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pro vyhledávání: '"McConnell, Gary"'
Autor:
McConnell, Gary
Fix a finite collection of primes $\{ p_j \}$, not containing $2$ or $3$. Using some observations which arose from attempts to solve the SIC-POVMs problem in quantum information, we give a simple methodology for constructing an infinite family of sim
Externí odkaz:
http://arxiv.org/abs/2406.14632
The existence problem for maximal sets of equiangular lines (or SICs) in complex Hilbert space of dimension $d$ remains largely open. In a previous publication (arXiv:2112.05552) we gave a conjectural algorithm for how to construct a SIC if $d = n^2+
Externí odkaz:
http://arxiv.org/abs/2403.02872
Publikováno v:
J. Math. Phys. 63, 112205 (2022)
We propose a recipe for constructing a SIC fiducial vector in complex Hilbert space of dimension of the form $d=n^2+3$, focussing on prime dimensions $d=p$. Such structures are shown to exist in thirteen prime dimensions of this kind, the highest bei
Externí odkaz:
http://arxiv.org/abs/2112.05552
The problem of finding provably maximal sets of mutually unbiased bases in $\mathbb{C}^d$, for composite dimensions $d$ which are not prime powers, remains completely open. In the first interesting case, $d=6$, Zauner predicted that there can exist n
Externí odkaz:
http://arxiv.org/abs/2103.08703
Publikováno v:
Found. Phys., 47(8), 1042--1059 (2017)
We give an overview of some remarkable connections between symmetric informationally complete measurements (SIC-POVMs, or SICs) and algebraic number theory, in particular, a connection with Hilbert's 12th problem. The paper is meant to be intelligibl
Externí odkaz:
http://arxiv.org/abs/1701.05200
Publikováno v:
Acta Arith. 192 (2020), 211-233
For certain real quadratic fields $K$ with sufficiently small discriminant we produce explicit unit generators for specific ray class fields of $K$ using a numerical method that arose in the study of complete sets of equiangular lines in $\mathbb{C}^
Externí odkaz:
http://arxiv.org/abs/1604.06098
Autor:
McConnell, Gary
The notion of Symmetric Informationally Complete Positive Operator-Valued Measures (SIC-POVMs) arose in physics as a kind of optimal measurement basis for quantum systems. However the question of their existence is equivalent to that of the existence
Externí odkaz:
http://arxiv.org/abs/1402.7330
Autor:
McConnell, Gary
Let m and n be any integers with n>m>=2. Using just the entropy function it is possible to define a partial order on S_mn (the symmetric group on mn letters) modulo a subgroup isomorphic to S_m x S_n. We explore this partial order in the case m=2, n=
Externí odkaz:
http://arxiv.org/abs/1209.2674
Autor:
McConnell, Gary, Jennings, David
We study the correlation structure of separable and classical states in 2x2- and 2x3-dimensional quantum systems with fixed spectra. Even for such simple systems the maximal correlation - as measured by mutual information - over the set of unitarily
Externí odkaz:
http://arxiv.org/abs/1205.3517