相关论文: Invariants for maximally entangled vectors and uni…
The purpose of this paper is to introduce techniques of obtaining optimal ways to determine a d-level quantum state or distinguish such states. It entails designing constrained elementary measurements extracted from maximal abelian subsets…
We explore the set of unitary matrices characterized by a given structure in the context of their applications in the field of Quantum Information. In the first part of the Thesis we focus on classification of special classes of unitary…
We provide formulas for invariants defined on a tensor product of defining representations of unitary groups, under the action of the product group. This situation has a physical interpretation, as it is related to the quantum mechanical…
Bargmann invariants, multivariate traces of states, completely characterize any unitary-invariant property of a set of states. Unitary invariants enable the description of quantum resources such as basis-independent coherence and…
We analyze the set of real and complex Hadamard matrices with additional symmetry constrains. In particular, we link the problem of existence of maximally entangled multipartite states of $2k$ subsystems with $d$ levels each to the set of…
The aim of this paper is to present an extragradient method for variational inequality associated to a point-to-set vector field in Hadamard manifolds and to study its convergence properties. In order to present our method the concept of…
The notion of equivalence of maximally entangled bases of bipartite d-dimensional Hilbert spaces is introduced. An explicit method of inequivalent bases construction is presented.
Unitary error bases have a great number of applications across quantum information and quantum computation, and are fundamentally linked to quantum teleportation, dense coding and quantum error correction. Werner's combinatorial…
In this paper, we study the superposition invariance of unitary operators and maximally entangled state respectively. Furthermore, we discuss the set of orthogonal maximally entangled states. We find that orthogonal basis of maximally…
We consider dual unitary operators and their multi-leg generalizations that have appeared at various places in the literature. These objects can be related to multi-party quantum states with special entanglement patterns: the sites are…
The quantum entanglements are studied in terms of the invariants under local unitary transformations. A generalized formula of concurrence for $N$-dimensional quantum systems is presented. This generalized concurrence has potential…
Some new identities for quantum variance and covariance involving commutators are presented, in which the density matrix and the operators are treated symmetrically. A measure of entanglement is proposed for bipartite systems, based on…
Kronecker products of unitary Fourier matrices play important role in solving multilevel circulant systems by a multidimensional Fast Fourier Transform. They are also special cases of complex Hadamard (Zeilinger) matrices arising in many…
Uncertainty relations are fundamental in quantum mechanics. Here I propose state-independent variance-based uncertainty relations for two or more arbitrary observables in finite dimensional spaces. The uncertainty relations provide…
In this paper an inexact proximal point method for variational inequalities in Hadamard manifolds is introduced and studied its convergence properties. The main tool used for presenting the method is the concept of enlargement of monotone…
We study bipartite unitary operators which stay invariant under the local actions of diagonal unitary and orthogonal groups. We investigate structural properties of these operators, arguing that the diagonal symmetry makes them suitable for…
Local unitary invariants allow one to test whether multipartite states are equivalent up to local basis changes. Equivalently, they specify the geometry of the "orbit space" obtained by factoring out local unitary action from the state…
Uncertainty relations play a significant role in drawing a line between classical physics and quantum physics. Since the introduction by Heisenberg, these relations have been considerably explored. However, the effect of quantum…
Let $V$ be a norm-closed subset of the unit sphere of a Hilbert space $H$ that is stable under multiplication by scalars of absolute value 1. A {\em maximal vector} (for $V$) is a unit vector $\xi\in H$ whose distance to $V$ is maximum…
Following the work of Semyon Alesker in the scalar valued case and of Thomas Wannerer in the vector valued case, the dimensions of the spaces of continuous translation invariant and unitary equivariant tensor valuations are computed. In…