Related papers: Qubit entanglement: A Jordan algebraic perspective
We present a fine-structure entanglement classification under stochastic local operation and classical communication (SLOCC) for multiqubit pure states. To this end, we employ specific algebraic-geometry tools that are SLOCC invariants,…
We revisit qubit-qutrit quantum systems under collective dephasing and answer some of the questions which have not been asked and addressed so far in the literature. In particular, we examine the possibilities of non-trivial phenomena of…
We introduce a natural notion of determinant in matrix JB$^*$-algebras, i.e., for hermitian matrices of biquaternions and for hermitian $3\times 3$ matrices of complex octonions. We establish several properties of these determinants which…
By a classical result of Jordan, each finite subgroup G of a complex linear group GL_n(C) has an abelian subgroup whose index in G is bounded by a constant depending only on n. We consider the problem if this remains true for finite…
Most quantum logics do not allow for a reasonable calculus of conditional probability. However, those ones which do so provide a very general and rich mathematical structure, including classical probabilities, quantum mechanics as well as…
In this paper we present the novel qualities of entanglement of formation for general (so also infinite dimensional) quantum systems. A major benefit of our presentation is a rigorous description of entanglement of formation. In particular,…
We establish a natural correspondence between (the equivalence classes of) cubic solutions of an eiconal type equation and (the isomorphy classes of) cubic Jordan algebras.
We investigate three superconducting flux qubits coupled in a loop. In this setup, tripartite entanglement can be created in a natural, controllable, and stable way. Both generic kinds of tripartite entanglement -the W type as well as the…
We give the presentation of exceptional bounded symmetric domains using the Albert algebra and exceptional Jordan triple systems. The first chapter is devoted to Cayley-Graves algebras, the second to exceptional Jordan triple systems. In…
Several entanglement measures are used to define equivalence classes in the set of hypergraph states of three qubits. Our classifications reveal that (i) under local unitary transformations, hypergraph states of three qubits are split into…
In their 2002 article, Ghirardi, Marinatto and Weber have proposed a formal analysis of the entanglement properties for a system consisting of N distinguishable particles. Their analysis leads to the differentiation of three possible…
We characterize entanglement subject to its definition over real and complex, composite quantum systems. In particular, a method is established to assess quantum correlations with respect to a selected number system, illuminating the deeply…
Freudenthal algebras over a field are basically the same as Jordan algebras of degree $3$ remaining simple under all base field extensions. These algebras are intimately linked, via their automorphism groups and structure groups, to simple…
We consider the coupling of quantum fields to classical gravity in the formalism of ensembles on configuration space, a model that allows a consistent formulation of interacting classical and quantum systems. Explicit calculations show that…
The state of an entangled q-bit pair is specified by 15 numerical parameters that are naturally regarded as the components of two 3-vectors and a $3\times3$-dyadic. There are easy-to-use criteria to check whether a given pair of 3-vectors…
If only limited control over a multiparticle quantum system is available, a viable method to characterize correlations is to perform random measurements and consider the moments of the resulting probability distribution. We present…
Algebraic approach to quantum non - separability is applied to the case of two qubits. It is based on the partition of the algebra of observables into independent subalgebras and the tensor product structure of the Hilbert space is not…
The notion of derivation with invertible values as a derivation of ring with unity that only takes multiplicatively invertible or zero values appeared in a paper of Bergen, Herstein and Lanski, in which they determined the structure of…
Various topics concerning the entanglement of composite quantum systems are considered with particular emphasis concerning the strict relations of such a problem with the one of attributing objective properties to the constituents. Most of…
In this paper, we develop a method to obtain the algebraic classification of noncommutative Jordan algebras from the classification of Jordan algebras of the same dimension. We use this method to obtain the algebraic classification of…