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The mainstream textbooks of quantum mechanics explains the quantum state
collapses into an eigenstate in the measurement, while other explanations such
as hidden variables and multi-universe deny the collapsing. Here we propose an
ideal thinking experiment on measuring the spin of an electron with 3 steps. It
is simple and straightforward, in short, to measure a spin-up electron in
x-axis, and then in z-axis. Whether there is a collapsing predicts different
results of the experiment. The future realistic experiment will show the

It is NP-complete to find non-negative factors $W$ and $H$ with fixed rank
$r$ from a non-negative matrix $X$ by minimizing $\|X-WH^\top\|_F^2$. Although
the separability assumption (all data points are in the conical hull of the
extreme rows) enables polynomial-time algorithms, the computational cost is not
affordable for big data. This paper investigates how the power of quantum
computation can be capitalized to solve the non-negative matrix factorization

A simple classical non-local dynamical system with random initial conditions
and an output projecting the state variable on selected axes has been defined
to mimic a two-channel quantum coincidence experiment. Non-locality is
introduced by a parameter connecting the initial conditions to the selection of
the projection axes. The statistics of the results shows violations up to 100%
of the Bell's inequality, in the form of Clauser-Horne- Shimony-Holt (CHSH),
strongly depending on the non-locality parameter. Discussions on the

We prove spatial decay estimates on disorder-averaged position-momentum
correlations in a gapless class of random oscillator models. First, we prove a
decay estimate on dynamic correlations for general eigenstates with a bound
that depends on the magnitude of the maximally excited mode. Then, we consider
the situation of a quantum quench. We prove that the full time-evolution of an
initially chosen (uncorrelated) product state has disorder-averaged
correlations which decay exponentially in space, uniformly in time.

The Kronig-Penney model, an exactly solvable one-dimensional model of crystal
in solid physics, shows how the allowed and forbidden bands are formed in
solids. In this paper, we study this model in the presence of both strong
spin-orbit coupling and the Zeeman field. We analytically obtain four
transcendental equations that represent an implicit relation between the energy
and the Bloch wavevector. Solving these four transcendental equations, we
obtain the spin-orbital bands exactly. In addition to the usual band gap opened

This tutorial article provides a concise and pedagogical overview on
negatively-charged nitrogen-vacancy (NV) centers in diamond. The research on
the NV centers has attracted enormous attention for its application to quantum
sensing, encompassing the areas of not only physics and applied physics but
also chemistry, biology and life sciences. Nonetheless, its key technical
aspects can be understood from the viewpoint of magnetic resonance. We focus on
three facets of this ever-expanding research field, to which our viewpoint is

We provide a study of various quantum phase transitions occurring in the XY
Heisenberg chain in a transverse magnetic field using the Meyer-Wallach (MW)
measure of (global) entanglement. Such a measure, while being readily
evaluated, is a multipartite measure of entanglement as opposed to more
commonly used bipartite measures. Consequently, we obtain analytic expression
of the measure for finite-size systems and show that it can be used to obtain
critical exponents via finite-size scaling with great accuracy for the Ising

Collinear antiferromagnets (AFs) support two degenerate magnon excitations
carrying opposite spin polarizations, by which magnons can function as
electrons in spin transport. We explore the interlayer coupling mediated by
antiferromagnetic magnons in an insulating ferromagnet (F)/AF/F trilayer
structure. The internal energy of the AF depends on the orientations of the two
Fs, which manifests as effective interlayer interactions JS1.S2 and K(S1.S2)^2.
Both J and K are functions of temperature and the AF thickness. Interestingly,

We demonstrate a Bayesian quantum game on an ion trap quantum computer with
five qubits. The players share an entangled pair of qubits and perform
rotations on their qubit as the strategy choice. Two five-qubit circuits are
sufficient to run all 16 possible strategy choice sets in a game with four
possible strategies. The data are then parsed into player types randomly in
order to combine them classically into a Bayesian framework. We exhaustively
compute the possible strategies of the game so that the experimental data can

Hereunder we continue the study of the representation theory of the algebra
of permutation operators acting on the $n$-fold tensor product space, partially
transposed on the last subsystem. We develop the concept of partially reduced
irreducible representations, which allows to simplify significantly previously
proved theorems and what is the most important derive new results for
irreducible representations of the mentioned algebra. In our analysis we are