We numerically investigate the low-lying entanglement spectrum of the ground
state of random one dimensional spin chains obtained after a partition of the
chain in two equal halves. We consider two paradigmatic models: the spin-1/2
random transverse field Ising model, solved exactly, and the spin-1 random
Heisenberg model, simulated using the density matrix renormalization group. In
both cases we analyse the mean Schmidt gap, defined as the difference of the
two largest eigenvalues of the reduced density matrix of one of the two

Quantum multiparameter estimation involves estimating multiple parameters
simultaneously and was shown to be more accurate than estimating the parameters
individually. Our interest here is to determine multiparameter quantum
Cramer-Rao bounds (QCRBs) for noisy metrology. We do so, in particular, using
anti-symmetric logarithmic derivatives (ALDs) for the quantum Fisher
information matrix (QFIM). A recent work studied the simultaneous estimation of
all three components of a magnetic field using a pure probe state and unitary

Recently, the search for topological states of matter has turned to
non-Hermitian systems, which exhibit a rich variety of unique properties
without Hermitian counterparts. Lattices modeled through non-Hermitian
Hamiltonians appear in the context of photonic systems, where one needs to
account for gain and loss, circuits of resonators, and also when modeling the
lifetime due to interactions in condensed matter systems. Here we provide a
brief overview of this rapidly growing subject, the search for topological

Quantum state tomography aims to determine the quantum state of a system from
measured data and is an essential tool for quantum information science. When
dealing with continuous variable quantum states of light, tomography is often
done by measuring the field amplitudes at different optical phases using
homodyne detection. The quadrature-phase homodyne measurement outputs a
continuous variable, so to reduce the computational cost of tomography,
researchers often discretize the measurements. We show that this can be done

We show that it is possible to consistently describe dynamical systems, whose
equations of motion are of degree higher than two, in the microcanonical
ensemble, even if the higher derivatives aren't coordinate artifacts. Higher
time derivatives imply that there are more than one Hamiltonians, conserved
quantities due to time translation invariance, and, if the volume in phase
space, defined by their intersection, is compact, microcanonical averages can

We study fermionic topological phases using the technique of fermion
condensation. We give a prescription for performing fermion condensation in
bosonic topological phases which contain a fermion. Our approach to fermion
condensation can roughly be understood as coupling the parent bosonic
topological phase to a phase of physical fermions, and condensing pairs of
physical and emergent fermions. There are two distinct types of objects in
fermionic theories, which we call "m-type" and "q-type" particles. The

Recent theoretical and experiments have explored the use of entangled photons
as a spectroscopic probe of material systems. We develop here a theoretical
description for entropy production in the scattering of an entangled biphoton
state within an optical cavity. We develop this using perturbation theory by
expanding the biphoton scattering matrix in terms of single-photon terms in
which we introduce the photon-photon interaction via a complex coupling
constant, $\xi$. We show that the von Neumann entropy provides a succinct

In this paper we numerically analyze the 1D self-localized solutions of the
Kundu-Eckhaus equation (KEE) in nonlinear waveguides using the spectral
renormalization method (SRM) and compare our findings with those solutions of
the nonlinear Schrodinger equation (NLSE). We show that single, dual and
N-soliton solutions exist for the case with zero optical potentials, i.e. V=0.
We also show that these soliton solutions do not exist, at least for a range of
parameters, for the photorefractive lattices with optical potentials in the

The effect of disorder in the intensity of the driving laser on the dynamics
of a disordered three-cavity system of four-level atoms is investigated. This
system can be described by a Bose-Hubbard Hamiltonian for dark-state
polaritons. We examine the evolution of the first- and second-order correlation
functions, the photon and atomic excitation numbers and the basis state
occupation probabilities. We use the full Hamiltonian and the approximate
Bose-Hubbard Hamiltonian with uniform and speckle disorder, as well as with

In a recent paper [Phys. Rev. A {\bf 96}, 053822 (2017)], we proposed a
strategy to generate bipartite and quadripartite continuous-variable
entanglement of bright quantum states based on degenerate down-conversion in a
pair of evanescently coupled nonlinear $\chi^{(2)}$ waveguides. Here, we show
that the resources needed for obtaining these features can be optimized by
exploiting the regime of second harmonic generation: the combination of
depletion and coupling among pump beams indeed supplies all necessary