The Ryu-Takayanagi (RT) formula relates the entanglement entropy of a region
in a holographic theory to the area of a corresponding bulk minimal surface.
Using the max flow-min cut principle, a theorem from network theory, we rewrite
the RT formula in a way that does not make reference to the minimal surface.
Instead, we invoke the notion of a "flow", defined as a divergenceless
norm-bounded vector field, or equivalently a set of Planck-thickness "bit

We investigate the effect of spatial disorder on the edge states localized at
the interface between two topologically different regions. Rotation disorder
can localize the quantum walk if it is strong enough to change the topology,
otherwise the edge state is protected. Nonlinear spatial disorder, dependent on
the walker's state, attracts the walk to the interface even for very large
coupling, preserving the ballistic transport characteristic of the clean

Simulating quantum nonlocality and steering requires augmenting pre-shared
randomness with non-vanishing communication cost. This prompts the question of
how one may provide such an operational characterization for the quantumness of
correlations due even to unentangled states. Here we show that for a certain
class of states, such quantumness can be pointed out by superlocality, the
requirement for a larger dimension of the pre-shared randomness to simulate the

For any given channel $W$ with classical inputs and possibly quantum outputs,
a dual classical-input channel $W^\perp$ can be defined by embedding the
original into a channel $\mathcal N$ with quantum inputs and outputs. Here we
give new uncertainty relations for a general class of entropies that lead to
very close relationships between the original channel and its dual. Moreover,
we show that channel duality can be combined with duality of linear codes,

We study characteristics of quantum evolution which can be called curvature
and torsion. The curvature shows a deviation of the state vector in quantum
evolution from the geodesic line. The torsion shows a deviation of state vector
from the plane of evolution (a two-dimensional subspace) at a given time.

We illustrate the adiabatic quantum computing solution of the knapsack
problem with both integer profits and weights. For problems with $n$ objects
(or items) and integer capacity $c$, we give specific examples using both an
Ising class problem Hamiltonian requiring $n+c$ qubits and a much more
efficient one using $n+[\log_2 c]+1$ qubits. The discussion includes a brief
mention of classical algorithms for knapsack, applications of this commonly
occurring problem, and the relevance of further studies both theoretically and

One of the main interest in quantum cosmology is to determine boundary
conditions for the wave function of the universe which can predict
observational data of our universe. For this purpose, we solve the
Wheeler-DeWitt equation for a closed universe with a scalar field numerically
and evaluate probabilities for boundary conditions of the wave function of the
universe. To impose boundary conditions of the wave function, we use exact
solutions of the Wheeler-DeWitt equation with a constant scalar field

The aim of this paper is to bring together the notions of quantum game and
game isomorphism. The work is intended as an attempt to introduce a new
criterion for quantum game schemes. The generally accepted requirement forces a
quantum scheme to generate the classical game in a particular case. Now, given
a quantum game scheme and two isomorphic classical games, we additionally
require the resulting quantum games to be isomorphic as well. We are concerned
with the Eisert-Wilkens-Lewenstein quantum game scheme and the strong

Establishing a quantum interface between different physical systems is of
special importance for developing the practical versatile quantum networks.
Entanglement between low- and high-lying atomic spin waves is essential for
building up Rydberg-based quantum information engineering, otherwhile be more
helpful to study the dynamics behavior of entanglement under external pertur-
bations. Here, we report on the successful storage of a single photon as a
high-lying atomic spin wave in quantum regime. Via storing a K-vector

Consecutive measurements performed on the same quantum system can reveal
fundamental insights into quantum theory's causal structure, and probe
different aspects of the quantum measurement problem. According to the
Copenhagen interpretation, measurements affect the quantum system in such a way
that the quantum superposition collapses after the measurement, erasing any
knowledge of the prior state. We show here that counter to this view,
unamplified measurements (measurements where all variables comprising a pointer