Related papers: On PSI-complete and PSIR-complete measurements
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…
We introduce a new kind of quantum measurement that is defined to be symmetric in the sense of uniform Fisher information across a set of parameters that injectively represent pure quantum states in the neighborhood of a fiducial pure…
Informationally overcomplete measurements find important applications in quantum tomography and quantum state estimation. The most popular are maximal sets of mutually unbiased bases, for which trace relations between measurement operators…
We introduce a new method to estimate unknown pure $d$-dimensional quantum states using the probability distributions associated with only three measurement bases. Measurement results of $2d$ projectors are employed to generate a set of…
A long standing problem in quantum mechanics is the minimum number of observables required for the characterisation of unknown pure quantum states. The solution to this problem is specially important for the developing field of…
Given an ensemble of qubits, which we are told consists of a mixture of two pure states, one with probability $\eta_{0}$ and one with probability $\eta_{1}$, we want to find a POVM that will discriminate between the two states by measuring…
Concentrating on finite dimensional systems, we show that one can limit to extremal rank-1 POVMs if two simple procedures of mixing and relabeling are permitted. We demonstrate that any finite outcome POVM can be obtained from extremal…
We discuss the uniqueness of quantum states compatible with given results for measuring a set of observables. For a given pure state, we consider two different types of uniqueness: (1) no other pure state is compatible with the same…
This short note reviews the notion and fundamental properties of SIC-POVM and its connection with the length of separable states. We also review the t-design.
In quantum estimation for a $d$-parameter family of density operators on a finite-dimensional Hilbert space $\mathcal{H}$, an estimator is specified by a pair $\left(M,\hat{\theta}\right)$, where $M$ is a POVM with a finite outcome set…
An unexpected connection exists between compatibility criteria for quantum states and symmetric informationally complete POVMs. Beginning with Caves, Fuchs and Schack's "Conditions for compatibility of quantum state assignments" [Phys. Rev.…
We design an efficient and constructive algorithm to decompose any generalized quantum measurement into a convex combination of extremal measurements. We show that if one allows for a classical post-processing step only extremal rank-1…
This investigation continues a program aiming at obtaining effective quantum models to describe measurement statistics. In [Stark, arXiv:1209.5737 (2012)], we have described how the Gram matrix associated to the prepared states and the…
This paper considers completions of COMs (complexes oriented matroids) to ample partial cubes of the same VC-dimension. We show that these exist for OMs (oriented matroids) and CUOMs (complexes of uniform oriented matroids). This implies…
Minimal informationally complete positive operator-valued measures (MIC-POVMs) are special kinds of measurement in quantum theory in which the statistics of their $d^2$-outcomes are enough to reconstruct any $d$-dimensional quantum state.…
The physical problem behind informationally complete (IC) measurements is determining an unknown state statistically by measurement outcomes, known as state tomography. It is of central importance in quantum information processing such as…
We consider the implementation of a symmetric informationally complete probability-operator measurement (SIC POM) in the Hilbert space of a d-level system by a two-step measurement process: a diagonal-operator measurement with high-rank…
In quantum theory general measurements are described by so-called Positive Operator-Valued Measures (POVMs). We show that in $d$-dimensional quantum systems an application of depolarizing noise with constant (independent of $d$) visibility…
Generalized quantum measurements (also known as POVMs) are of great importance in quantum information and quantum foundations, but often difficult to perform. We present an experimental approach which can in principle be used to perform…
We show that a one-dimensional discrete time quantum walk can be used to implement a generalized measurement in terms of positive operator value measure (POVM) on a single qubit. More precisely, we show that for a single qubit any set of…