Related papers: A State Polytope Decomposition Formula
We derive a sharp decomposition formula for the state polytope of the Hilbert point and the Hilbert-Mumford index of reducible varieties by using the decomposition of characters and basic convex geometry. This proof captures the essence of…
In this short note we show explicitly how to decompose a generalized permutohedron into semi-polytopes.
We describe a purely algebraic method for finding the best separable approximation to a mixed state of a composite 2x2 quantum system, consisting of a decomposition of the state into a linear combination of a mixed separable part and a pure…
We give in this note a weighted version of Brianchon-Gram's decomposition for a simple polytope. This weighted version is a direct consequence of the ordinary Brianchon-Gram formula.
In this paper, we present a general formula for obtaining the reduced density opeator for any biparticle pure entangled state. Using this formula, we derive, in a compact form, the explicit formula of the entanglement for any bipartical…
Polytope numbers for a polytope are a sequence of nonnegative integers that are defined by the facial information of a polytope. Every polygon is triangulable and a higher dimensional analogue of this fact states that every polytope is…
With any state of a multipartite quantum system its separability polytope is associated. This is an algebro-topological object (non-trivial only for mixed states) which captures the localisation of entanglement of the state. Particular…
We give a closed formula for the graded decomposition numbers of the blob algebra over a field of characteristic zero at a root of unity.
A split of a polytope is a (necessarily regular) subdivision with exactly two maximal cells. A polytope is totally splittable if each triangulation (without additional vertices) is a common refinement of splits. This paper establishes a…
By definition a separable state has the form \sum A_i \otimes B_i, where 0 \leq A_i, B_i for each i. In this paper we consider the class of states which admit such a decomposition with B_1, ..., B_p having independent images. We give a…
We study certain quantum states for which the PPT criterion is both sufficient and necessary for separability. A class of $n\times n$ bipartite mixed states is presented and the conditions of PPT for these states are derived. The separable…
We describe an algorithm to decompose rational functions from which we determine the poset of groups fixing these functions.
We show how to decompose any density matrix of the simplest binary composite systems, whether separable or not, in terms of only product vectors. We determine for all cases the minimal number of product vectors needed for such a…
We obtain the black body radiation formula of Planck by considering independent contributions of multiphoton states
In this paper, we present a formula describing the formation and decay of shock wave type solutions in some special cases.
We introduce a new decomposition of the multiqubit states of the form $\rho^{\otimes N}$ and employ it to construct the optimal single qubit purification procedure. The same decomposition allows us to study optimal quantum cloning and state…
We present a two-part program for state space decomposition. States are classified into entanglement classes based on local unitary transformations, and then characterized as elements of topological spaces using the language of fibre…
Production and verification of multipartite quantum state are an essential step in quantum information processing. In this work, we propose an efficient method to decompose symmetric multipartite observables, which are invariant under…
In this report, a scheme different from the PT and Wootters concurrence is developed to acquire a criterion to investigate the bipartite separability of the Werner state.
Quantum states can be written in infinitely many ways depending on the choices of basis. Schmidt decomposition of a quantum state has a lot of properties useful in the study of entanglement. All bipartite states admit Schmidt decomposition,…