of thermodynamics, in which the role of correlations becomes evident, and this formulation reduces to the standard classical picture in relevant systems. We next discuss the emergence of the second law of thermodynamics under certain-but fairly general-conditions such as the Markovian assumption. We illustrate the role of correlations and interactions in thermodynamics through two examples.

Many-body entanglement is studied within the algebraic approach to quantum physics in systems made of Majorana fermions. In this framework, the notion of separability stems from partitions of the algebra of observables and properties of the associated correlation functions, rather than on particle tensor products. This allows a complete characterization of non-separable Majorana fermion states to be obtained. These results may have direct application in quantum metrology: using Majorana systems, sub-shot-noise accuracy in parameter estimations can be achieved without preliminary resource-consuming, state entanglement operations.

We consider two non-interacting infinite quantum spin chains immersed in a common thermal environment and undergoing a local dissipative dynamics of Lindblad type. We study the time evolution of collective mesoscopic quantum spin fluctuations that, unlike macroscopic mean-field observables, retain a quantum character in the thermodynamical limit. We show that the microscopic dissipative dynamics is able to entangle these mesoscopic degrees of freedom, through a purely mixing mechanism. Further, the behaviour of the dissipatively generated quantum correlations between the two chains is studied as a function of temperature and dissipation strength.

We study the dissipative dynamics of N quantum spins with Lindblad generator consisting of operators scaling as fluctuations, namely with the inverse square-root of N. In the large N limit, the microscopic dissipative time-evolution converges to a non-Markovian unitary dynamics on strictly local operators, while at the mesoscopic level of fluctuations it gives rise to a dissipative non-Markovian dynamics. The mesoscopic time-evolution is Gaussian and exhibits either a stable or an unstable asymptotic character; furthermore, the mesoscopic dynamics builds correlations among fluctuations that survive in time even when the original microscopic dynamics is unable to correlate local observables.

Fluctuations of the atomic positions are at the core of a large class of unusual material properties ranging from quantum para-electricity to high temperature superconductivity. Their measurement in solids is the subject of an intense scientific debate focused on seeking a methodology capable of establishing a direct link between the variance of the atomic displacements and experimentally measurable observables. Here we address this issue by means of non-equilibrium optical experiments performed in shot-noise-limited regime. The variance of the time-dependent atomic positions and momenta is directly mapped into the quantum fluctuations of the photon number of the scattered probing light. A fully quantum description of the non-linear interaction between photonic and phononic fields is benchmarked by unveiling the squeezing of thermal phonons in α-quartz.

When dealing with the classical limit of two quantum mechanical oscillators on a noncommutative configuration space, the limits corresponding to the removal of configuration-space noncommutativity and position-momentum noncommutativity do not commute. We address this behaviour from the point of view of the phase-space localisation properties of the Wigner functions of coherent states under the two limits.

One way to look for complex behaviours in many-body quantum systems is to let the number N of degrees of freedom become large and focus upon collective observables. Mean-field quantities scaling as 1/N tend to commute, whence complexity at the quantum level can only be inherited from complexity at the classical level. Instead, fluctuations of microscopic observables scale as 1/N and exhibit collective Bosonic features, typical of a mesoscopic regime half-way between the quantum one at the microscopic level and the classical one at the level of macroscopic averages. Here, we consider the mesoscopic behaviour emerging from an infinite quantum spin chain undergoing a microscopic dissipative, irreversible dynamics and from global states without long-range correlations and invariant under lattice translations and dynamics. We show that, from the fluctuations of one site spin observables whose linear span is mapped into itself by the dynamics, there emerge bosonic operators obeying a mesoscopic dissipative dynamics mapping Gaussian states into Gaussian states. Instead of just depleting quantum correlations because of decoherence effects, these maps can generate entanglement at the collective, mesoscopic level, a phenomenon with no classical analogue that embodies a peculiar complex behaviour at the interface between micro and macro regimes.

While it is well known that complete positivity guarantees the fulfilment of the second law of thermodynamics, its possible violations have never been proposed as a check of the complete positivity of a given open quantum dynamics. We hereby consider an open quantum micro-circuit, effectively describable as a two-level open quantum system, whose asymptotic current might be experimentally accessible. This latter could indeed be used to discriminate between its possible non-completely positive Redfield dynamics and a completely positive one obtained by standard weak-coupling limit techniques, at the same time verifying the fate of the second law of thermodynamics in such a context.

We consider a recently proposed model of driven open quantum micro-circuit (Pellegrini F., Phys. Rev. Lett., 107 (2011) 060401) amenable to experimental investigations. We show that such an open quantum system provides a concrete physical instance where we can prove that modeling its time evolution with a dynamics lacking complete positivity conflicts with the second law of thermodynamics.

We extend the notion of Gacs quantum algorithmic entropy, originally formulated for finitely many qubits, to infinite dimensional quantum spin chains and investigate the relation of this extension with two quantum dynamical entropies that have been proposed in recent years.

Subentropy is an entropy-like quantity that arises in quantum information theory; for example, it provides a tight lower bound on the accessible information for pure state ensembles, dual to the von Neumann entropy upper bound in Holevo's theorem. Here we establish a series of properties of subentropy, paralleling the well-developed analogous theory for von Neumann entropy. Further, we show that subentropy is a lower bound for min-entropy. We introduce a notion of conditional subentropy and show that it can be used to provide an upper bound for the guessing probability of any classical-quantum state of two qubits; we conjecture that the bound applies also in higher dimensions. Finally, we give an operational interpretation of subentropy within classical information theory.

We show that two, non-interacting, infinitely long spin chains can become globally entangled at the mesoscopic level of their fluctuation operators through a purely noisy microscopic mechanism induced by the presence of a common heat bath. By focusing on a suitable class of mesoscopic observables, the behaviour of the dissipatively generated quantum correlations between the two chains is studied as a function of the dissipation strength and bath temperature. © 2014 Elsevier B.V.

Entanglement in fermion many-body systems is studied using a generalized definition of separability based on partitions of the set of observables, rather than on particle tensor products. In this way, the characterizing properties of nonseparable fermion states can be explicitly analyzed, allowing a precise description of the geometric structure of the corresponding state space. These results have direct applications in fermion quantum metrology: Sub-shot-noise accuracy in parameter estimation can be obtained without the need of a preliminary state entangling operation. © 2014 American Physical Society.

In the case of systems composed of identical particles, a typical instance in quantum statistical mechanics, the standard approach to separability and entanglement ought to be reformulated and rephrased in terms of correlations between operators from subalgebras localized in spatially disjoint regions. While this algebraic approach is straightforward for bosons, in the case of fermions it is subtler since one has to distinguish between micro-causality, that is the anti-commutativity of the basic creation and annihilation operators, and algebraic independence that is the commutativity of local observables. We argue that a consistent algebraic formulation of separability and entanglement should be compatible with micro-causality rather than with algebraic independence. © 2014 World Scientific Publishing Company.