In this paper we introduce a definition for conditional energy changes due to
general quantum measurements, as the change in conditional energies of the
system evaluated before, and after, the measurement process. By imposing
minimal physical requirements on these conditional energies, we show that the
most general expression for the conditional energy after the measurement is
simply the expected value of the Hamiltonian given the post-measurement state.

In recent years, digraph induced generators of quantum dynamical semigroups
have been introduced and studied, particularly in the context of unique
relaxation and invariance. In this article we define the class of pair block
diagonal generators, which allows for additional interaction coefficients but
preserves the main structural properties. Namely, when the basis of the
underlying Hilbert space is given by the eigenbasis of the Hamiltonian (for
example the generic semigroups), then the action of the semigroup leaves

When a quantum system is divided into two local subsystems, measurements on
the two subsystems can exhibit correlations beyond those possible in a
classical joint probability distribution; these are partially explained by
entanglement, and more generally by a wider class of measures such as the
quantum discord. In this work, I introduce a simple thought experiment defining
a new measure of quantum correlations, which I call the accord, and write the
result as a minimax optimization over unitary matrices. I find the exact result

The probabilistic interpretation of quantum mechanics has been a point of
discussion since the earliest days of the theory. The development of quantum
technologies transfer these discussions from philosophical interest to
practical importance. We propose a synthesis of ideas appeared from the field's
founders to modern contextual approaches. The concept is illustrated by a
simple numerical experiment imitating photon interference in two beamsplitters.
This example demonstrates that deterministic physical principles can replicate

The Capacitated Vehicle Routing Problem (CVRP) is an NP-optimization problem
(NPO) that has been of great interest for decades for both, science and
industry. The CVRP is a variant of the vehicle routing problem characterized by
capacity constrained vehicles. The aim is to plan tours for vehicles to supply
a given number of customers as efficiently as possible. The problem is the
combinatorial explosion of possible solutions, which increases
superexponentially with the number of customers. Classical solutions provide

The Quadratic Unconstrained Binary Optimization (QUBO) model has gained
prominence in recent years with the discovery that it unifies a rich variety of
combinatorial optimization problems. By its association with the Ising problem
in physics, the QUBO model has emerged as an underpinning of the quantum
computing area known as quantum annealing and has become a subject of study in
neuromorphic computing. Through these connections, QUBO models lie at the heart

We show that a system of three trapped ultracold and strongly interacting
atoms in one-dimension can be emulated using an optical fiber with a
graded-index profile and thin metallic slabs. While the wave-nature of single
quantum particles leads to direct and well known analogies with classical
optics, for interacting many-particle systems with unrestricted statistics such
analoga are not straightforward. Here we study the symmetries present in the
fiber eigenstates by using discrete group theory and show that, by spatially

We state a number of related questions on the structure of perfect matchings.
Those questions are inspired by and directly connected to Quantum Physics. In
particular, they concern the constructability of general quantum states using
modern photonic technology. For that we introduce a new concept, denoted as
inherited vertex coloring. It is a vertex coloring for every perfect matching.
The colors are inherited from the color of the incident edge for each perfect
matching. First, we formulate the concepts and questions in pure

We present the Shannon entropy as an indicator of spatial resolution for
morphology of resonance mode pattern in dielectric micro cavity. We obtain two
types of optimized mesh point for the minimum and maximum sizes, respectively.
The critical mesh point for the minimum size is determined by the barely
identifiable quantum number through chi square test whereas the saturation of
difference of the Shannon entropy corresponds to the maximum size. We can also
show that the critical mesh point increases as the (real) wave number of

We derive a quasiclassical expression for the density of states (DOS) of an
arbitrary, ultracold, $N$-atom collision complex, for a general potential
energy surface (PES). We establish the accuracy of our quasiclassical method by
comparing to exact quantum results for the K$_2$-Rb and NaK-NaK systems, with
isotropic model PESs. Next, we calculate the DOS for an accurate NaK-NaK PES to
be 0.124~$\mu$K$^{-1}$, with an associated Rice-Ramsperger-Kassel-Marcus (RRKM)