Mean King’s problem is formulated as a retrodiction problem among noncommutative observables. In this paper, we reformulate Mean King’s problem using Shannon’s entropy as a first step of introducing quantum uncertainty relation with delayed classical information. As a result, we give informational and statistical meanings to the estimation on Mean King problem. As its application, we give an alternative proof of nonexistence of solutions of Mean King’s problem for qubit system without using entanglement.

Abstract:
We make a brief historical revision of action-at-a-distance in quantum mechanics. Non-locality has been mostly related to systems of two particles in an entangled state. We show that this effect is also apparent in some experiments with individual particles. An easily performed experiment in this regard is introduced.

Abstract:
The quantum metric tensor was introduced for defining the distance in the parameter space of a system. However, it is also useful for other purposes, like predicting quantum phase transitions. Due to the physical information this tensor provides, its gauge independence sounds reasonable. Moreover, its original construction was made by looking for this gauge independence. The aim of this paper, however, is to prove that the quantum metric tensor does depend on the gauge. In addition, a real gauge invariant quantum metric tensor is introduced. A related concept is the quantum fidelity, which is also shown to depend on the gauge in this paper. The gauge dependences are explicitly shown by computing the quantum metric tensor and the quantum fidelity of the Landau problem in different gauges. Then, a real gauge independent metric tensor is proposed and computed for the same Landau problem. Since the gauge dependences have not been observed before, the results of this paper might lead to a new study of topics that are believed to be completely understood.

Abstract:
In this paper, it showed that the orthodox version of quantum mechanics contradicts the idea that conservation laws are valid in individual processes of measurement.

Abstract:
We report on interviews conducted with twenty-one elementary school children (grades 1-5) about a number of Earth science concepts. These interviews were undertaken as part of a teacher training video series designed specifically to assist elementary teachers in learning essential ideas in Earth science. As such, children were interviewed about a wide array of earth science concepts, from rock formation to the Earth’s interior. We analyzed interview data primarily to determine whether or not young children are capable of inferring understanding of the past based on present-day observation (retrodictive reasoning) in the context of Earth science. This work provides a basis from which curricula for teaching earth and environmental sciences can emerge, and suggests that new studies into the retrodictive reasoning abilities of young children are needed, including curricula that encourage inference of the past from modern observations.

Abstract:
Loop quantum gravity is considered to be one of the two major candidates for a theory of quantum gravity. The most appealing aspect about this theory is it predicts that spacetime is not continuous; both space and time have a discrete nature. Simply, space is not infinitely divisible, but it has a granular structure, and time does not flow continuously like a smooth river. This paper demonstrates a review for two missed (unnoted) observations that support the discreteness of the spacetime. The content of this paper does not validate the specific model of quantized geometry of the spacetime which is predicted by the theory itself. Instead, it proves that time does not flow continuously. But it flows in certain, discrete steps, like a ticking of a clock, due to a simple observation which is absence of any possible value of time that can exist between the present and the future. Regarding space, it validates the spatial discreteness, and the existence of spatial granules (space quanta) due to a simple observation which is the existence of the origin position in a coordinates system. All of this is achieved by reviewing the concept of discreteness itself, and applied directly to the observations.

Abstract:
A
well-known, classical conundrum, which is related to conditional probability,
has heretofore only been used for games and puzzles. It is shown here, both
empirically and formally, that the counterintuitive phenomenon in question has
consequences that are far more profound, especially for physics. A simple card
game the reader can play at home demonstrates the counterintuitive phenomenon,
and shows how it gives rise to hidden variables. These variables are “hidden”
in the sense that they belong to the past and no longer exist. A formal proof
shows that the results are due to the duration of what can be thought of as a
gambler’s bet, without loss of generalization. The bet is over when it is won
or lost, analogous to the collapse of a wave function. In the meantime, new and
empowering information does not change the original probabilities. A related
thought experiment involving a pregnant woman demonstrates that macroscopic
systems do not always have states that are completely intrinsic. Rather, the
state of a macroscopic system may depend upon how the experiment is set up and
how the system is measured even though no wave functions are involved. This
obviously mitigates the chasm between the quantum mechanical and the classical.

Abstract:
Artificial
intelligence has permeated all aspects of our lives today. However, to make AI
behave like real AI, the critical bottleneck lies in the speed of computing.
Quantum computers employ the peculiar and unique properties of quantum states
such as superposition, entanglement, and interference to process information in
ways that classical computers cannot. As a new paradigm of computation, quantum
computers are capable of performing tasks intractable for classical processors,
thus providing a quantum leap in AI research and making the development of real
AI a possibility. In this regard, quantum machine learning not only enhances
the classical machine learning approach but more importantly it provides an
avenue to explore new machine learning models that have no classical
counterparts. The qubit-based quantum computers cannot naturally represent the
continuous variables commonly used in machine learning, since the measurement
outputs of qubit-based circuits are generally discrete. Therefore, a
continuous-variable (CV) quantum architecture based on a photonic quantum computing
model is selected for our study. In this work, we employ machine learning and
optimization to create photonic quantum circuits that can solve the contextual
multi-armed bandit problem, a problem in the domain of reinforcement learning,
which demonstrates that quantum reinforcement learning algorithms can be
learned by a quantum device.

Abstract:
The classical Ambarzumian's Theorem for Schrodinger operators $-D^2 + q$ on an interval, with Neumann conditions at the endpoints, says that if the spectrum of $(-D^2+q)$ is the same as the spectrum of $(-D^2)$ then $q=0$. This theorem is generalized to Schrodinger operators on metric trees with Neumann conditions at the boundary vertices.

Abstract:
a quantum version of the monty hall problem, based upon the positive operator valued measures (povm) formalism, is proposed. it is shown that basic normalization and symmetry arguments lead univocally to the associated povm elements, and that the classical probabilities associated with the monty hall scenario are recovered for a natural choice of the measurement operators.