相关论文: Operational approach to the Uhlmann holonomy
A unifying framework for identifying distance and holonomy for decompositions of density operators is introduced. Parallelity between quantum ensembles is defined by minimizing this distance over allowed decompositions. The minimum is a…
Uhlmann's concept of quantum holonomy for paths of density operators is generalised to the off-diagonal case providing insight into the geometry of state space when the Uhlmann holonomy is undefined. Comparison with previous off-diagonal…
The Feynman integral is one of the most accurate methods for calculating density operator dynamics in open quantum systems. However, the number of time steps that can realistically be used is always limited, therefore one often obtains an…
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…
In this paper, we find the boundary dual of the symplectic form for the bulk fields in any entanglement wedge. The key ingredient is Uhlmann holonomy, which is a notion of parallel transport of purifications of density matrices based on a…
Transition Probability (fidelity) for pairs of density operators can be defined as "functor" in the hierarchy of "all" quantum systems and also within any quantum system. The introduction of "amplitudes" for density operators allows for a…
Information about the behavior of dynamical systems can often be obtained by analyzing the eigenvalues and corresponding eigenfunctions of linear operators associated with a dynamical system. Examples of such operators are the…
In this paper, the notion of simultaneous universality is introduced, concerning operators having orbits that simultaneously approximate any given vector. This notion is related to the well known concepts of universality and disjoint…
We consider a new approach to describe a quantum optical Bose-system with internal Gell-Mann symmetry by the SU(3)-symmetry polarization map in Hilbert space. The operational measurement in density (or coherency) matrix elements for the…
Exponential operator decompositions are an important tool in many fields of physics, for example, in quantum control, quantum computation, or condensed matter physics. In this work, we present a method for obtaining such decompositions,…
Partial transpose is an important operation for quantifying the entanglement, here we study the (partial) transpose of any single (two-mode) operators. Using the Fock-basis expansion, it is found that the transposed operator of an arbitrary…
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…
In this paper, we investigate the power of nearly purely operational techniques in the study of umbral calculus. We present a concise reconstruction of the theory based on a systematic use of linear operators, with particular attention to…
Quantum mechanics predicts the joint probability distribution of the outcomes of simultaneous measurements of commuting observables, but, in the state of the art, has lacked the operational definition of simultaneous measurements. The…
We present exact results for the optical response in the one-dimensional Holstein model. In particular, by means of a refined kernel polynomial method, we calculate the ac and dc electrical conductivities at finite temperatures for a wide…
A sequence of completely positive maps can be decomposed into quantum trajectories. The geometric phase or holonomy of such a trajectory is delineated. For nonpure initial states, it is shown that well-defined holonomies can be assigned by…
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…
The problem of geometric phase for an open quantum system is reinvestigated in a unifying approach. Two of existing methods to define geometric phase, one by Uhlmann's approach and the other by kinematic approach, which have been considered…
We derive how to incorporate topological features of Riemann surfaces in string amplitudes by insertions of bi-local operators called handle operators. The resulting formalism is exact and globally well-defined in moduli space. After a…
The Koopman operator approach to the state estimation problem for nonlinear systems is a promising research area. The main goal of this paper is an attempt to provide a rigorous theoretical framework for this approach. In particular, the…