In the interface between general relativity and relativistic quantum
mechanics, we analyse rotating effects on the scalar field subject to a
hard-wall confining potential. We consider three different scenarios of general
relativity given by the cosmic string spacetime, the spacetime with space-like
dislocation and the spacetime with a spiral dislocation. Then, by searching for
a discrete spectrum of energy, we analyse analogues effects of the
Aharonov-Bohm effect for bound states and the Sagnac effect.

We combine the multigrid (MG) method with state-of-the-art concepts from the
variational formulation of the numerical renormalization group. The resulting
MG renormalization (MGR) method is a natural generalization of the MG method
for solving partial differential equations. When the solution on a grid of $N$
points is sought, our MGR method has a computational cost scaling as
$\mathcal{O}(\log(N))$, as opposed to $\mathcal{O}(N)$ for the best standard MG

Bhat characterizes the family of linear maps defined on $B(\mathcal{H})$
which preserve unitary conjugation. We generalize this idea and study the maps
with a similar equivariance property on finite-dimensional matrix algebras. We
show that the maps with equivariance property are significant to study
$k$-positivity of linear maps defined on finite-dimensional matrix algebras.
Choi showed that $n$-positivity is different from $(n-1)$-positivity for the
linear maps defined on $n$ by $n$ matrix algebras. In this paper, we present a

The modular valued operator $\widehat{V}_m$ of the von Neumann interaction
operator for a projector is defined. The properties of $\widehat{V}_m$ are
discussed and contrasted with those of the standard modular value of a
projector. The associated notion of a faux qubit is introduced and its possible
utility in quantum computation is noted. An experimental implementation of
$\widehat{V}_m$ is also highlighted.

Secure communication is of paramount importance in modern society. Asymmetric
cryptography methods such as the widely used RSA method allow secure exchange
of information between parties who have not shared secret keys. However, the
existing asymmetric cryptographic schemes rely on unproven mathematical
assumptions for security. Further, the digital keys used in their
implementation are susceptible to copying that might remain unnoticed. Here we
introduce a secure communication method that overcomes these two limitations by

As a toy model for the capacity problem in quantum information theory we
investigate finite and asymptotic regularizations of the maximum pure-state
input-output fidelity $F(\cal N$) of a general quantum channel $\cal N$. We
show that the asymptotic regularization $\tilde F(\cal N$) is lower bounded by
the maximum output $\infty$-norm $\nu_\infty(\cal N)$ of the channel. For $\cal
N$ being a Pauli channel we find that both quantities are equal.

Minimally twisted bilayer graphene exhibits a lattice of AB and BA stacked
regions. At small carrier densities and large displacement field, topological
channels emerge and form a network. We fabricate small-angle twisted bilayer
graphene and tune it with local gates. In our transport measurements we observe
Fabry-P\'erot and Aharanov-Bohm oscillations which are robust in magnetic
fields ranging from 0 to 8T. The Fabry-P\'erot trajectories in the bulk of the

We derive an attainable bound on the precision of quantum state estimation
for finite dimensional systems, providing a construction for the asymptotically
optimal measurement. Our results hold under an assumption called local
asymptotic covariance, which is weaker than unbiasedness or local unbiasedness.
The derivation is based on an analysis of the limiting distribution of the
estimator's deviation from the true value of the parameter, and takes advantage
of quantum local asymptotic normality, a duality between sequences of

We present an algorithm that extends existing quantum algorithms for
simulating fermion systems in quantum chemistry and condensed matter physics to
include phonons. The phonon degrees of freedom are represented with exponential
accuracy on a truncated Hilbert space with a size that increases linearly with
the cutoff of the maximum phonon number. The additional number of qubits
required by the presence of phonons scales linearly with the size of the
system. The additional circuit depth is constant for systems with finite-range

We study unextendible maximally entangled bases (UMEBs) in \(\mathbb
{C}^{d}\otimes \mathbb {C}^{d^{\prime}}\) ($d<d'$). An operational method to
construct UMEBs containing $d(d^{\prime}-1)$ maximally entangled vectors is
established, and two UMEBs in \(\mathbb {C}^{5}\otimes \mathbb {C}^{6}\) and
\(\mathbb {C}^{5}\otimes \mathbb {C}^{12}\) are given as examples. Furthermore,
a systematic way of constructing UMEBs containing $d(d^{\prime}-r)$ maximally