Related papers: MUBs from bent functions
Large sets of equiangular lines are constructed from sets of mutually unbiased bases, over both the complex and the real numbers.
In order to describe the right setting to handle Zauner's conjecture on mutually unbiased bases (MUBs) (saying that in $\mathbb{C}^d$, a set of MUBs of the theoretical maximal size $d + 1$ exists only if $d$ is a prime power), we pose some…
The construction of integrity bases for invariant and covariant polynomials built from aset of three dimensional vectors under the SO(3) and O(3) symmetries is presented. Thispaper is a follow--up to our previous work that dealt with a set…
These course notes are about computing modular forms and some of their arithmetic properties. Their aim is to explain and prove the modular symbols algorithm in as elementary and as explicit terms as possible, and to enable the devoted…
In this study, we first use a three-qubit system as an example to demonstrate the construction of quantum circuits for the eight maximally entangled basis vectors, subsequently extending the approach to N-qubit systems. We employ a…
Clones are specializations of operads forming powerful instruments to describe varieties of algebras wherein repeating variables are allowed in their equations. They allow us in this way to realize and study a large range of algebraic…
By using exclusively real analysis, we give explicit estimates of some classical summatory functions involving the M\"obius function.
In this paper, on the basis of a specific question raised in [6], we further continue our investigations on the uniqueness of a meromorphic function with its higher derivatives sharing two sets and answer the question affirmatively.…
In this paper we characterize (octal) bent generalized Boolean functions defined on $\BBZ_2^n$ with values in $\BBZ_8$. Moreover, we propose several constructions of such generalized bent functions for both $n$ even and $n$ odd.
This paper defines the beta function and other linear orbit parameters using the exact equations of motion. The orbit functions are redefined using the exact equations. Expressions are found for the transfer matrix and the emittances.…
We present a general, constructive procedure to find the basis for tensors of arbitrary order subject to linear constraints by transforming the problem to that of finding the nullspace of a linear operator. The proposed method utilizes…
Bent functions can be classified into regular bent functions, weakly regular but not regular bent functions, and non-weakly regular bent functions. Regular and weakly regular bent functions always appear in pairs since their duals are also…
We study generalized sums of linear orders. These are binary operations that, given linear orders $A$ and $B$, return an order $A \oplus B$ that can be decomposed as an isomorphic copy of $A$ interleaved with a copy of $B$. We show that…
The paper studies complementary choice functions, i.e. monotonic and consistent choice functions. Such choice functions were introduced and used in the work \cite{RY} for investigation of matchings with complementary contracts. Three…
Mutually unbiased bases (MUBs) are highly symmetric bases on complex Hilbert spaces, and the corresponding rank-1 projective measurements are ubiquitous in quantum information theory. In this work, we study a recently introduced…
Mutually unbiased bases plays a central role in quantum mechanics and quantum information processing. As an important class of mutually unbiased bases, mutually unbiased maximally entangled bases (MUMEBs) in bipartite systems have attracted…
We consider the problem of mutually unbiased bases as a polynomial optimization problem over the reals. We heavily reduce it using known symmetries before exploring it using two methods, combining a number of optimization techniques. The…
In this paper we prove that in opposite to the cases of 6 and 8 variables, the Maiorana-McFarland construction does not describe the whole class of cubic bent functions in $n$ variables for all $n\ge 10$. Moreover, we show that for almost…
We define a higher-order generalisation of the CPM construction based on arbitrary finite abelian group symmetries of symmetric monoidal categories. We show that our new construction is functorial, and that its closure under iteration can…
Though modern neural networks have achieved impressive performance in both vision and language tasks, we know little about the functions that they implement. One possibility is that neural networks implicitly break down complex tasks into…