相关论文: Exploring the geometry of qutrit state space using…

Symmetric informationally complete measurements (SICs in short) are highly symmetric structures in the Hilbert space. They possess many nice properties which render them an ideal candidate for fiducial measurements. The symmetry of SICs is…

Symmetric informationally complete measurements (SICs) are elegant, celebrated and broadly useful discrete structures in Hilbert space. We introduce a more sophisticated discrete structure compounded by several SICs. A SIC-compound is…

Every quantum state can be represented as a probability distribution over the outcomes of an informationally complete measurement. But not all probability distributions correspond to quantum states. Quantum state space may thus be thought…

Coherence, treated as a resource in quantum information theory, is a basis-dependent quantity. Looking for states that have constant coherence under canonical changes of basis yields highly symmetric structures in state space. For the case…

The geometry of the Quantum State Space, described by Bloch vectors, is a very intricate one. A deeper understanding of this geometry could lead to the solution of some difficult problems in Quantum Foundations and Quantum Information such…

We take a tour of a set of equiangular lines in eight-dimensional Hilbert space. This structure defines an informationally complete measurement, that is, a way to represent all quantum states of three-qubit systems as probability…

An unavoidable task in quantum information processing is how to obtain data about the state of an individual system by suitable measurements. Informationally complete measurements are relevant in quantum state tomography, quantum…

In this thesis we study symmetric structures in Hilbert spaces known as symmetric informationally complete positive operator-valued measures (SIC-POVMs), mutually unbiased bases (MUBs), and MUB-balanced states. Our tools include symmetries…

We express the matrix elements of the density matrix of the qutrit state in terms of probabilities associated with artificial qubit states. We show that the quantum statistics of qubit states and observables is formally equivalent to the…

Since Renes et al. [J. Math. Phys. 45, 2171 (2004)], there has been much effort in the quantum information community to prove (or disprove) the existence of symmetric informationally complete (SIC) sets of quantum states in arbitrary finite…

We present geometric methods for uniformly discretizing the continuous N-qubit Hilbert space. When considered as the vertices of a geometrical figure, the resulting states form the equivalent of a Platonic solid. The discretization…

We consider a system with a discrete configuration space. We show that the geometrical structures associated with such a system provide the tools necessary for a reconstruction of discrete quantum mechanics once dynamics is brought into the…

Recently, several intriguing conjectures have been proposed connecting symmetric informationally complete quantum measurements (SIC POVMs, or SICs) and algebraic number theory. These conjectures relate the SICs and their minimal defining…

We study the invariant theory of trilinear forms over a three-dimensional complex vector space, and apply it to investigate the behaviour of pure entangled three-partite qutrit states and their normal forms under local filtering operations…

This paper develops a geometric model for coupled two-state quantum systems (qubits), which is formulated using geometric (aka Clifford) algebra. It begins by showing how Euclidean spinors can be interpreted as entities in the geometric…

We consider the existence in arbitrary finite dimensions d of a POVM comprised of d^2 rank-one operators all of whose operator inner products are equal. Such a set is called a ``symmetric, informationally complete'' POVM (SIC-POVM) and is…

We examine qubit states under symmetric informationally-complete measurements, representing state vectors as probability 4-vectors within a 3-simplex in $bb(R)^4$. Using geometric transformations, this 3-simplex is mapped to a tetrahedron…

Generalized symmetric informationally complete (SIC) measurements are SIC measurements that are not necessarily rank one. They are interesting originally because of their connection with rank-one SICs. Here we reveal several merits of…

The symmetry SU(2) and its geometric Bloch Sphere rendering are familiar for a qubit (spin-1/2) but extension of symmetries and geometries have been investigated far less for multiple qubits, even just a pair of them, that are central to…

In this paper we study the geometrical structures of multi-qubit states based on symplectic toric manifolds. After a short review of symplectic toric manifolds, we discuss the space of a single quantum state in terms of these manifolds. We…