Topological phases protected by symmetry can occur in gapped
and---surprisingly---in critical systems. We consider non-interacting fermions
in one dimension with spinless time-reversal symmetry. It is known that the
phases are classified by a topological invariant $\omega$ and a central charge
$c$. We investigate the correlations of string operators, giving insight into
the interplay between topology and criticality. In the gapped phases, these
non-local string order parameters allow us to extract $\omega$. Remarkably,

For many completely positive maps repeated compositions will eventually
become entanglement breaking. To quantify this behaviour we develop a technique
based on the Schmidt number: If a completely positive map breaks the
entanglement with respect to any qubit ancilla, then applying it to part of a
bipartite quantum state will result in a Schmidt number bounded away from the
maximum possible value. Iterating this result puts a successively decreasing
upper bound on the Schmidt number arising in this way from compositions of such

Clarifying the nature of the quantum state $|\Psi\rangle$ is at the root of
the problems with insight into (counterintuitive) quantum postulates. We
provide a direct -- and math axiom-free -- empirical derivation of this object
as an element of a vector space. Establishing the linearity of this structure
-- quantum superposition -- is based on a set-theoretic creation of ensemble
formations and invokes the following three principia: ($\textsf{I}$) quantum
statics, ($\textsf{II}$) doctrine of a number in a physical theory, and

The recent direct experimental measurement of quantum entanglement paves the
way towards a better understanding of many-body quantum systems and their
correlations. Nevertheless, the experimental and theoretical advances had so
far been predominantly limited to bosonic systems. Here, we study fermionic
systems. Using experimental setups where multiple copies of the same state are
prepared, arbitrary order Renyi entanglement entropies and entanglement
negativities can be extracted by utilizing spatially-uniform beam splitters and

Coherence is a basic phenomenon in quantum mechanics and considered to be an
essential resource in quantum information processing. Although the
quantification of coherence has attracted a lot of interest, the lack of
efficient methods to measure the coherence in experiments limits the
applications. We address this problem by introducing an experiment-friendly
method for coherence and spectrum estimation. This method is based on the
theory of majorization and can not only be used to prove the presence of

In recent decades, various multipartite entanglement measures have been
proposed by many researchers, with different characteristics. Meanwhile, Scott
studied various interesting aspects of multipartite entanglement measures and
he has defined a class of related multipartite entanglement measures in an
obvious manner. Recently, Jafarpour et al. (Int. J. Quantum Inform. 13, 1550047
2015) have calculated the entanglement quantity of two-dimensional 5-site spin

We study effects of perturbation Hamiltonian to quantum spin systems which
can include quenched disorder. Model-independent inequalities are derived,
using an additional artificial disordered perturbation. These inequalities
enable us to prove that the variance of the perturbation Hamiltonian density
vanishes in the infinite volume limit even if the artificial perturbation is
switched off. This theorem is applied to spontaneous symmetry breaking
phenomena in a disordered classical spin model, a quantum spin model without

Hybrid variational quantum algorithms have been proposed for simulating
many-body quantum systems with shallow quantum circuits, and are therefore
relevant to Noisy Intermediate Scale Quantum devices. These algorithms are
often discussed as a means to solve static energy spectra and simulate the
dynamics of real and imaginary time evolutions. Here we consider broader uses
of the variational method to simulate general processes. We first show a
variational algorithm for simulating the generalised time evolution with a

The entanglement and resonance energy transfer between two-level quantum
emitters are typically limited to sub-wavelength distances due to the
inherently short-range nature of the dipole-dipole interactions. Moreover, the
entanglement of quantum systems is hard to preserve for a long time period due
to decoherence and dephasing mainly caused by radiative and nonradiative
losses. In this work, we outperform the aforementioned limitations by
presenting efficient long-range inter-emitter entanglement and large

Mechanical modes are a potentially useful resource for quantum information
applications, such as quantum-level wavelength transducers, due to their
ability to interact with electromagnetic radiation across the spectrum. A
significant challenge for wavelength transducers is thermomechanical noise in
the mechanical mode, which pollutes the transduced signal with thermal states.
In this paper, we eliminate thermomechanical noise in the GHz-frequency
mechanical breathing mode of a piezoelectric optomechanical crystal using