4 citations · 9 across the 11 of their papers we have counts for
17 papers
On the rational invariants of quantum systems of -qubits
Luca Candelori, Vladimir Y. Chernyak, John R. Klein
For an -qubit system, a rational function on the space of mixed states which is invariant with respect to the action of the group of local symmetries may be viewed as a detailed…
On the variety of X-states
Luca Candelori, Vladimir Y. Chernyak, John R. Klein
We introduce the notion of an X-state on -qubits. After taking the Zariski closure of the set of X-states in the space of all mixed states, we obtain a complex algebraic variety…
Effective Rationality for Local Unitary Invariants of Mixed States of Two Qubits
Luca Candelori, Vladimir Y. Chernyak, John R. Klein +1
We calculate the field of rational local unitary invariants for mixed states of two qubits, by employing methods from algebraic geometry. We prove that this field is rational (i.e.…
Rational Local Unitary Invariants of Symmetrically Mixed States of Two Qubits
Luca Candelori, Vladimir Y. Chernyak, John R. Klein +1
We compute the field of rational local unitary invariants for locally maximally mixed states and symmetrically mixed states of two qubits. In both cases, we prove that the field of…
The topological Petersson product
Luca Candelori, Andrew Salch
The nondegeneracy of the Petersson inner product on cusp forms, and the fact that Hecke operators are self-adjoint with respect to the Petersson product, together imply that the cu…
Quantum Neuron with Separable-State Encoding
London A. Cavaletto, Luca Candelori, Alex Matos-Abiague
The use of advanced quantum neuron models for pattern recognition applications requires fault tolerance. Therefore, it is not yet possible to test such models on a large scale in c…
Topological Hecke eigenforms
Luca Candelori, Andrew Salch
We study the eigenforms of the action of A. Baker's Hecke operators on the holomorphic elliptic homology of various topological spaces. We prove a multiplicity one theorem (i.e., o…
Minimal Integral Models for Principal Series Weil Characters
Luca Candelori, Yatin Patel
We prove a conjecture of Udo Riese about the minimal ring of definition for principal series Weil characters of , for an odd prime. More precisely, w…
Period relations for Riemann surfaces with many automorphisms
Luca Candelori, Jack Fogliasso, Christopher Marks +1
By employing the theory of vector-valued automorphic forms for non-unitarizable representations, we provide a new bound for the number of linear relations with algebraic coefficien…
The Chevalley-Weil Formula for Orbifold Curves
Luca Candelori
In the 1930s Chevalley and Weil gave a formula for decomposing the canonical representation on the space of differential forms of the Galois group of a ramified Galois cover of Rie…
Indecomposable vector-valued modular forms and periods of modular curves
Luca Candelori, Tucker Hartland, Christopher Marks +1
We classify the three-dimensional representations of the modular group that are reducible but indecomposable, and their associated spaces of holomorphic vector-valued modular forms…
Vector bundles and modular forms for Fuchsian groups of genus zero
Luca Candelori, Cameron Franc
This article lays the foundations for the study of modular forms transforming with respect to representations of Fuchsian groups of genus zero. More precisely, we define geometrica…
The transformation laws of algebraic theta functions
Luca Candelori
We give a comprehensive treatment of the transformation laws of theta functions from an algebro-geometric perspective, that is, in terms of moduli of abelian schemes. This is accom…
Generating weights for the Weil representation attached to an even order cyclic quadratic module
Luca Candelori, Cameron Franc, Gene S. Kopp
We develop geometric methods to study the generating weights of free modules of vector valued modular forms of half-integral weight, taking values in a complex representation of th…
A geometric perspective on p-adic properties of mock modular forms
Luca Candelori, Francesc Castella
Bringmann, Guerzhoy and Kane have shown how to correct mock modular forms by a certain linear combination of the Eichler integral of their shadows in order to obtain p-adic modular…
The algebraic functional equation of Riemann's theta function
Luca Candelori
We give an algebraic analog of the functional equation of Riemann's theta function. More precisely, we define a `theta multiplier' line bundle over the moduli stack of principally…
Vector valued modular forms and the modular orbifold of elliptic curves
Luca Candelori, Cameron Franc
This paper presents the theory of holomorphic vector valued modular forms from a geometric perspective. More precisely, we define certain holomorphic vector bundles on the modular…