相关论文: Simple Minimal Informationally Complete Measuremen…
It is the purpose of the present contribution to demonstrate that the generalization of the concept of a quantum mechanical observable from the Hermitian operator of standard quantum mechanics to a positive operator-valued measure is not a…
We show that a symmetric informationally-complete positive operator-valued measure exists in a given dimension $d$ if and only if there exists a $d^2$-dimensional operator system satisfying certain order-theoretic conditions. We also…
We present a general formalism for giving a measure space paired with a separable Hilbert space a quantum version based on normalized positive operator-valued measure. The latter are built from families of density operators labelled by…
In many a traditional physics textbook, a quantum measurement is defined as a projective measurement represented by a Hermitian operator. In quantum information theory, however, the concept of a measurement is dealt with in complete…
We present a systematic perturbative construction of the most general metric operator (and positive-definite inner product) for quasi-Hermitian Hamiltonians of the standard form, H= p^2/2 + v(x), in one dimension. We show that this problem…
A new measure of information in quantum mechanics is proposed which takes into account that for quantum systems the only feature known before an experiment is performed are the probabilities for various events to occur. The sum of the…
We define a complete measurement of a quantum observable (POVM) as a measurement of the maximally refined version of the POVM. Complete measurements give information from the multiplicities of the measurement outcomes and can be viewed as…
Wigner functions provide a way to do quantum physics using quasiprobabilities, that is, "probability" distributions that can go negative. Informationally complete POVMs, a much younger subject than phase space formulations of quantum…
A simple model of quantum particle is proposed in which the particle in a {\it macroscopic} rest frame is represented by a {\it microscopic d}-dimensional oscillator, {\it s=(d-1)/2} being the spin of the particle. The state vectors are…
We consider positive operator valued measures whose image is the bounded operators acting on an infinite-dimensional Hilbert space, and we relax, when possible, the usual assumption of positivity of the operator valued measure seen in the…
We obtain a simple formula for the average gate fidelity of a linear map acting on qudits. It is given in terms of minimal sets of pure state preparations alone, which may be interesting from the experimental point of view. These…
We address the problem of constructing positive operator-valued measures (POVMs) in finite dimension $n$ consisting of $n^2$ operators of rank one which have an inner product close to uniform. This is motivated by the related question of…
In quantum mechanics the statistics of the outcomes of a measuring apparatus is described by a positive operator valued measure (POVM). A quantum channel transforms POVM's into POVM's, generally irreversibly, thus loosing some of the…
Symmetric informationally complete positive operator valued measures (SIC-POVMs) are studied within the framework of the probability representation of quantum mechanics. A SIC-POVM is shown to be a special case of the probability…
We give an explicit characterization of the most general quasi-Hermitian operator H, the associated metric operators \eta_+, and \eta_+-pseudo-Hermitian operators acting in two-dimensional complex Euclidean space C^2. These operators…
We explicitly calculate information, fidelity, and reversibility of an arbitrary single-qubit measurement on a completely unknown state. These quantities are expressed as functions of a single parameter, which is the ratio of the two…
We explore precision in a measurement process incorporating pure probe states, unitary dynamics and complete measurements via a simple formalism. The concept of `information complement' is introduced. It undermines measurement precision and…
The representation of measurements by positive operator valued measures and the description of the most general state transformations by means of completely positive maps are two basic concepts of quantum information theory. These concepts…
Informationally complete (IC) positive operator-valued measures (POVMs) are generalized quantum measurements that offer advantages over the standard computational basis readout of qubits. For instance, IC-POVMs enable efficient extraction…
The notion of Symmetric Informationally Complete Positive Operator-Valued Measures (SIC-POVMs) arose in physics as a kind of optimal measurement basis for quantum systems. However the question of their existence is equivalent to that of the…