Related papers: Geometry of Discrete Quantum Computing
This paper presents an introduction to geometric representations of quantum states in which each distinct quantum state, pure and mixed, corresponds to a unique point in a Euclidean space. Beginning with a review of some underappreciated…
The degree to which a pure quantum state is entangled can be characterized by the distance or angle to the nearest unentangled state. This geometric measure of entanglement is explored for bi-partite and multi-partite pure and mixed states.…
A general framework is described which associates geometrical structures to any set of $D$ finite-dimensional hermitian matrices $X^a, \ a=1,...,D$. This framework generalizes and systematizes the well-known examples of fuzzy spaces, and…
Quantum computation in solid state quantum dots faces two significant challenges: Decoherence from interactions with the environment and the difficulty of generating local magnetic fields for the single qubit rotations. This paper presents…
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…
The original Wigner function provides a way of representing in phase space the quantum states of systems with continuous degrees of freedom. Wigner functions have also been developed for discrete quantum systems, one popular version being…
The paper explores the basic geometrical properties of the observables characterizing two-qubit systems by employing a novel projective ring geometric approach. After introducing the basic facts about quantum complementarity and maximal…
Quantum computational complexity estimates the difficulty of constructing quantum states from elementary operations, a problem of prime importance for quantum computation. Surprisingly, this quantity can also serve to study a completely…
The aim of the paper is to propose geometric descriptions of multipartite entangled states using algebraic geometry. In the context of this paper, geometric means each stratum of the Hilbert space, corresponding to an entangled state, is an…
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…
We work out the phase-space structure for a system of $n$ qubits. We replace the field of real numbers that label the axes of the continuous phase space by the finite field $\Gal{2^n}$ and investigate the geometrical structures compatible…
PhD thesis investigating homological quantum codes derived from curved and higher dimensional geometries. In the first part we will consider closed surfaces with constant negative curvature. We show how such surfaces can be constructed and…
The "Power of One Qubit" refers to a computational model that has access to only one pure bit of quantum information, along with n qubits in the totally mixed state. This model, though not as powerful as a pure-state quantum computer, is…
Geometric quantum mechanics aims to express the physical properties of quantum systems in terms of geometrical features preferentially selected in the space of pure states. Geometric characterisations are given here for systems of one, two,…
This is a review of the geometry of quantum states using elementary methods and pictures. Quantum states are represented by a convex body, often in high dimensions. In the case of n-qubits, the dimension is exponentially large in n. The…
Using the natural connection equivalent to the SU(2) Yang-Mills instanton on the quaternionic Hopf fibration of $S^7$ over the quaternionic projective space ${\bf HP}^1\simeq S^4$ with an $SU(2)\simeq S^3$ fiber the geometry of entanglement…
An important problem in quantum information theory is to understand what makes entangled quantum systems non-local or hard to simulate efficiently. In this work we consider situations in which various parties have access to a restricted set…
A new geometric representation of qubit and qutrit states based on probability simplexes is used to describe the separability and entanglement properties of density matrices of two qubits. The Peres--Horodecki positive partial transpose…
We consider a Quantum Computer with n quantum-bits (`qubits'), where each qubit is coupled independently to an environment affecting the state in a dephasing or depolarizing way. For mixed states we suggest a quantification for the property…
The recent debate on hyper-computation has raised new questions both on the computational abilities of quantum systems and the Church-Turing Thesis role in Physics. We propose here the idea of geometry of effective physical process as the…