Related papers: State Space Realizations and Monomial Equivalence …
Crystal bases are powerful combinatorial tools in the representation theory of quantum groups $U_q(\mathfrak{g})$ for a symmetrizable Kac-Moody algebras $\mathfrak{g}$. The polyhedral realizations are combinatorial descriptions of the…
We establish a strong monogamy-of-entanglement property for subspace coset states, which are uniform superpositions of vectors in a linear subspace of $\mathbb{F}_2^n$ to which has been applied a quantum one-time pad. This property was…
The linear code equivalence (LCE) problem is shown to be equivalent to the point set equivalence (PSE) problem, i.e., the problem to check whether two sets of points in a projective space over a finite field differ by a linear change of…
We consider generalizations of Reed-Muller codes, toric codes, and codes from certain plane curves, such as those defined by norm and trace functions on finite fields. In each case we are interested in codes defined by evaluating arbitrary…
The aim of this work is to study the dual and the algebraic dual of an evaluation code using standard monomials and indicator functions. We show that the dual of an evaluation code is the evaluation code of the algebraic dual. We develop an…
We introduce a sequence of numerical tests that can determine the entanglement or separability of a state even when there is not enough information to completely determine its density matrix. Given partial information about the state in the…
What can representational similarity matrices (RSMs) tell us about a neural code? As the popularity of these summary statistics grows, so too does the need for a more complete characterization of their properties. Here, we show that…
This paper presents necessary and sufficient conditions under which a linear system of relative degree either one or two is state feedback equivalent to a negative imaginary (NI) system. More precisely, we show for a class of linear…
We investigate the equivalence of quantum mixed states under local unitary transformations. For a class of rank-two mixed states, a sufficient and necessary condition of local equivalence is obtained by giving a complete set of invariants…
Spatially coupled codes have been shown to universally achieve the capacity for a large class of channels. Many variants of such codes have been introduced to date. We discuss a further such variant that is particularly simple and is…
We describe a method for reconstructing multi-scale entangled states from a small number of efficiently-implementable measurements and fast post-processing. The method only requires single particle measurements and the total number of…
Two matrices are said to be principal minor equivalent if they have equal corresponding principal minors of all orders. We give a characterization of principal minor equivalence and a deterministic polynomial time algorithm to check if two…
We consider the transformations of quantum states obtainable by a process of the following sort. Combine the given input state with a specially prepared initial state of an auxiliary system. Apply a unitary transformation to the combined…
We generalize the Majorana stellar representation of spin-$s$ pure states to mixed states, and in general to any hermitian operator, defining a bijective correspondence between three spaces: the spin density-matrices, a projective space of…
For a code $C$ in a space with maximal distance $n$, we say that $C$ has symmetric distances if its distance set $S(C)$ is symmetric with respect to $n / 2$. In this paper, we prove that if $C$ is a binary code with length $2n$, constant…
One-dimensional multi-component Fermi or Bose systems with strong zero-range interactions can be described in terms of local exchange coefficients and mapping the problem into a spin model is thus possible. For arbitrary external confining…
In this paper, several conjectures proposed in [2] are studied, involving the equivalence and duality of polycyclic codes associated with trinomials. According to the results, we give methods to construct isodual and self-dual polycyclic…
A framework of monomial codes is considered, which includes linear codes generated by the evaluation of certain monomials. Polar and Reed-Muller codes are the two best-known representatives of such codes and can be considered as two extreme…
We examine distinct measures of fermionic entanglement in the exact ground state of a finite superconducting system. It is first shown that global measures such as the one-body entanglement entropy, which represents the minimum relative…
In mutation testing the question whether a mutant is equivalent to its program is important in order to compute the correct mutation score. Unfortunately, answering this question is not always possible and can hardly be obtained just by…