Related papers: States on EMV-algebras
`Hypergeometric states', which are a one-parameter generalization of binomial states of the single-mode quantized radiation field, are introduced and their nonclassical properties are investigated. Their limits to the binomial states and to…
We describe representation theorems for local and perfect MV-algebras in terms of ultraproducts involving the unit interval [0,1]. Furthermore, we give a representation of local Abelian lattice-ordered groups with strong unit as…
We want to relate the concepts of entropy and pressure to that of KMS states for $C^*$-Algebras. Several different definitions of entropy are known in our days. The one we describe here is quite natural and extends the usual one for…
Absolutely maximally entangled, AME, states are pure multipartite states that give rise to the maximally mixed states when half or more of the parties are traced out. AME states find applications in fields like teleportation or quantum…
We introduce a non-commutative generalization of the notion of (approximately proper) equivalence relation and propose the construction of a "quotient space". We then consider certain one-parameter groups of automorphisms of the resulting…
Classes of algebraic structures that are defined by equational laws are called varieties or equational classes. A variety is finitely generated if it is defined by the laws that hold in some fixed finite algebra. We show that every…
This paper provides a systematic study of the operational idea that a quantum ``state'' is only defined up to what can be distinguished by a chosen family of observables. Concretely, any von Neumann algebra of observables $\mathscr{M}$…
A unified conceptual foundation of classical and quantum physics is given, free of undefined terms. Ensembles are defined by extending the `probability via expectation' approach of Whittle to noncommuting quantities. This approach carries…
We consider the possible quantum effect for infinite systems produced by variations of the Planck's constant. Using the algebraic formulation of quantum theory we study behaviour of states $\omega$ defined as positive, normalized…
Joint measurements of two observables reveal that every state is nonclassical, with the only trivial exception of the state with density matrix proportional to the identity. This naturally includes states considered universally as…
We consider a family of continuous variable (CV) states being a superposition of displaced number states with equal modulo but opposite in sign displacement amplitudes. Either an even or odd CV state is mixed with a delocalized photon at a…
We extend the concept of classicality in quantum optics to spin states. We call a state ``classical'' if its density matrix can be decomposed as a weighted sum of angular momentum coherent states with positive weights. Classical spin states…
Let S_k be the set of separable states on B(C^m \otimes C^n) admitting a representation as a convex combination of k pure product states, or fewer. If m>1, n> 1, and k \le max(m,n), we show that S_k admits a subset V_k such that V_k is…
We define various type of states on implicative involutive BE algebras (Jauch-Piron state, (P)-state, (B)-state, subadditive state, valuation), and we investigate the relationships between these states. Moreover, we introduce the unital,…
We develop the theory of quasi--invariant (resp. strongly quasi--invariant) states under the action of a group $G$ of normal $*$--automorphisms of a $*$--algebra (or von Neumann alegbra) $\mathcal{A}$. We prove that these states are…
In a finite dimensional Hilbert space, each normalized vector (state) can be chosen as a member of an orthonormal basis of the space. We give a proof of this statement in a manner that seems to be more comprehensible for physics students…
Consider a symmetric quantum state on an n-fold product space, that is, the state is invariant under permutations of the n subsystems. We show that, conditioned on the outcomes of an informationally complete measurement applied to a number…
In any probabilistic theory, we may say a bipartite state on a composite system AB steers its marginal state (on, say, system B) if, for any decomposition of the marginal as a mixture, with probabilities p_i, of states b_i of B, there…
In this sequence of papers, noncommutative analysis is used to give a consistent axiomatic approach to a unified conceptual foundation of classical and quantum physics. The present Part I defines the concepts of observables, states and…
Let $\rho_1$ and $\rho_2$ be two states on $\mathbb{C}^{d_1}$ and $\mathbb{C}^{d_2}$ respectively. The marginal state space, denoted by $\mathcal{C}(\rho_1,\rho_2)$, is the set of all states $\rho$ on $\mathbb{C}^{d_1}\otimes…