Related papers: Subspace preserving completely positive maps
We discuss a wide class of time inhomogeneous quantum evolution which is represented by two-parameter family of completely positive trace-preserving maps. These dynamical maps are constructed as infinite series of jump processes. It is…
Unital quantum channels, defined by their property of leaving the maximally mixed state invariant, form an important class of quantum operations. A distinguished subset of these channels can be represented as a probabilistic mixture of…
Quantum maps are fundamental to quantum information theory and open quantum systems. Covariant or weakly symmetric quantum maps, in particular, play a key role in defining quantum evolutions that respect thermodynamics, establish free…
Many fundamental and key objects in quantum mechanics are linear mappings between particular affine/linear spaces. This structure includes basic quantum elements such as states, measurements, channels, instruments, non-signalling channels…
This paper continues the study of stochastic maps, or channels, which break entanglement. We give a detailed description of entanglement-breaking qubit channels, and show that such maps are precisely the convex hull of those known as…
Subsystem codes protect quantum information by encoding it in a tensor factor of a subspace of the physical state space. Subsystem codes generalize all major quantum error protection schemes, and therefore are especially versatile. This…
In this work, we consider optimal state discrimination for a quantum system that interacts with an environment, i.e., states evolve under a quantum channel. We show the conditions on a quantum channel and an ensemble of states such that a…
This survey contains a selection of topics unified by the concept of positive semi-definiteness (of matrices or kernels), reflecting natural constraints imposed on discrete data (graphs or networks) or continuous objects (probability or…
The objective of this manuscript is to understand the structure of an invertible linear map on the space of real symmetric matrices $\mathcal{S}^n$ that leaves invariant the closed convex cones of copositive and completely positive matrices…
We introduce a generalization of the set of completely positive matrices that we call "pairwise completely positive" (PCP) matrices. These are pairs of matrices that share a joint decomposition so that one of them is necessarily positive…
We present an algorithm for projecting superoperators onto the set of completely positive, trace-preserving maps. When combined with gradient descent of a cost function, the procedure results in an algorithm for quantum process tomography:…
Quantum devices are subject to natural decay. We propose to study these decay processes as the Markovian evolution of quantum channels, which leads us to dynamical semigroups of superchannels. A superchannel is a linear map that maps…
The transport and continuum equations exhibit a number of conservation laws. For example, scalar multiplication is conserved by the transport equation, while positivity of probabilities is conserved by the continuum equation. Certain…
This work introduces a rigorous notion of localization probability of a quantum state within a given subspace of its Hilbert space. A non-negative operator A is uniquely decomposed as A=B+C, where B is the maximal positive operator…
Quantum supermaps are higher-order maps transforming quantum operations into quantum operations. Here we extend the theory of quantum supermaps, originally formulated in the finite dimensional setting, to the case of higher-order maps…
Assume that $\Phi:\mathbb{M}_{n}(\mathbb{C})\rightarrow\mathbb{M}_{n}(\mathbb{C})$ is a superoperator which preserves hermiticity. We give an algorithm determining whether $\Phi$ preserves semipositivity (we call $\Phi$ positive in this…
Symmetries impose structure on the Hilbert space of a quantum mechanical model. The mathematical units of this structure are the irreducible representations of symmetry groups and I consider how they function as conceptual units of…
We characterise the respective semigroups of mappings that preserve, or that preserve or reverse orientation of a finite cycle, in terms of their actions on oriented triples and oriented quadruples. This leads to a proof that the latter…
We examine stochastic maps in the context of quantum optics. Making use of the master equation, the damping basis, and the Bloch picture we calculate a non-unital, completely positive, trace-preserving map with unequal damping eigenvalues.…
Supmech, which is noncommutative Hamiltonian mechanics \linebreak (NHM) (developed in paper I) with two extra ingredients : positive observable valued measures (PObVMs) [which serve to connect state-induced expectation values and classical…