Related papers: Tensor 2-sums and entanglement
We show that any quantum density matrix can be represented by a Bayesian network (a directed acyclic graph), and also by a Markov network (an undirected graph). We show that any Bayesian or Markov net that represents a density matrix, is…
This work is an enquiry into the circumstances under which entropy methods can give an answer to the questions of both quantum separability and classical correlations of a composite state. Several entropy functionals are employed to examine…
Our investigation aims to study the specific role played by entanglement in the quantum computation process, by elaborating an entangled spin model developed within the 'hidden measurement approach' to quantum mechanics. We show that an…
We attempt to reveal the geometry, emerged from the entanglement structure of any general $N$-party pure quantum many-body state by representing entanglement entropies corresponding to all $2^N $ bipartitions of the state by means of a…
Recently, Braunstein et al. [1] introduced normalized Laplacian matrices of graphs as density matrices in quantum mechanics and studied the relationships between quantum physical properties and graph theoretical properties of the underlying…
We introduce a sequence of numerical tests that can determine the entanglement or separability of a state even when there is not enough information to completely determine its density matrix. Given partial information about the state in the…
Many experiments in quantum information aim at creating multi-partite entangled states. Quantifying the amount of entanglement that was actually generated can, in principle, be accomplished using full-state tomography. This method requires…
Entanglement is a striking feature of quantum mechanics, and it has a key property called unextendibility. In this paper, we present a framework for quantifying and investigating the unextendibility of general bipartite quantum states.…
A separable quantum state shared between parties $A$ and $B$ can be symmetrically extended to a quantum state shared between party $A$ and parties $B_1,\ldots ,B_k$ for every $k\in\mathbf{N}$. Quantum states that are not separable, i.e.,…
A new geometric representation of qubit and qutrit states based on probability simplexes is used to describe the separability and entanglement properties of density matrices of two qubits. The Peres--Horodecki positive partial transpose…
One of the most challenging problems in quantum physics is to quantify the entanglement of $d$-partite states and their separability. We show here that these problems are best addressed using tensors. The geometric measure of entanglement…
It is known that the tensor product of two sequences, in the tensor product of two separable Hilbert spaces, is a frame if and only if each component of that product is a frame. This paper proposes a sort of generalization of the…
In this paper, I will derive a measure of entanglement that coincides with the generalized concurrence for a general pure bi-and three-partite state based on wedge product. I will show that a further generalization of this idea to a general…
Quantum tomography is a method to experimentally extract all that is observable about a quantum mechanical system. We introduce quantum tomography to collider physics with the illustration of the angular distribution of lepton pairs. The…
Separability problem is a long-standing tough issue in quantum information theory. In this paper, we propose a general method to detect entanglement via arbitrary measurement $\boldsymbol{X}$, by which several novel criteria are…
We propose a universal decomposition of unitary maps over a tensorial power of C^2, introducing the key concept of "phase maps", and investigate how this decomposition can be used to implement unitary maps directly in the measurement-based…
The problem of entanglement produced by an arbitrary operator is formulated and a related measure of entanglement production is introduced. This measure of entanglement production satisfies all properties natural for such a characteristic.…
A general mathematical framework is presented to describe local equivalence classes of multipartite quantum states under the action of local unitary and local filtering operations. This yields multipartite generalizations of the singular…
This paper studies symmetric tensor decompositions. For symmetric tensors, there exist linear relations of recursive patterns among their entries. Such a relation can be represented by a polynomial, which is called a generating polynomial.…
A graphical model encodes conditional independence relations via the Markov properties. For an undirected graph these conditional independence relations can be represented by a simple polytope known as the graph associahedron, which can be…