Quantum operations frequently occur in quantum measurement theory, quantum probability, quantum computation and quantum information theory. If an operator A is invariant under a quantum operation Ï†â€¦ (More)

A new approach to quantum Markov chains is presented. We first define a transition operation matrix (TOM) as a matrix whose entries are completely positive maps whose column sums form a quantumâ€¦ (More)

Quantum effects are represented by operators on a Hilbert space satisfying 0 â‰¤ A â‰¤ I, and sharp quantum effects are represented by projection operators. We say that an effect A is almost sharp if A =â€¦ (More)

Effect algebras have important applications in the foundations of quantum mechanics and in fuzzy probability theory. An effect algebra that possesses a convex structure is called a convex effectâ€¦ (More)

This article begins with a review of quantum measure spaces. Quantum forms and indefinite inner-product spaces are then discussed. The main part of the paper introduces a quantum integral and derivesâ€¦ (More)

A covariant causal set (c-causet) is a causal set that is invariant under labeling. Such causets are well-behaved and have a rigid geometry that is determined by a sequence of positive integersâ€¦ (More)

We present a mathematical theory for a new type of quantum computer called a duality quantum computer that has recently been proposed. We discuss the nonunitarity of certain circuits of a dualityâ€¦ (More)

This paper first reviews quantum measure and integration theory. A new representation of the quantum integral is presented. This representation is illustrated by computing some quantum (Lebesgue)2â€¦ (More)