Related papers: On G\'acs' quantum algorithmic entropy
We extend algorithmic information theory to quantum mechanics, taking a universal semicomputable density matrix (``universal probability'') as a starting point, and define complexity (an operator) as its negative logarithm. A number of…
A new model of a Quantum Automaton (QA), working with qubits is proposed. The quantum states of the automaton can be pure or mixed and are represented by density operators. This is the appropriated approach to deal with measurements and…
In the study of quantum limits to parameter estimation, the high dimensionality of the density operator and that of the unknown parameters have long been two of the most difficult challenges. Here we propose a theory of quantum…
A general classification of linear differential and finite-difference operators possessing a finite-dimensional invariant subspace with a polynomial basis is given. The main result is that any operator with the above property must have a…
We gave a simple derivation of density operator with the quantum analysis. We dealt with the functional of a density operator, and applied maximum entropy principle. We obtained easily the density operators for the Tsallis entropy and…
We introduce superdensity operators as a tool for analyzing quantum information in spacetime. Superdensity operators encode spacetime correlation functions in an operator framework, and support a natural generalization of Hilbert space…
We study the most general continuous transformation on the generators of bilinear master equations of a quantum oscillator. We find that transformation operators that preserve the hermiticity of density operators and conserve the…
The residual finite-dimensionality of a $\mathrm{C}^*$-algebra is known to be encoded in a topological property of its space of representations, stating that finite-dimensional representations should be dense therein. We extend this…
Let $S(\rho)$ be the von Neumann entropy of a density matrix $\rho$. Weak monotonicity asserts that $S(\rho_{AB}) - S(\rho_A) + S(\rho_{BC}) - S(\rho_C)\geq 0$ for any tripartite density matrix $\rho_{ABC}$, a fact that is equivalent to the…
In this work, the definition of the density operator on quantum states in Hilbert spaces and some of its aspects relevant in thermodynamics and information-theoretical entropy calculations are given. In this framework, a physical model…
We first introduce and discuss density operator interpretations of quantum theory as a special case of a more general class of interpretations, giving special attention to a version that we call the `atomic version'. We then review some…
An elementary proof is given for the existence of infinite dimensional abelian subalgebras in quantum W-algebras. In suitable realizations these subalgebras define the conserved charges of various quantum integrable systems. We consider all…
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…
This paper is the second part of our series of works to establish $L^2$ estimates and existence theorems for the $\overline{\partial}$ operators in infinite dimensions. In this part, we consider the most difficult case, i.e., the underlying…
We introduce and systematically develop the theory of \emph{quantum doubly stochastic operators}, i.e. positive, trace-preserving maps on non-commutative $L_p$-spaces associated to semifinite von Neumann algebras. After establishing basic…
We derive an expression for a density operator estimated via Bayesian quantum inference in the limit of an infinite number of measurements. This expression is derived under the assumption that the reconstructed system is in a pure state. In…
The paper is devoted to the investigation of Segal's entropy in semifinite von Neumann algebras. The following questions are dealt with: semicontinuity, the 'ideal-like' structure of the linear span of the set of operators with finite…
We show that, on a standard non-atomic probability space, invertible measure-preserving transformations form a dense $G_\delta$ subset of the space of all measure-preserving transformations endowed with the strong (=weak) operator topology.…
An algebraic approach to the study of entanglement entropy of quantum systems is reviewed. Starting with a state on a $C^*$-algebra, one can construct a density operator describing the state in the GNS representation state. Applications of…
We derive novel concentration inequalities for the operator norm of the sum of self-adjoint operators that do not explicitly depend on the underlying dimension of the operator, but rather an intrinsic notion of it. Our analysis leads to…