Zobrazeno 1 - 10
of 53
pro vyhledávání: '"Frenkel, Péter E."'
Autor:
Bencze, Tamás, Frenkel, Péter E.
We introduce the triangulant of two matrices, and relate it to the existence of orthogonal eigenvectors. We also use it for a new characterization of mutually unbiased bases. Generalizing the notion, we introduce higher order triangulants of two matr
Externí odkaz:
http://arxiv.org/abs/2406.13421
Autor:
Frenkel, Péter E.
Publikováno v:
Quantum 7, 1102 (2023)
Integral representations of quantum relative entropy, and of the directional second and higher order derivatives of von Neumann entropy, are established, and used to give simple proofs of fundamental, known data processing inequalities: the Holevo bo
Externí odkaz:
http://arxiv.org/abs/2208.12194
Autor:
Frenkel, Péter E., Weiner, Mihály
Publikováno v:
Quantum 6, 662 (2022)
For a classical channel, neither the Shannon capacity, nor the sum of conditional probabilities corresponding to the cases of successful transmission can be increased by the use of shared entanglement, or, more generally, a non-signaling resource. Ye
Externí odkaz:
http://arxiv.org/abs/2103.08567
Autor:
Frenkel, Péter E.
Publikováno v:
Quantum 6, 751 (2022)
We investigate whether certain non-classical communication channels can be simulated by a classical channel with a given number of states and a given `amount' of noise. It is proved that any noisy quantum channel can be simulated by a corresponding c
Externí odkaz:
http://arxiv.org/abs/2101.10985
Autor:
Frenkel, Péter E., Zábrádi, Gergely
Let $p$ be a fixed prime, and let $v(a)$ stand for the exponent of $p$ in the prime factorization of the integer $a$. Let $f$ and $g$ be two monic polynomials with integer coefficients and nonzero resultant $r$. Write $S$ for the maximum of $v(\gcd (
Externí odkaz:
http://arxiv.org/abs/1712.01054
Autor:
Frenkel, Péter E., Pelikán, József
Publikováno v:
Amer. Math. Monthly 124 (2017), no. 5, 446--450
We show that if two monic polynomials with integer coefficients have square-free resultant, then all positive divisors of the resultant arise as the greatest common divisor of the values of the two polynomials at a suitable integer.
Comment: 6 p
Comment: 6 p
Externí odkaz:
http://arxiv.org/abs/1608.07936
Autor:
Frenkel, Péter E.
We propose a notion of graph convergence that interpolates between the Benjamini--Schramm convergence of bounded degree graphs and the dense graph convergence developed by L\'aszl\'o Lov\'asz and his coauthors. We prove that spectra of graphs, and al
Externí odkaz:
http://arxiv.org/abs/1602.05937
Autor:
Frenkel, Péter E.
Publikováno v:
J. Math. Phys. 57 (2016), no. 3, 032301, 3 pp
We determine the automorphisms and the continuous endomorphisms of the Einstein gyrogroup in arbitrary dimension. This generalizes a recent result of Lajos Moln\'ar and D\'aniel Virosztek, who have determined the continuous endomorphisms in the three
Externí odkaz:
http://arxiv.org/abs/1512.04666
Publikováno v:
Discrete Math. 340 (2017), no. 5, 1129-1135
In this short note we observe that recent results of Abert and Hubai and of Csikvari and Frenkel about Benjamini--Schramm continuity of the holomorphic moments of the roots of the chromatic polynomial extend to the theory of dense graph sequences. We
Externí odkaz:
http://arxiv.org/abs/1511.09429
Autor:
Frenkel, Péter E.
We determine minimal Cayley--Hamilton and Capelli identities for matrices over a Grassmann algebra of finite rank. For minimal standard identities, we give lower and upper bounds on the degree. These results improve on upper bounds given by L.\ M\'ar
Externí odkaz:
http://arxiv.org/abs/1511.05540