Related papers: LST Numbers for $Q^{\text{e.c.}}$ and $I$ style qu…

In this work, we present new connections between three types of quantum states: positive under partial transpose states, symmetric with positive coefficients states and invariant under realignment states. First, we obtain a common upper…

In this paper we present several classes of asymptotically good concatenated quantum codes and derive lower bounds on the minimum distance and rate of the codes. We compare these bounds with the best-known bound of…

Boltzmann codes are used extensively by several groups for constraining cosmological parameters with Cosmic Microwave Background and Large Scale Structure data. This activity is computationally expensive, since a typical project requires…

This paper introduces some methods to determine the simultaneous approximation constants of a class of well approximable numbers $\zeta_{1},\zeta_{2},...,\zeta_{k}$. The approach relies on results on the connection between the set of all…

In this paper we study the equivalence of quantum stabilizer codes via symplectic isometries of stabilizer codes. We define monomially and symplectically equivalent stabilizer codes and determine how different the two notions can be.…

The bound state extension of Skyrme's topological soliton model for the heavy baryons is quantized canonically in arbitrary reducible representations of the SU(3) flavor group. The canonical quantization leads to an additional negative mass…

Let $0<p,q\leq \infty$ and denote by $\mathcal S_p^N$ and $\mathcal S_q^N$ the corresponding Schatten classes of real $N\times N$ matrices. We study approximation quantities of natural identities $\mathcal S_p^N\hookrightarrow \mathcal…

Density matrices are positively semi-definite Hermitian matrices with unit trace that describe the states of quantum systems. Many quantum systems of physical interest can be represented as high-dimensional low rank density matrices. A…

In this initial paper in a series, we first discuss why classical motions of small particles should be treated statistically. Then we show that any attempted statistical description of any nonrelativistic classical system inevitably yields…

We develop an adequate description of non-topological solitons with a small charge, for which the thin-wall approximation is not valid. There is no classical lower limit on the charge of a stable Q-ball. We examine the parameters of these…

In this paper we provide explicit upper and lower bounds on certain $L^2$ $n$-widths, i.e., best constants in $L^2$ approximation. We further describe a numerical method to compute these $n$-widths approximately, and prove that this method…

We adopt a continuous model to estimate the Grothendieck constants. An analytical formula to compute the lower bounds of Grothendieck constants has been explicitly derived for arbitrary orders, which improves previous bounds. Moreover, our…

We study the list decodability of different ensembles of codes over the real alphabet under the assumption of an omniscient adversary. It is a well-known result that when the source and the adversary have power constraints $ P $ and $ N $…

Mathematical modeling should present a consistent description of physical phenomena. We illustrate an inconsistency with two Hamiltonians -- the standard Hamiltonian and an example found in Goldstein -- for the simple harmonic oscillator…

Usually the only difference between relativistic quantization and standard one is that the Lagrangian of the system under consideration should be Lorentz invariant. The standard approaches are logically incomplete and produce solutions with…

We employ signed measures that are positive definite up to certain degrees to establish Levenshtein-type upper bounds on the cardinality of codes with given minimum and maximum distances, and universal lower bounds on the potential energy…

Some quantal systems require only a small part of the full quantum theory for their analysis in classical terms. In such understanding we review some recent literature on semiclassical treatments. An analysis of it allows one to see that…

We consider a generalized Cantor set $E(\omega)$ for an infinite sequence $\omega=(q_n)_{n=1}^{\infty}$ of positive numbers with $0<q_n<1$, and examine the quasiconformal equivalence to the standard middle one-third Cantor set…

In a recent work, Jungnickel, Magliveras, Tonchev, and Wassermann derived an overexponential lower bound on the number of nonisomorphic resolvable Steiner triple systems (STS) of order $v$, where $v=3^k$, and $3$-rank $v-k$. We develop an…

In this paper we show that many well-known counting coefficients, including the Catalan numbers, the Motzkin numbers, the central binomial coefficients, the central Delannoy numbers are Hausdorff moment sequences in a unified approach. In…