相关论文: On the Monomiality of Nice Error Bases

We present a construction method for complete sets of cyclic mutually unbiased bases (MUBs) in Hilbert spaces of even prime power dimensions. In comparison to usual complete sets of MUBs, complete cyclic sets possess the additional property…

In this paper, we classify a type of abstract groups by the central products of dihedral groups and quaternion groups. We recognize them as abstract error groups which are often not isomorphic to the Pauli groups in the literature. We show…

In this note, we extend modular techniques for computing Gr\"obner bases from the commutative setting to the vast class of noncommutative $G$-algebras. As in the commutative case, an effective verification test is only known to us in the…

We look at explicit ways to bring one or two antiunitary symmetries into a standard form via unitary conjugation. We carefully reproduce Wigner's proof in two special cases, where the antiunitary operators square to $+I$, or to $-I$.…

We define a method which produces explicit cellular bases for algebras obtained via a Jones basic construction. For the class of algebras in question, our method gives formulas for generic Murphy--type cellular bases indexed by paths on…

Probabilistic programming systems generally compute with probability density functions, leaving the base measure of each such function implicit. This mostly works, but creates problems when densities with respect to different base measures…

Mutually unbiased bases generalize the X, Y and Z qubit bases. They possess numerous applications in quantum information science. It is well-known that in prime power dimensions N=p^m (with p prime and m a positive integer) there exists a…

Columns of d^2 x N matrices are shown to create different sets of N operators acting on $d$-dimensional Hilbert space. This construction corresponds to a formalism of the star-product of operator symbols. The known bases are shown to be…

Recently, we have shown that von Neumann algebras form a model for Selinger and Valiron's quantum lambda calculus. In this paper, we explain our choice of interpretation of the duplicability operator "!" by studying those von Neumann…

We increase the scope of previous work on change of basis between finite bases of polynomials by defining ascending and descending bases and introducing three techniques for defining them from known ones. The minimum degrees of polynomials…

Classical orthogonal polynomials have widespread applications including in numerical integration, solving differential equations, and interpolation. Changing basis between classical orthogonal polynomials can affect the convergence,…

Let q be a power of 2. We show by representation theory that there exists a q x q unitary matrix of multiplicative order q+1 whose powers generate q+1 pairwise mutually unbiased base in C^q. When q is a power of an odd prime, there is a q x…

We propose an alternative approach for the construction of the unitary matrix which performs generalized unitary rotations of the system consisting of independent identical subsystems (for example spin system). This matrix, when applied to…

Sum rules in effective field theories, predicated upon causality, place restrictions on scattering amplitudes mediated by effective contact interactions. Through unitarity of the $S$-matrix, these imply that the size of higher dimensional…

The purpose of this paper is to study the equivalence relation on unitary bases defined by R. F. Werner [{\it J. Phys. A: Math. Gen.} {\bf 34} (2001) 7081], relate it to local operations on maximally entangled vectors bases, find an…

We provide a construction of sets of (d/2+1) mutually unbiased bases (MUBs) in dimensions d=4,8 using maximal commuting classes of Pauli operators. We show that these incomplete sets cannot be extended further using the operators of the…

We show that the multiplicative domain of a completely positive map yields a new class of quantum error correcting codes. In the case of a unital quantum channel, these are precisely the codes that do not require a measurement as part of…

We collect here elementary properties of differentiation matrices for univariate polynomials expressed in various bases, including orthogonal polynomial bases and non-degree-graded bases such as Bernstein bases and Lagrange \& Hermite…

We study a novel spline-like basis, which we name the "falling factorial basis", bearing many similarities to the classic truncated power basis. The advantage of the falling factorial basis is that it enables rapid, linear-time computations…

For a system of N qubits, spanning a Hilbert space of dimension d=2^N, it is known that there exists d+1 mutually unbiased bases. Different construction algorithms exist, and it is remarkable that different methods lead to sets of bases…