We construct quantum MDS codes for quantum systems of dimension $q$ of length
$q^2+1$ and minimum distance $d$ for all $d \leqslant q+1$, $d \neq q$. These
codes are shown to exist by proving that there are classical generalised
Reed-Solomon codes which are contained in their Hermitian-dual. These
constructions include many constructions which were previously known but in
some cases these codes appear to be new. We go on to prove that if $d\geqslant
q+2$ then there in no generalised Reed-Solomon code which is contained in its

In this manuscript, we investigate the exact bound state solution of the
Klein Gordon equation with an energy-dependent Coulomb-like potential energy in
the presence of position-energy dependent mass. First, we examine the case
where the mixed vector and scalar potential energy possess equal magnitude and
equal sign. Then, we extend the investigation with the cases where the mixed
potential energies have equal magnitude and opposite sign. Furthermore, we

We present and analyze a proposal for a macroscopic quantum delayed-choice
experiment with massive mechanical resonators. In our approach, the electronic
spin of a single nitrogen-vacancy impurity is employed to control the coherent
coupling between the mechanical modes of two carbon nanotubes. We demonstrate
that a mechanical phonon can be in a coherent superposition of wave and
particle, thus exhibiting both behaviors at the same time. We also discuss the

Fixed node diffusion quantum Monte Carlo (FN-DMC) is an increasingly used
computational approach for investigating the electronic structure of molecules,
solids, and surfaces with controllable accuracy. It stands out among equally
accurate electronic structure approaches for its favorable cubic scaling with
system size, which often makes FN-DMC the only computationally affordable
high-quality method in large condensed phase systems with more than 100 atoms.
In such systems FN-DMC deploys pseudopotentials to substantially improve

Kippenhahn's Theorem asserts that the numerical range of a matrix is the
convex hull of a certain algebraic curve. Here, we show that the joint
numerical range of finitely many hermitian matrices is similarly the convex
hull of a semi-algebraic set. We discuss an analogous statement regarding the
dual convex cone to a hyperbolicity cone and prove that the class of convex
bases of these dual cones is closed under linear operations. The result offers
a new geometric method to analyze quantum states.

We present a secure multi-party quantum summation protocol based on quantum
teleportation, in which a malicious, but non-collusive, third party (TP) helps
compute the summation. In our protocol, TP is in charge of entanglement
distribution and Bell states are shared between participants. Users encode the
qubits in their hand according to their private bits and perform Bell-state
measurements. After obtaining participants' measurement results, TP can figure

Hybrid quantum/classical variational algorithms can be implemented on noisy
intermediate-scale quantum computers and can be used to find solutions for
combinatorial optimization problems. Approaches discussed in the literature
minimize the expectation of the problem Hamiltonian for a parameterized trial
quantum state. The expectation is estimated as the sample mean of a set of
measurement outcomes, while the parameters of the trial state are optimized
classically. This procedure is fully justified for quantum mechanical

Imperfect measurement can degrade a quantum error correction scheme. A
solution that restores fault tolerance is to add redundancy to the process of
syndrome extraction. In this work, we show how to optimize this process for an
arbitrary ratio of data qubit error probability to measurement error
probability. The key is to design the measurements so that syndromes that
correspond to different errors are separated by the maximum distance in the
signal space, in close analogy to classical error correction codes. We find

Entanglement entropy in free scalar field theory at its ground state is
dominated by an area law term. However, when mixed states are considered this
property ceases to exist. We show that in such cases the mutual information
obeys an "area law". The proportionality constant connecting the area to the
mutual information has an interesting dependence on the temperature. At
infinite temperature it tends to a finite value which coincides with the
classical calculation.

In classical mechanics, external constraints on the dynamical variables can
be easily implemented within the Lagrangian formulation. Conversely, the
extension of this idea to the quantum realm, which dates back to Dirac, has
proven notoriously difficult due to the noncommutativity of observables.
Motivated by recent progress in the experimental control of quantum systems, we
propose a framework for the implementation of quantum constraints based on the
idea of work protocols, which are dynamically engineered to enforce the