Related papers: Polytope compatibility -- from quantum measurement…
Testing the symmetries of quantum states and channels provides a way to assess their usefulness for different physical, computational, and communication tasks. Here, we establish several complexity-theoretic results that classify the…
In optimal transport, quadratic regularization is a sparse alternative to entropic regularization: the solution measure tends to have small support. Computational experience suggests that the support decreases monotonically to the…
This article presents numerical methods in order to solve problems of tolerance analysis. A geometric specification, a contact specification and a functional requirement can be respectively characterized by a finite set of geometric…
A formula for the commutator of tensor product matrices is used to shows that, for qubits, compatibility of quantum multiparty observables almost never implies local compatibility at each site and to predict when this happens/does not…
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.…
Measure synchronization is a well-known phenomenon in coupled classical Hamiltonian systems over last two decades. In this paper, synchronization for coupled Harper system is investigated in both classical and quantum contexts. The concept…
We say that two (or more) state assignments for one and the same quantum system are compatible if they could represent the assignments of observers with differing information about the system. A criterion for compatibility was proposed in…
We study the concepts of compatibility and separability and their implications for quantum and classical systems. These concepts are illustrated on a macroscopic model for the singlet state of a quantum system of two entangled spin 1/2 with…
It is a hard and important problem to find the criterion of the set of positive-definite matrixes which can be written as reduced density operators of a multi-partite quantum state. This problem is closely related to the study of many-body…
I study the class of problems efficiently solvable by a quantum computer, given the ability to "postselect" on the outcomes of measurements. I prove that this class coincides with a classical complexity class called PP, or Probabilistic…
One of the hallmarks of quantum theory is the realization that distinct measurements cannot in general be performed simultaneously, in stark contrast to classical physics. In this context the notions of coexistence and joint measurability…
We generalize the recent invariant polytope algorithm for computing the joint spectral radius and extend it to a wider class of matrix sets. This, in particular, makes the algorithm applicable to sets of matrices that have finitely many…
We propose quantum devices that can realize probabilistically different projective measurements on a qubit. The desired measurement basis is selected by the quantum state of a program register. First we analyze the phase-covariant…
Two vertex-labelled polygons are \emph{compatible} if they have the same clockwise cyclic ordering of vertices. The definition extends to polygonal regions (polygons with holes) and to triangulations---for every face, the clockwise cyclic…
We consider the problem of a state determination for a two-level quantum system which can be in one of two nonorthogonal mixed states. It is proved that for the two independent identical systems the optimal combined measurement (which…
In quantum theory, there exist sets of operations that cannot be performed simultaneously. These sets of operations are referred to as incompatible. While this definition of incompatibility extends to general probabilistic theories (GPTs),…
Consider a real point configuration $\mathbf{A}$ of size $n$ and an integer $r \leq n$. The vertices of the $r$-lineup polytope of $\mathbf{A}$ correspond to the possible orderings of the top $r$ points of the configuration obtained by…
We introduce a multivariate Markov transform which generalizes the well-known one-dimensional Stieltjes transform from the Moment problem and Spectral theory. Our main result states that two measures {\mu} and {\nu} with bounded support…
When studying entropy functions of multivariate probability distributions, polymatroids and matroids emerge. Entropy functions of pure multiparty quantum states give rise to analogous notions, called here polyquantoids and quantoids.…
The mixing operation for abstract polytopes gives a natural way to construct the minimal common cover of two polytopes. In this paper, we apply this construction to the regular convex polytopes, determining when the mix is again a polytope,…