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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