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Quantum finite automata with control language

Carlo Mereghetti, Beatrice Palano (2006)

RAIRO - Theoretical Informatics and Applications

Bertoni et al.  introduced in Lect. Notes Comput. Sci.2710 (2003) 1–20 a new model of 1-way quantum finite automaton (1qfa) called 1qfa with control language (1qfc). This model, whose recognizing power is exactly the class of regular languages, generalizes main models of 1qfa's proposed in the literature. Here, we investigate some properties of 1qfc's. In particular, we provide algorithms for constructing 1qfc's accepting the inverse homomorphic images and quotients of languages accepted...

Quantum moment equations for a two-band k p Hamiltonian

Luigi Barletti (2005)

Bollettino dell'Unione Matematica Italiana

The hydrodynamic moment equations for a quantum system described by a two-band k p Hamiltonian are derived. In the case of pure states, it is proved that the order-0 and order-1 moment equations yield a closed system which is the two band analogue of Madelung's fluid equations.

Quantum states satisfying classical probability constraints

Elena R. Loubenets (2006)

Banach Center Publications

For linear combinations of quantum product averages in an arbitrary bipartite state, we derive new quantum Bell-form and CHSH-form inequalities with the right-hand sides expressed in terms of a bipartite state. This allows us to specify bipartite state properties sufficient for the validity of a classical CHSH-form inequality and the perfect correlation form of the original Bell inequality for any bounded quantum observables. We also introduce a new general condition on a bipartite state and quantum...

Relative conditional expectations on a logic

Oľga Nánásiová, Sylvia Pulmannová (1985)

Aplikace matematiky

In this paper, the authors introduce the notion of conditional expectation of an observable x on a logic with respect to a sublogic, in a state m , relative to an element a of the logic. This conditional expectation is an analogue of the expectation of an integrable function on a probability space.

Relatively additive states on quantum logics

Pavel Pták, Hans Weber (2005)

Commentationes Mathematicae Universitatis Carolinae

In this paper we carry on the investigation of partially additive states on quantum logics (see [2], [5], [7], [8], [11], [12], [15], [18], etc.). We study a variant of weak states — the states which are additive with respect to a given Boolean subalgebra. In the first result we show that there are many quantum logics which do not possess any 2-additive central states (any logic possesses an abundance of 1-additive central state — see [12]). In the second result we construct a finite 3-homogeneous...

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