arXiv subjects

P. Facchi

Publications and source records attributed to P. Facchi.

At least 19 recordsLinked to original sources

arXiv2025

Bridging Classical and Quantum Worlds: Maps, States, and Evolutions

In this work, we present several aspects of the interplay between classical and quantum theories. After reviewing the equivalence between positivity and complete positivity in the commutative setting, we introduce and analyze intermediate notions that interpolate between these two properties for linear maps on the space of operators on a Hilbert space, highlighting their natural connections to quantum dynamics and entanglement theory. Finally, we discuss possible constructions that allow one to derive quantum states and evolutions from classical counterparts, and vice versa.

quant-ph↗

arXiv2024

Directional emission and photon bunching from a qubit pair in waveguide

Waveguide quantum electrodynamics represents a powerful platform to generate entanglement and tailor photonic states. We consider a pair of identical qubits coupled to a parity invariant waveguide in the microwave domain. By working in the one- and two-excitation sectors, we provide a unified view of decay processes and we show the common origin of directional single photon emission and two photon directional bunching. Unveiling the quantum trajectories, we demonstrate that both phenomena are rooted in the selective coupling of orthogonal qubits Bell states with different photon propagation directions. We comment on how to use this mechanism to implement optimized post-selection of Bell states, heralded by the detection of photons on one qubits side.

quant-ph↗

arXiv2024

Multi-parameter estimation of the state of two interfering photonic qubits

It is demonstrated a two-photon interfering technique based on polarization-resolved measurements for the simultaneous estimation with the maximum sensitivity achievable in nature of multiple parameters associated with the polarization state of two interfering photonic qubits. This estimation is done by exploiting a novel interferometry technique based on polarization-resolved two-photon interference. We show the experimental feasibility and accuracy of this technique even when a limited number of sampling measurements is employed. This work is relevant for the development of quantum technologies with photonic qubits and sheds light on the physics at the interface between multiphoton interference, boson sampling, multi-parameter quantum sensing and quantum information processing.

quant-ph↗

arXiv2015

A large-N approximated field theory for multipartite entanglement

We study the characterization of multipartite entanglement for the random states of an $n$-qbit system. Unable to solve the problem exactly we generalize it, changing complex numbers into real vectors with $N_c$ components (the original problem is recovered for $N_c=2$). Studying the leading diagrams in the large-$N_c$ 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-$N_c$ limit.

quant-ph↗

arXiv2015

Generalized tomographic maps and star-product formalism

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.

quant-ph↗

arXiv2014

Interference in a two-mode Bose system with $N$ particles is typical

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 condensates.

quant-ph↗

arXiv2014

Spatial separation and entanglement of identical particles

We reconsider the effect 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 different 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.

math-ph↗

arXiv2013

Quantum parameter estimation affected by unitary disturbance

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 necessary imply a loss in the optimal estimation precision.

quant-ph↗

arXiv2013

Polarized ensembles of random pure states

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.

math-ph↗

arXiv2013

Invariant measures on multimode quantum Gaussian states

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.

quant-ph↗

arXiv2012

Generalized quantum tomographic maps

Some non-linear generalizations of classical Radon tomography were recently introduced by M. Asorey et al [Phys. Rev. A 77, 042115 (2008), where the straight lines of the standard Radon map are replaced by quadratic curves (ellipses, hyperbolas, circles) or quadratic surfaces (ellipsoids, hyperboloids, spheres). We consider here the quantum version of this novel non-linear approach and obtain, by systematic use of the Weyl map, a tomographic encoding approach to quantum states. Non-linear 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 for quantum state measurements of photons and matter waves are discussed.

quant-ph↗

arXiv2012

Entanglement-assisted tomography of a quantum target

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 Cramér-Rao bounds, we compare the accuracy efficiency that one can get 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.

quant-ph↗

arXiv2012

Wave Function Renormalization Effects in Resonantly Enhanced Tunneling

We study the time evolution of ultra-cold atoms in an accelerated optical lattice. For a Bose- Einstein condensate with a narrow quasi-momentum distribution in a shallow optical lattice the decay of the survival probability in the ground band has a step-like structure. In this regime we establish a connection between the wave function renormalization parameter Z introduced in [Phys. Rev. Lett. 86, 2699 (2001)] to characterize non-exponential 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.

quant-ph↗

arXiv2011

Statistical distribution of the local purity in a large quantum system

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. Since the computation of the partition function is far more challenging than in the pure case, we focus on the computation of the first moments of the local purity. Finally, we establish a connection with the theory of twirling maps in quantum channels.

quant-ph↗

arXiv2011

Binary mixtures of condensates in generic confining potentials

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.

math-ph↗

arXiv2011

Further evidence of antibunching of two coherent beams of fermions

We describe an experiment confirming the evidence of the antibunching effect on a beam of non interacting 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.

quant-ph↗

arXiv2011

Robustness of raw quantum tomography

We scrutinize the effects of non-ideal data acquisition on the homodyne tomograms of photon quantum states. The presence of a weight function, schematizing the effects of the finite thickness of the probing beam 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.

quant-ph↗

arXiv2011

Classical Statistical Mechanics Approach to Multipartite Entanglement

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.

quant-ph↗