Related papers: Map-Dependent Quantum Characteristic Functions and…
We demonstrate that a quantum graph exhibits a $\mathcal{PT}$-symmetry provided the coefficients in the condition describing the wave function matching at the vertices are circulant matrices; this symmetry is nontrivial if they are not…
Characteristic functions (CFs) provide a very efficient method for evaluating the probability density functions of stochastic thermodynamic quantities and investigating their statistical features in quantum master equations (QMEs). A…
The general formalism of quantum mechanics for the description of statistical experiments is briefly reviewed, introducing in particular position and momentum observables as POVM characterized by their covariance properties with respect to…
The description of the dynamics of an open quantum system in the presence of initial correlations with the environment needs different mathematical tools than the standard approach to reduced dynamics, which is based on the use of a…
Classical matching theory can be defined in terms of matrices with nonnegative entries. The notion of Positive operator, central in Quantum Theory, is a natural generalization of matrices with nonnegative entries. Based on this point of…
We present a general characterization of k-positivity for a positive map in terms of the estimation of the Ky Fan norm of the matrix constructed from the Kraus operators of the associated completely positive map. Combining this with the…
For a given set of input-output pairs of quantum states or observables, we ask the question whether there exists a physically implementable transformation that maps each of the inputs to the corresponding output. The physical maps on…
We construct a dynamical map which is not positive divisible and does not present information backflow either (as measured by trace norm quantifiers). It is formulated for a qutrit system undergoing noninvertible dynamics. This provides an…
There are two ways to turn a categorical model for pure quantum theory into one for mixed quantum theory, both resulting in a category of completely positive maps. One has quantum systems as objects, whereas the other also allows classical…
We investigate the evolution of open quantum systems in the presence of initial correlations with an environment. Here the standard formalism of describing evolution by completely positive trace preserving (CPTP) quantum operations can fail…
There are several important abstract operator systems with the convex cone of positive semidefinite matrices at the first level. Well-known are the operator systems of separable matrices, of positive semidefinite matrices, and of block…
We investigate elementary topological properties of sets of completely positive (CP) maps that arise in quantum Perron-Frobenius theory. We prove that the set of primitive CP maps of fixed Kraus rank is path-connected and we provide a…
Quantum entanglement can be studied through the theory of completely positive maps in a number of ways, including by making use of the Choi-Jamilkowski isomorphism, which identifies separable states with entanglement breaking quantum…
Completely positive trace preserving maps are widely used in quantum information theory. These are mostly studied using the master equation perspective. A central part in this theory is to study whether a given system of dynamical maps…
Continuity properties of the output entropy of positive linear maps between Banach spaces of trace class operators are investigated with the special attention to the classes of quantum channels and operations. It is shown that finiteness of…
We derive quantum kinetic equations for fermions in a homogeneous time-dependent background in presence of decohering collisions, by use of the Schwinger-Keldysh CTP-formalism. The quantum coherence (between particles and antiparticles) is…
We describe the dynamics of a detector modeled by a harmonic oscillator coupled with an otherwise free quantum field in a curved spacetime in terms of covariant equations of motion leading to local observables. To achieve this, we derive…
We prove additivity of the minimal conditional entropy associated with a quantum channel Phi, represented by a completely positive (CP), trace-preserving map, when the infimum of S(gamma_{12}) - S(gamma_1) is restricted to states of the…
Using a diagrammatic reformulation of Bayes' theorem, we provide a necessary and sufficient condition for the existence of Bayesian inference in the setting of finite-dimensional $C^*$-algebras. In other words, we prove an analogue of…
It is known that the time evolution of a subsystem from an initial state to two later times, t1, t2 (t2 > t1), are both completely positive (CP) but it is shown here that in the intermediate times between t1 and t2, in general, it need not…