相关论文: A probabilistic operator symbol framework for quan…
We use tools from non-standard analysis to formulate the building blocks of quantum field theory within the framework of categorical quantum mechanics. Building upon previous work, we construct an object of *Hilb having quantum fields as…
Starting from the famous Pauli problem on the possibility to associate quantum states with probabilities, the formulation of quantum mechanics in which quantum states are described by fair probability distributions (tomograms, i.e.…
In view of the tomographic-probability representation of quantum states, we reconsider the approach to quantumness tests of a single system developed in [Alicki and Van Ryn 2008 J. Phys. A: Math. Theor. 41 062001]. For qubits we introduce a…
The random matrix ensembles are applied to the quantum chaotic systems. The quantum systems are studied using the finite dimensional real, complex and quaternion Hilbert spaces of the eigenfunctions. The linear operators describing the…
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…
The random matrix ensembles are applied to the quantum statistical two-dimensional systems of electrons. The quantum systems are studied using the finite dimensional real, complex and quaternion Hilbert spaces of the eigenfunctions. The…
Quantum operations describe any state change allowed in quantum mechanics, including the evolution of an open system or the state change due to a measurement. In this letter we present a general method based on quantum tomography for…
We define a generalization of the T\''oplitz quantization, suitable for operators whose T\''oplitz symbols are singular. We then show that singular curve operators in Topological Quantum Fields Theory (TQFT) are precisely generalized…
The most standard description of symmetries of a mathematical structure produces a group. However, when the definition of this structure is motivated by physics, or information theory, etc., the respective symmetry objects might become more…
We present a probabilistic quantum processor for qudits. The processor itself is represented by a fixed array of gates. The input of the processor consists of two registers. In the program register the set of instructions (program) is…
A powerful tool for studying geometrical problems in Hilbert space is developed. In particular, we study the quantum pure state tomography problem in finite dimensions from the point of view of dynamical systems and bifurcations theory.…
The state of quantum systems, their energetics, and their time evolution is modeled by abstract operators. How can one visualize such operators for coupled spin systems? A general approach is presented which consists of several shapes…
Consider the question: what statistical ensemble corresponds to minimal prior knowledge about a quantum system ? For the case where the system is in fact known to be in a pure state there is an obvious answer, corresponding to the unique…
It is now well established that quantum tomography provides an alternative picture of quantum mechanics. It is common to introduce tomographic concepts starting with the Schrodinger-Dirac picture of quantum mechanics on Hilbert spaces. In…
We study measures of quantum information when the space spanned by the set of accessible observables is not closed under products, i.e., we consider systems where an observer may be able to measure the expectation values of two operators,…
The existing relation between the tomographic description of quantum states and the convolution algebra of certain discrete groupoids represented on Hilbert spaces will be discussed. The realizations of groupoid algebras based on qudit,…
We present a general formalism for giving a measure space paired with a separable Hilbert space a quantum version based on normalized positive operator-valued measure. The latter are built from families of density operators labelled by…
It is proposed the scheme of quantum mechanics, in which a Hilbert space and the linear operators are not primary elements of the theory. Instead of it certain variant of the algebraic approach is considered. The elements of noncommutative…
On the base of symplectic quantum tomogram we define a probability distribution on the plane. The dual map transfers all observables which are polynomials of the position and momentum operators to the set of polynomials of two variables. In…
In this work, the operator-sum representation of a quantum process is extended to the probability representation of quantum mechanics. It is shown that each process admitting the operator-sum representation is assigned a kernel, convolving…