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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

- Read more about Multigrid Renormalization. (arXiv:1802.07259v1 [physics.comp-ph])
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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

- Read more about Electron-Phonon Systems on a Universal Quantum Computer. (arXiv:1802.07347v1 [quant-ph])
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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