Related papers: The Geometry of Single-Qubit Maps
Classical methods of differential geometry are used to construct equations of motion for particles in quantum, electrodynamic and gravitational fields. For a five dimensional geometrical system, the equivalence principle can be extended.…
We examine evolutions where each component of a given decomposition of a mixed quantal state evolves independently in a unitary fashion. The geometric phase and parallel transport conditions for this type of decomposition dependent…
Standard particle theory is based on quantized matter embedded in a classical geometry. Here, a complementary model is proposed, based on classical matter -- massive bodies, without quantum properties -- embedded in a quantum geometry. It…
We describe in detail a set of ideas for implementing qubits, quantum gates and quantum gate networks in a semiconductor heterostructure device. Our proposal is based on an extension of the technology used for surface acoustic wave (SAW)…
We introduce the concept of regular quantum graphs and construct connected quantum graphs with discrete symmetries. The method is based on a decomposition of the quantum propagator in terms of permutation matrices which control the way…
Inspired by the Solovay-Kitaev decomposition for approximating unitary operations as a sequence of operations selected from a universal quantum computing gate set, we introduce a method for approximating any single-qubit channel using…
Invertible compositions of one-dimensional maps are studied which are assumed to include maps with non-positive Schwarzian derivative and others whose sum of distortions is bounded. If the assumptions of the Koebe principle hold, we show…
We introduce and explore the notion of texture of an arbitrary quantum state, in a selected basis. In the first part of this letter we develop a resource theory and show that state texture is adequately described by an easily computable…
We briefly review single-qubit quantum process tomography for trace-preserving and nontrace-preserving processes, and derive explicit forms of the general constraints for fitting experimental data. These new forms provide additional insight…
We study the problem of approximating a quantum channel by one with as few Kraus operators as possible (in the sense that, for any input state, the output states of the two channels should be close to one another). Our main result is that…
The most general evolution of the density matrix of a quantum system with a finite-dimensional state space is by stochastic maps which take a density matrix linearly into the set of density matrices. These dynamical stochastic maps form a…
Photons are a natural resource in quantum information, and the last decade showed significant progress in high-quality single photon generation and detection. Furthermore, photonic qubits are easy to manipulate and do not require…
Quantum matrix geometry is the underlying geometry of M(atrix) theory. Expanding upon the idea of level projection, we propose a quantum-oriented non-commutative scheme for generating the matrix geometry of the coset space $G/H$. We employ…
We present a way of understanding the curvature of space-time, the basic philosophy being that the (linear) geometry of any space is determined by the (linear) functionals on the algebra(s) of any fields defined on the space. It is known…
Compatibility conditions of quantum channels featuring symmetry through covariance are studied. Compatibility here means the possibility of obtaining two or more channels through partial trace out of a broadcasting channel. We see that…
A large-scalable quantum computer model, whose qubits are represented by the subspace subtended by the ground state and the single exciton state on semiconductor quantum dots, is proposed. A universal set of quantum gates in this system may…
The use of geometric methods has proved useful in the hamiltonian description of classical constrained systems. In this note we provide the first steps toward the description of the geometry of quantum constrained systems. We make use of…
In the first part of this review we introduce the basics theory behind geometric phases and emphasize their importance in quantum theory. The subject is presented in a general way so as to illustrate its wide applicability, but we also…
A quantum version of the action principle in a simple covariant dynamical theory of two relativistic particles is formulated. The central object of this new formulation of quantum theory is a stationary eigenvalue of the quantum action.…
For a quantum channel (completely positive, trace-preserving map), we prove a generalization to the infinite dimensional case of a result by Baumgartner and Narnhofer. This result is, in a probabilistic language, a decomposition of a…