Related papers: Unital Positive Maps and Quantum States
Axiomatic approach to measurement theory is developed. All the possible statistical properties of apparatuses measuring an observable with nondegenerate spectrum allowed in standard quantum mechanics are characterized.
This article comprehensively explores matrices and their prerequisites for achieving positive semidefiniteness. The study delves into a series of theorems concerning pure quantum states in the context of weighted graphs. The main objective…
The questions we raise in this letter are as follows: What is the most general representation of a quantum state at a single point in time? Can we adapt the current formalisms to situations where the order of quantum operations is…
We study the equivalence of mixed states under local unitary transformations. First we express quantum states in Bloch representation. Then based on the coefficient matrices, some invariants are constructed. This method and results can be…
The density matrix of composite spin system is discussed in relation to the adjoint representation of unitary group U(n). The entanglement structure is introduced as an additional ingredient to the description of the linear space carrying…
Two interesting phenomena for the construction of quantum states are that of mutually unbiased bases and that of balanced states. We explore a constructive approach to each phenomenon that involves orthogonal polynomials on the unit circle.…
We show that a quantum channel $\mathcal{N}$ constructed by averaging over $\mathcal{O}(\log d/\epsilon^2)$ randomly chosen unitaries gives a local $\epsilon$-randomizing map with non-negative probability. The idea comes from a small…
We give a new geometric interpretation of quantum pure states. Using Voronoi diagrams, we reinterpret the structure of the space of pure states as a subspace of the quantum state space. In addition to the known coincidence of some Voronoi…
State transformations in quantum mechanics are described by completely positive maps which are constructed from quantum channels. We call a finest sharp quantum channel a context. The result of a measurement depends on the context under…
Any bipartite quantum state has quasi-probability representations in terms of separable states. For entangled states these quasi-probabilities necessarily exhibit negativities. Based on the general structure of composite quantum states, one…
We consider transformation maps on the space of states which are symmetries in the sense of Wigner. Due to the convex nature of the space of states, the set of these maps has a convex structure. We investigate the possibility of a complete…
A class of unital qubit maps displaying diagonal unitary and orthogonal symmetries is analyzed. Such maps already found a lot applications in quantum information theory. We provide a complete characterization of this class of maps showing…
Quantum state discrimination is a fundamental concept in quantum information theory, which refers to a class of techniques to identify a specific quantum state through a positive operator-valued measure. In this work, we investigate how…
Recently, it has been argued that quantum mechanics is a complete theory, and that different quantum states do necessarily correspond to different elements of reality, under the assumptions that quantum mechanics is correct and that…
Quantum state separation is a probabilistic map that transforms a given set of pure states into another set of more distinguishable ones. Here we investigate such a map acting onto uniparametric families of symmetric linearly dependent or…
We build apon our previous work, the Buckley-\vSivic method for simultaneous construction of families of positive maps on $3 \times 3$ self-adjoint matrices by prescribing a set of complex zeros to the associated forms. Positive maps that…
We provide a class of positive and trace-preserving maps based on symmetric measurements. From these positive maps we present separability criteria, entanglement witnesses, as well as the lower bounds of concurrence. We show by detailed…
We provide a general and consistent formulation for linear subsystem quantum dynamical maps, developed from a minimal set of postulates, primary among which is a relaxation of the usual, restrictive assumption of uncorrelated initial…
We introduce $\mathfrak{F}$-positive elements in planar algebras. We establish the Perron-Frobenius theorem for $\mathfrak{F}$-positive elements. We study the existence and uniqueness of the Perron-Frobenius eigenspace. When it is not…
We develop a unitary dependence theory to characterize the behaviors of quantum circuits and states in terms of how quantum gates manipulate qubits and determine their measurement probabilities. A qubit has dependence on a 1-qubit unitary…