We analyze the quantum dynamics of a non-relativistic particle moving in a bounded domain of physical space, when the boundary conditions are rapidly changed. In general, this yields new boundary conditions, via a dynamical composition law that is a very simple instance of the superposition of different topologies. In all cases, unitarity is preserved and the quick change of boundary conditions does not introduce any decoherence in the system. Among the emerging boundary conditions, the Dirichlet case (vanishing wavefunction at the boundary) plays the role of an attractor. Possible experimental implementations with superconducting quantum interference devices are explored and analyzed.

We analyze the non-relativistic problem of a quantum particle that bounces back and forth between two moving walls. We recast this problem into the equivalent one of a quantum particle in a fixed box whose dynamics is governed by an appropriate time-dependent Schrodinger operator.

We study a binary mixture of Bose–Einstein condensates, confined in a generic potential, in the Thomas–Fermi approximation. We search for the zero- temperature ground state of the system, both in the case of fixed numbers of particles and fixed chemical potentials. For generic potentials, we analyze the transition from mixed to separated ground-state configurations as the inter- species interaction increases. We derive a simple formula that enables one to determine the location of the domain walls. Finally, we find criteria for the energetic stability of separated configurations, depending on the number and the position of the domain walls separating the two species.

The tomographic picture of quantum mechanics has brought the description of quantum states closer to that of classical probability and statistics. On the other hand, the geometrical formulation of quantum mechanics introduces a metric tensor and a symplectic tensor (Hermitian tensor) on the space of pure states. By putting these two aspects together, we show that the Fisher information metric, both classical and quantum, can be described by means of the Hermitian tensor on the manifold of pure states.

We characterize the multipartite entanglement of a system of n qubits in terms of the distribution function of the bipartite purity over balanced bipartitions. We search for maximally multipartite entangled states, whose average purity is minimal, and recast this optimization problem into a problem of statistical mechanics, by introducing a cost function, a fictitious temperature and a partition function. By investigating the high-temperature expansion, we obtain the first three moments of the distribution. We find that the problem exhibits frustration.

We propose alternative definitions of classical states and quantumness witnesses by focusing on the algebra of observables of the system. A central role is assumed by the anticommutator of the observables, namely the Jordan product. This approach turns out to be suitable for generalizations to infinite dimensional systems. We then show that the whole algebra of observables can be generated by three elements by repeated application of the Jordan product.

We study a lattice gauge theory in Wilson's Hamiltonian formalism. In view of the realization of a quantum simulator for QED in one dimension, we introduce an Abelian model with a discrete gauge symmetry Z_n, approximating the U(1) theory for large n. We analyze the role of the finiteness of the gauge fields and the properties of physical states, that satisfy a generalized Gauss's law. We finally discuss a possible implementation strategy, that involves an effective dynamics in physical space.

The ground-state energy of a binary mixture of Bose-Einstein condensates can be estimated for large atomic samples by making use of suitably regularized Thomas-Fermi density profiles. By exploiting a variational method on the trial densities the energy can be computed by explicitly taking into account the normalization condition. This yields analytical results and provides the basis for further improvement of the approximation. As a case study, we consider a binary mixture of 87Rb atoms in two different hyperfine states in a double-well potential and discuss the energy crossing between density profiles with different numbers of domain walls, as the number of particles and the interspecies interaction vary.

Bipartite entanglement between two parties of a composite quantum system can be quantified in terms of the purity of one party and there always exists a pure state of the total system that maximizes it (and minimizes purity). When many different bipartitions are considered, the requirement that purity be minimal for all bipartitions gives rise to the phenomenon of entanglement frustration. This feature, observed in quantum systems with both discrete and continuous variables, can be studied by means of a suitable cost function whose minimizers are the maximally multipartite-entangled states (MMES). In this paper we extend the analysis of multipartite entanglement frustration of Gaussian states in multimode bosonic systems. We derive bounds on the frustration, under the constraint of finite mean energy, in the low- and high-energy limits.

We study the efficiency of quantum tomographic reconstruction where the system under investigation (quantum target) is indirectly monitored by looking at the state of a quantum probe that has been scattered off the target. In particular, we focus on the state tomography of a qubit through a one-dimensional scattering of a probe qubit, with a Heisenberg-type interaction. Via direct evaluation of the associated quantum Crame ́r–Rao bounds, we compare the accuracy efficiency that one can obtain by adopting entanglement-assisted strategies with that achievable when entanglement resources are not available. Even though sub-shot noise accuracy levels are not attainable, we show that quantum correlations play a significant role in the estimation. A comparison with the accuracy levels obtainable by direct estimation (not through a probe) of the quantum target is also performed.

We study the behavior of bipartite entanglement at fixed von Neumann entropy. We look at the distribution of the entanglement spectrum, that is, the eigenvalues of the reduced density matrix of a quantum system in a pure state. We report the presence of two continuous phase transitions, characterized by different entanglement spectra, which are deformations of classical eigenvalue distributions.

The ability of quantum systems to host exponentially complex dynamics has the potential to revolutionize science and technology. Therefore, much effort has been devoted to developing of protocols for computation, communication and metrology, which exploit this scaling, despite formidable technical difficulties. Here we show that the mere frequent observation of a small part of a quantum system can turn its dynamics from a very simple one into an exponentially complex one, capable of universal quantum computation. After discussing examples, we go on to show that this effect is generally to be expected: almost any quantum dynamics becomes universal once ‘observed’ as outlined above. Conversely, we show that any complex quantum dynamics can be ‘purified’ into a simpler one in larger dimensions. We conclude by demonstrating that even local noise can lead to an exponentially complex dynamics.

We describe an experiment confirming the evidence of the antibunching effect on a beam of noninteracting thermal neutrons. The comparison between the results recorded with a high-energy-resolution source of neutrons and those recorded with a broad-energy-resolution source enables us to clarify the role played by the beam coherence in the occurrence of the antibunching effect.

Some nonlinear generalizations of classical Radon tomography were introduced by Asorey et al (2008 Phys. Rev. A 77 042115), where the straight lines of the standard Radon map are replaced by quadratic curves (ellipses, hyperbolas and circles) or quadratic surfaces (ellipsoids, hyperboloids and spheres). We consider here the quantum version of this novel nonlinear approach and obtain, by the systematic use of the Weyl map, a tomographic encoding approach to quantum states. Nonlinear quantum tomograms admit a simple formulation within the framework of the star-product quantization scheme and the reconstruction formulae of the density operators are explicitly given in a closed form, with an explicit construction of quantizers and dequantizers. The role of symmetry groups behind the generalized tomographic maps is analyzed in some detail. We also introduce new generalizations of the standard singular dequantizers of the symplectic tomographic schemes, where the Dirac delta-distributions of operator-valued arguments are replaced by smooth window functions, giving rise to the new concept of thick quantum tomography. Applications in quantum state measurements of photons and matter waves are discussed.

We elaborate on the notion of generalized tomograms, both in the classical and quantum domains. We construct a scheme of star-products of thick tomographic symbols and obtain in explicit form the kernels of classical and quantum generalized tomograms. Some of the new tomograms may have interesting applications in quantum optical tomography.

The generation of Greenberger-Horne-Zeilinger (GHZ) states is a crucial problem in quantum information. We derive general conditions for obtaining GHZ states as eigenstates of a Hamiltonian. We find that a necessary condition for an n-qubit GHZ state to be a nondegenerate eigenstate of a Hamiltonian is the presence of m-qubit couplings with $m \geq [(n+1)/2]$. Moreover, we introduce a Hamiltonian with a GHZ eigenstate and derive sufficient conditions for the removal of the degeneracy.

The problem of Hamiltonian purification introduced by Burgarth et al. [Nat. Commun. 5, 5173 (2014)] is formalized and discussed. Specifically, given a set of non-commuting Hamiltonians {h1, …, hm} operating on a d-dimensional quantum system ℋd, the problem consists in identifying a set of commuting Hamiltonians {H1, …, Hm} operating on a larger dE-dimensional system ℋdE which embeds ℋd as a proper subspace, such that hj = PHjP with P being the projection which allows one to recover ℋd from ℋdE. The notions of spanning-set purification and generator purification of an algebra are also introduced and optimal solutions for (d) are provided.

When a Bose-Einstein condensate is divided into two parts that are subsequently released and overlap, interference fringes are observed. We show here that this interference is typical, in the sense that most wave functions of the condensate, randomly sampled out of a suitable ensemble, display interference. We make no hypothesis of decoherence between the two parts of the condensate.

We derive the invariant measure on the manifold of multimode quantum Gaussian states, induced by the Haar measure on the group of Gaussian unitary transformations. To this end, by introducing a bipartition of the system in two disjoint subsystems, we use a parameterization highlighting the role of nonlocal degrees of freedom—the symplectic eigenvalues—which characterize quantum entanglement across the given bipartition. A finite measure is then obtained by imposing a physically motivated energy constraint. By averaging over the local degrees of freedom we finally derive the invariant distribution of the symplectic eigenvalues in some cases of particular interest for applications in quantum optics and quantum information.

We study the joint statistics of conductance G and shot noise P in chaotic cavities supporting a large number N of open electronic channels in the two attached leads. We determine the full phase diagram in the (G, P)-plane, employing a Coulomb gas technique on the joint density of transmission eigenvalues, as dictated by random matrix theory. We find that in the region of typical fluctuations, conductance and shot noise are uncorrelated and jointly Gaussian, and away from it they fluctuate according to a different joint rate function in each phase of the (G, P)-plane. Different functional forms of the rate function in different regions emerge as a direct consequence of third-order phase transitions in the associated Coulomb gas problem.

We try to characterize the statistics of multipartite entanglement of the random states of an n-qubit system. Unable to solve the problem exactly we generalize it, replacing complex numbers with real vectors with Nc components (the original problem is recovered for Nc=2). Studying the leading diagrams in the large−Nc approximation, we unearth the presence of a phase transition and, in an explicit example, show that the so-called entanglement frustration disappears in the large−Nc limit.

We study the conditions for obtaining maximally multipartite-entangled states (MMESs) as nondegenerate eigenstates of Hamiltonians that involve only short-range interactions. We investigate small-size systems (with a number of qubits ranging from 3 to 5) and show some example Hamiltonians with MMESs as eigenstates.

Some features of the global entanglement of a composed quantum system can be quantified in terms of the purity of a balanced bipartition, made up of half of its subsystems. For the given bipartition, purity can always be minimized by taking a suitable (pure) state. When many bipartitions are considered, the requirement that purity be minimal for all bipartitions can engender conflicts and frustration will arise. This unearths an interesting link between frustration and multipartite entanglement, defined as the average purity over all (balanced) bipartitions.

A connection is established between the non-Abelian phases obtained via adiabatic driving and those acquired via quantum Zeno dynamics induced by repeated projective measurements. In comparison to the adiabatic case, the Zeno dynamics is shown to be more flexible in tuning the system evolution, which paves the way for the implementation of unitary quantum gates and applications in quantum control.

We compare the Radon transform in its standard and symplectic formulations and argue that the analytical inversion of the latter is easier to perform.

We study the distribution of the Schmidt coefficients of the reduced density matrix of a quantum system in a pure state. By applying general methods of statistical mechanics, we introduce a fictitious temperature and a partition function and translate the problem in terms of the distribution of the eigenvalues of random matrices. We investigate the appearance of two phase transitions, one at a positive temperature, associated with very entangled states, and one at a negative temperature, signaling the appearance of a significant factorization in the many-body wave function. We also focus on the presence of metastable states (related to two-dimensional quantum gravity) and study the finite size corrections to the saddle point solution.

We discuss an implementation of quantum Zeno dynamics in a cavity quantum electrodynamics experiment. By performing repeated unitary operations on atoms coupled to the field, we restrict the field evolution in chosen subspaces of the total Hilbert space. This procedure leads to promising methods for tailoring nonclassical states. We propose to realize ‘‘tweezers’’ picking a coherent field at a point in phase space and moving it towards an arbitrary final position without affecting other nonoverlapping coherent components. These effects could be observed with a state-of-the-art apparatus.

A new family of polarized ensembles of random pure states is presented. These ensembles are obtained by linear superposition of two random pure states with suitable distributions, and are quite manageable. We will use the obtained results for two purposes: on the one hand we will be able to derive an efficient strategy for sampling states from isopurity manifolds. On the other, we will characterize the deviation of a pure quantum state from separability under the influence of noise.

If the state of a quantum system is sampled out of a suitable ensemble, the measurement of some observables will yield (almost) always the same result. This leads us to the notion of quantum typicality: for some quantities the initial conditions are immaterial. We discuss this problem in the framework of Bose–Einstein condensates.

If frequent measurements ascertain whether a quantum system is still in a given subspace, it remains in that subspace and a quantum Zeno effect takes place. The limiting time evolution within the projected subspace is called quantum Zeno dynamics. This phenomenon is related to the limit of a product formula obtained by intertwining the time evolution group with an orthogonal projection. By introducing a novel product formula, we will give a characterization of the quantum Zeno effect for finite-rank projections in terms of a spectral decay property of the Hamiltonian in the range of the projections. Moreover, we will also characterize its limiting quantum Zeno dynamics and exhibit its -- not necessarily bounded from below -- generator as a generalized mean value Hamiltonian.

We provide a general framework for handling the effects of a unitary disturbance on the estimation of the amplitude λ associated to a unitary dynamics. By computing an analytical and general expression for the quantum Fisher information, we prove that the optimal estimation precision for λ cannot be outperformed through the addition of such a unitary disturbance. However, if the dynamics of the system is already affected by an external field, increasing its strength does not necessarily imply a loss in the optimal estimation precision.

We analyze the quantum Zeno dynamics that takes place when a field stored in a cavity undergoes frequent interactions with atoms. We show that repeated measurements or unitary operations performed on the atoms probing the field state confine the evolution to tailored subspaces of the total Hilbert space. This confinement leads to nontrivial field evolutions and to the generation of interesting nonclassical states, including mesoscopic field state superpositions. We elucidate the main features of the quantum Zeno mechanism in the context of a state-of-the-art cavity quantum electrodynamics experiment. A plethora of effects is investigated, from state manipulations by phase space tweezers to nearly arbitrary state synthesis. We analyze in details the practical implementation of this dynamics and assess its robustness by numerical simulations including realistic experimental imperfections. We comment on the various perspectives opened by this proposal.

We analyze the recently introduced notion of quantumness witnesses and compare it to that of entanglement witnesses. We show that any entanglement witness is also a quantumness witness. We then consider some physically relevant examples and explicitly construct some witnesses.

We present here a set of lecture notes on quantum systems with time-dependent boundaries. In particular, we analyze the dynamics of a non-relativistic particle in a bounded domain of physical space, when the boundaries are moving or changing. In all cases, unitarity is preserved and the change of boundaries does not introduce any decoherence in the system.

We describe a cavity QED experiment on quantum Zeno effect with Rydberg atoms and a microwave superconducting cavity. We propose an implementation of quantum Zeno dynamics leading to promising methods for tailoring nonclassical field states. (C) 2010 Optical Society of America

We scrutinize the effects of non-ideal data acquisition on the tomograms of quantum states. The presence of a weight function, schematizing the effects of a finite window or equivalently noise, only affects the state reconstruction procedure by a normalization constant. The results are extended to a discrete mesh and show that quantum tomography is robust under incomplete and approximate knowledge of tomograms.

We derive the motion equations and the structure equations of neutral and charged test particles, starting from the gravitational field equations. The method consists in the ap- plication of conservation laws to singular tensor densities, which represent regions of strong matter concentration. Moreover, a Hamiltonian formulation of the particle equa- tions is given, in the form of implicit differential equations generated by Hamiltonian Morse families.

We reconsider the e®ect of indistinguishability on the reduced density operator of the internal degrees of freedom (tracing out the spatial degrees of freedom) for a quantum system composed of identical particles located in di®erent spatial regions. We explicitly show that if the spin measurements are performed in disjoint spatial regions then there are no constraints on the structure of the reduced state of the system. This implies that the statistics of identical particles has no role from the point of view of separability and entanglement when the measurements are spatially separated. We extend the treatment to the case of n particles and show the connection with some recent criteria for separability based on subalgebras of observables.

We analyze the energetic and dynamical properties of bright-bright (BB) soliton pairs in a binary mixture of Bose-Einstein condensates subjected to the action of a combined optical lattice, acting as an external potential for the first species while modulating the intraspecies coupling constant of the second. In particular, we use a variational approach and direct numerical integrations to investigate the existence and stability of bright-bright (BB) solitons in which the two species are either spatially separated (split soliton) or located at the same optical lattice site (overlapped soliton). The dependence of these solitons on the interspecies interaction parameter is explicitly investigated. For repulsive interspecies interaction we show the existence of a series of critical values at which transitions from an initially overlapped soliton to split solitons occur. For attractive interspecies interaction only single direct transitions from split to overlapped BB solitons are found. The possibility to use split solitons for indirect measurements of scattering lengths is also suggested.

The local purity of large many-body quantum systems can be studied by following a statistical mechanical approach based on a random matrix model. Restricting the analysis to the case of global pure states, this method proved to be successful, and a full characterization of the statistical properties of the local purity was obtained by computing the partition function of the problem. Here we generalize these techniques to the case of global mixed states. In this context, by uniformly sampling the phase space of states with assigned global mixedness, we determine the exact expression of the first two moments of the local purity and a general expression for the moments of higher order. This generalizes previous results obtained for globally pure configurations. Furthermore, through the introduction of a partition function for a suitable canonical ensemble, we compute the approximate expression of the first moment of the marginal purity in the high-temperature regime. In the process, we establish a formal connection with the theory of quantum twirling maps that provides an alternative, possibly fruitful, way of performing the calculation.

We study a Hamiltonian system describing a three-spin-1/2 clusterlike interaction competing with an Ising-like antiferromagnetic interaction. We compute free energy, spin-correlation functions, and entanglement both in the ground and in thermal states. The model undergoes a quantum phase transition between an Ising phase with a nonvanishing magnetization and a cluster phase characterized by a string order. Any two-spin entanglement is found to vanish in both quantum phases because of a nontrivial correlation pattern. Nevertheless, the residual multipartite entanglement is maximal in the cluster phase and dependent on the magnetization in the Ising phase. We study the block entropy at the critical point and calculate the central charge of the system, showing that the criticality of the system is beyond the Ising universality class.

The evolution of a quantum system subjected to infinitely many measurements in a finite time interval is confined in a proper subspace of the Hilbert space. This phenomenon is called ‘quantum Zeno effect’: a particle under intensive observation which does not evolve. This effect is at variance with the classical evolution, which obviously is not affected by any observations. By a semiclassical analysis, we will show that the quantum Zeno effect vanishes at all orders, when the Planck constant tends to zero, and thus it is a purely quantum phenomenon without classical analog, at the same level of tunneling.

The quantum Zeno effect is described in geometric terms. The quantum Zeno time (inverse standard deviation of the Hamiltonian) and the generator of the quantum Zeno dynamics are both given a geometric interpretation.

A time-dependent product is introduced between the observables of a dissipative quantum system, that accounts for the effects of dissipation on observables and commutators. In the t -> infinity limit this yields a contracted algebra. This product can be transported back by duality on the space of states. The general ideas are corroborated by a few explicit examples.

In this article we present a review of the Radon transform and the instability of the tomographic reconstruction process. We show some new mathematical results in tomography obtained by a variational formulation of the reconstruction problem based on the minimization of a Mumford–Shah type functional. Finally, we exhibit a physical interpretation of this new technique and discuss some possible generalizations.

We search for the optimal quantum pure states of identical bosonic particles for applications in quantum metrology, in particular, in the estimation of a single parameter for the generic two-mode interferometric setup. We consider the general case in which the total number of particles is fluctuating around an average N with variance ΔN2. By recasting the problem in the framework of classical probability, we clarify the maximal accuracy attainable and show that it is always larger than the one reachable with a fixed number of particles (i.e., ΔN=0). In particular, for larger fluctuations, the error in the estimation diminishes proportionally to 1/ΔN, below the Heisenberg-like scaling 1/N. We also clarify the best input state, which is a quasi-NOON state for a generic setup and, for some special cases, a two-mode Schrödinger-cat state with a vacuum component. In addition, we search for the best state within the class of pure Gaussian states with a given average N, which is revealed to be a product state (with no entanglement) with a squeezed vacuum in one mode and the vacuum in the other.

A class of k-particle observables in a two-mode system of Bose particles is characterized by typicality: if the state of the system is sampled out of a suitable ensemble, an experimental measurement of that observable (almost) always yields the same result. We investigate the general features of typical observables and the criteria to determine typicality and finally focus on the case of density correlation functions, which are related to spatial distribution of particles and interference.

Let a pure state vertical bar psi > be chosen randomly in an NM-dimensional Hilbert space, and consider the reduced density matrix rho(A) of an N-dimensional subsystem. The bipartite entanglement properties of vertical bar psi > are encoded in the spectrum of rho(A). By means of a saddle point method and using a "Coulomb gas" model for the eigenvalues, we obtain the typical spectrum of reduced density matrices. We consider the cases of an unbiased ensemble of pure states and of a fixed value of the purity. We finally obtain the eigenvalue distribution by using a statistical mechanics approach based on the introduction of a partition function.

We study the time evolution of a Bose-Einstein condensate in an accelerated optical lattice. When the condensate has a narrow quasi-momentum distribution and the optical lattice is shallow, the survival probability in the ground band exhibits a step-like structure. In this regime, we establish a connection between the wave-function renormalization parameter Z and the phenomenon of resonantly enhanced tunneling.

We study the time evolution of ultracold atoms in an accelerated optical lattice. For a Bose-Einstein condensate with a narrow quasimomentum distribution in a shallow optical lattice the decay of the survival probability in the ground band has a steplike structure. In this regime we establish a connection between the wave-function- renormalization parameter Z introduced by P. Facchi, H. Nakazato, and S. Pascazio [Phys. Rev. Lett. 86, 2699 (2001)] to characterize nonexponential decay and the phenomenon of resonantly enhanced tunneling, where the decay rate is peaked for particular values of the lattice depth and the accelerating force.