Related papers: The Conal representation of Quantum States and Non…
We exploit a well-known isomorphism between complex hermitian $2\times 2$ matrices and $\mathbb{R}^4$, which yields a convenient real vector representation of qubit states. Because these do not need to be normalized we find that they map…
The extended Bloch representation of quantum mechanics was recently derived to offer a (hidden-measurement) solution to the measurement problem. In this article we use it to investigate the geometry of superposition and entangled states,…
A quantum system's state is identified with a density matrix. Though their probabilistic interpretation is rooted in ensemble theory, density matrices embody a known shortcoming. They do not completely express an ensemble's physical…
A generalized Bloch sphere, in which the states of a quantum entity of arbitrary dimension are geometrically represented, is investigated and further extended, to also incorporate the measurements. This extended representation constitutes a…
The partial trace operation is usually considered in composite quantum systems, to reduce the state on a single subsystem. This operation has a key role in the decoherence effect and quantum measurements. However, partial trace operations…
Generalized quantum measurements with N distinct outcomes are used for determining the density matrix, of order d, of an ensemble of quantum systems. The resulting probabilities are represented by a point in an N-dimensional space. It is…
We present a general formalism for charecterizing 2-time quantum states, describing pre- and post-selected quantum systems. The most general 2-time state is characterized by a `density vector' that is independent of measurements performed…
We provide theory, algorithms, and simulations of non-equilibrium quantum systems using a one-dimensional (1D) completely-positive (CP), matrix-product (MP) density-operator ($\rho$) representation. By generalizing the matrix product…
Density matrices and Discrete Wigner Functions are equally valid representations of multiqubit quantum states. For density matrices, the partial trace operation is used to obtain the quantum state of subsystems, but an analogous…
We represent a two-qubit density matrix in the basis of Pauli matrix tensor products, with the coefficients constituting a Bloch matrix, analogous to the single qubit Bloch vector. We find the quantum state positivity requirements on the…
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…
This paper is the continuation of a study into the information paradox problem started by the author in his earlier works. As previously, the key instrument is a deformed density matrix in quantum mechanics of the early universe. It is…
We define the model of quantum circuits with density matrices, where non-unitary gates are allowed. Measurements in the middle of the computation, noise and decoherence are implemented in a natural way in this model, which is shown to be…
Reduced density matrices are a powerful tool in the analysis of entanglement structure, approximate or coarse-grained dynamics, decoherence, and the emergence of classicality. It is straightforward to produce a reduced density matrix with…
Usually models for quantum computations deal with unitary gates on pure states. In this paper we generalize the usual model. We consider a model of quantum computations in which the state is an operator of density matrix and the gates are…
We propose a generalization of the Bloch sphere representation for arbitrary spin states. It provides a compact and elegant representation of spin density matrices in terms of tensors that share the most important properties of Bloch…
We examine some properties of the non-normalized (or canonical) density matrix in the coherent states representation, by two equivalent ways. On the one hand by its definition, and on the other hand as a solution to Bloch's canonical…
Recent work has revealed that the wave function of a pure state can be measured directly and that complementary knowledge of a quantum system can be obtained simultaneously by weak measurements. However, the original scheme applies only to…
We interpret quantum computing as a geometric evolution process by reformulating finite quantum systems via Connes' noncommutative geometry. In this formulation, quantum states are represented as noncommutative connections, while gauge…
We explore the main processes involved in the evolution of general quantum systems by means of Diagrams of States, a novel method to graphically represent and analyze how quantum information is elaborated during computations performed by…