Related papers: Bipartite Mixed States of Infinite-Dimensional Sys…
Our main theorem is in the generality of the axioms of Hilbert space, and the theory of unbounded operators. Consider two Hilbert spaces such that their intersection contains a fixed vector space D. It is of interest to make a precise…
This paper is a detailed study of finite-dimensional modules defined on bicomplex numbers. A number of results are proved on bicomplex square matrices, linear operators, orthogonal bases, self-adjoint operators and Hilbert spaces, including…
We introduce a class of bipartite operators acting on $\mathcal{H} \otimes \mathcal{H}$ ($\mathcal{H}$ being an $n$-dimensional Hilbert space) defined by a set of $n$ Completely Different Permutations CDP. Bipartite operators are of…
Let $\mathcal{B}(H)$ be the bounded, linear operators on a separable Hilbert space equipped with the norm topology. A property is called typical if the set of operators fulfilling the property is co-meager. We show that having non-empty…
Strassen's theorem circa 1965 gives necessary and sufficient conditions on the existence of a probability measure on two product spaces with given support and two marginals. In the case where each product space is finite Strassen's theorem…
We show that several classes of mixed quantum states in finite-dimensional Hilbert spaces which can be characterized as being, in some respect, 'most classical' can be described and analyzed in a unified way. Among the states we consider…
It is a well-known fact that all the statistical predictions of quantum mechanics on the state of any physical system represented by a two-dimensional Hilbert space can always be duplicated by a noncontextual hidden-variables model. In this…
A notion of super operator system is defined which generalizes the usual notion of operator systems to include certain unital involutive operator spaces which cannot be represented completely isometric as a concrete operator system on some…
We provide a constructive algorithm to find the best separable approximation to an arbitrary density matrix of a composite quantum system of finite dimensions. The method leads to a condition of separability and to a measure of…
Let $S \subset \mathbb{Z}^{d}$ be a finitely generated subsemigroup. Let $E$ be a product system over $S$. We show that there exists an infinite dimensional separable Hilbert space $\mathcal{H}$ and a semigroup $\alpha:=\{\alpha_x\}_{x \in…
We analyze the dynamics of a system qubit interacting by means a sequence of pairwise collisions with an environment consisting of just two qubits. We show that the density operator of the qubits approaches a common time averaged…
Heterogeneous bipartite quantum pure states, composed of two subsystems with a different number of levels, cannot have both reductions maximally mixed. In this work, we demonstrate existence of a wide range of highly entangled states of…
The wedge product of vectors has been shown to yield the generalised entanglement measure I-concurrence, wherein the separability of the multiparty qubit system arises from the parallelism of vectors in the underlying Hilbert space of the…
Gleason's theorem asserts the equivalence of von Neumann's density operator formalism of quantum mechanics and frame functions, which are functions on the pure states that sum to 1 on any orthonormal basis of Hilbert space of dimension at…
We address the question of whether or not global entanglement of a quantum state can be inferred from local properties. Specifically, we are interested in genuinely multiparticle entangled states whose two-body marginals are all separable,…
The entanglement in a pure state of N qudits (d-dimensional distinguishable quantum particles) can be characterised by specifying how entangled its subsystems are. A generally mixed subsystem of m qudits is obtained by tracing over the…
Let $P \subset \mathbb{R}^{d}$ be a closed convex cone. Assume that $P$ is pointed, i.e. the intersection $P \cap -P=\{0\}$ and $P$ is spanning, i.e. $P-P=\mathbb{R}^{d}$. Denote the interior of $P$ by $\Omega$. Let $E$ be a product system…
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…
A new criterion necessary and sufficient for the separability of pure bipartite systems for arbitrary finite dimensions is demonstrated; and the corresponding finer quantitative measures or characterizations of entanglement (beyond mere…
We study the separability of bipartite quantum systems in arbitrary dimensions based on the Bloch representation of density matrices. We present two separability criteria for quantum states in terms of the matrices $T_{\alpha\beta}(\rho)$…