Related papers: Kakutani Dichotomy on Free States
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…
Entanglement in incoherent mixtures of pure states of two qubits is considered via the concurrence measure. A set of pure states is optimal if the concurrence for any mixture of them is the weighted sum of the concurrences of the generating…
We define algebras of quasi-quaternion type, which are symmetric algebras of tame representation type whose stable module category has certain structure similar to that of the algebras of quaternion type introduced by Erdmann. We observe…
The Kirkwood-Dirac (KD) quasiprobability distribution is a fundamental representation for quantum states and has been widely applied in quantum metrology, quantum chaos, weak values in recent years. A quantum state is KD-classical if its…
We report the prediction of quasi-bound states (resonant states with very long lifetimes) that occur in the eigenvalue continuum of propagating states for a wide region of parameter space. These quasi-bound states are generated in a quantum…
In this article, we investigate how quantum correlations behave for the so-called Werner and pseudo-pure families of states. The latter refers to states formed by mixing any pure state with the totally mixed state. We derive closed…
Within the framework of unitary easy quantum groups, we study an analogue of Brauer's Schur-Weyl approach to the representation theory of the orthogonal group. We consider concrete combinatorial categories whose morphisms are formed by…
We use the crystallised $C^*$-algebra $C(SU_{q}(2))$ at $q=0$ to obtain a unitary that gives an approximate equivalence involving the GNS representation on the $L^{2}$ space of the Haar state of the quantum $SU(2)$ group and the direct…
A quasi-representation of a group is a map from the group into a matrix algebra (or similar object) that approximately satisfies the relations needed to be a representation. Work of many people starting with Kazhdan and Voiculescu, and…
A kei, or 2-quandle, is an algebraic structure one can use to produce a numerical invariant of links, known as coloring invariants. Motivated by Mazur's analogy between prime numbers and knots, we define for every finite kei $\mathcal{K}$…
Quasi-states are certain not necessarily linear functionals on the space of continuous functions on a compact Hausdorff space. They were discovered as a part of an attempt to understand the axioms of quantum mechanics due to von Neumann. A…
A Nakayama algebra with almost separate relations is one where the overlap between any pair of relations is at most one arrow. In this paper we give a derived equivalence between such Nakayama algebras and path algebras of quivers of a…
We construct some infinite series of free and nearly free curves using pencils of conics with a base locus of cardinality at most two. These curves have an interesting topology, e.g. a high degree Alexander polynomial that can be explicitly…
We calculate the Kac determinant for the quasi-finite representation of \Winf algebra up to level 8. It vanishes only when the central charge is integer. We give an algebraic construction of null states and propose the character formulae.…
The quantum states which satisfy the equality in the generalised uncertainty relation are called intelligent states. We prove the existence of intelligent states for the Anandan-Aharonov uncertainty relation based on the geometry of the…
Photon subtraction and addition are experimental means of generating non-Gaussian states from Gaussian states. Coherent subtraction or addition is a combination of photon subtractions or additions. The resultant states are quite general…
We introduce new kinds of states of quantized radiation fields, which are the superpositions of negative binomial states. They exhibit remarkable non-classical properties and reduce to Schr\"odinger cat states in a certain limit. The…
We prove the quasi-Hopf algebra version of the Nichols-Zoeller theorem: A finite-dimensional quasi-Hopf algebra is free over any quasi-Hopf subalgebra.
A general algebraic procedure for constructing coherent states of a wide class of exactly solvable potentials e.g., Morse and P{\"o}schl-Teller, is given. The method, {\it a priori}, is potential independent and connects with earlier…
We find, for each $n\geq2$, the class of $n\times n$ compact quantum groups whose representation theory is similar to that of $SU(2)$: this is the class of "free analogues of $O(n)$" constructed by Van Daele and Wang.