Related papers: Triangle geometry for qutrit states in the probabi…
In quantum computation and information science, the geometrical representations based on the Bloch sphere representation for transformations of two state systems have been traditionally used. While this representation is very useful for the…
We examine the possible states of subsystems of a system of bits or qubits. In the classical case (bits), this means the possible marginal distributions of a probability distribution on a finite number of binary variables; we give necessary…
Quantum states can be described equivalently by density matrices, Wigner functions or quantum tomograms. We analyze the accuracy and performance of three related semiclassical approaches to quantum dynamics, in particular with respect to…
Multi-qudit systems are studied in tomographic probability representations of quantum qudit states. Results of calculations for Bell-type numbers within the framework of classical probability theory and in quantum tomography are compared.…
We provide new examples of pure entangled systems related to cluster state quantum computation that can be efficiently simulated classically. In cluster state quantum computation input qubits are initialised in the `equator' of the Bloch…
In the field of quantum information science and technology, the representation and visualization of quantum states and related processes are essential for both research and education. In this context, a focus especially lies on ensembles of…
We study the equivalence of mixed states under local unitary transformations. First we express quantum states in Bloch representation. Then based on the coefficient matrices, some invariants are constructed. This method and results can be…
We explore the conceptual usefulness of Riemannian geometric tools induced by the statistical concept of distinguishability in quantifying the effect of a depolarizing channel on quantum states. Specifically, we compare the geometries of…
We investigate the differential geometry of bipartite quantum states. In particular the manifold structures of pure bipartite states are studied in detail. The manifolds with respect to all normalized pure states of arbitrarily given…
A new method is developed to derive an algebraic equations for the geometric measure of entanglement of three qubit pure states. The equations are derived explicitly and solved in cases of most interest. These equations allow oneself to…
By the Majorana representation, for any $d > 1$ there is a one-one correspondence between a quantum state of dimension $d$ and $d-1$ qubits represented as $d-1$ points in the Bloch sphere. Using the theory of symmetry class of tensors, we…
We propose a method for classical simulation of finite-dimensional quantum systems, based on sampling from a quasiprobability distribution, i.e., a generalized Wigner function. Our construction applies to all finite dimensions, with the…
A canonical form for unital qubit channels under local unitary transforms is obtained. In particular, it is shown that the eigenvalues of the Choi matrix of a unital quantum channel form a complete set of invariants of the canonical form.…
We discuss a pairwise-comparison viewpoint on finite families of qubit states. Starting from transition amplitudes between pure states, we distinguish three associated levels of comparison data: complex amplitudes, transition probabilities,…
A statistical model M is a family of probability distributions, characterised by a set of continuous parameters known as the parameter space. This possesses natural geometrical properties induced by the embedding of the family of…
In 1989, Deutsch gave a basic physical explanation of why quantum-mechanical probabilities are squares of amplitudes. Essentially, a general state vector is transformed into a highly symmetric equal-amplitude superposition. The argument was…
For decades, ``geometry" in band theory has largely meant Berry phase and Berry curvature-quantities that reshape semiclassical dynamics and underpin modern topological matter. Yet the full geometric content of a Bloch band is richer and…
The quantum metric and Berry curvature capture essential properties of non-trivial Bloch states and underpin many fascinating phenomena. However, it becomes increasingly evident that a more comprehensive understanding of quantum state…
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 study geometric consistency relations between angles on 3-dimensional (3D) circular quadrilateral lattices -- lattices whose faces are planar quadrilaterals inscribable into a circle. We show that these relations generate canonical…