36 citations · 54 across the 14 of their papers we have counts for
14 papers
Quantum Conditional Stochastic Processes
Stan Gudder
Quantum mechanics contains certain novel mathematical concepts. Among these are complex numbers, Hilbert spaces with their unitary and self-adjoint operators, states represented by…
Geometric Algebras and Fermion Quantum Field Theory
Stan Gudder
Corresponding to a finite dimensional Hilbert space with , we define a geometric algebra $\gscript (H)$ with $\dim\sqbrac{\gscript (H)}=2^n$. The algebra $\gscript (H…
Uncertainty of Quantum States
Stan Gudder
The uncertainty of a quantum state is given by the composition of two components. The first is called the quantum component and is given by the probability distribution of an obser…
Finite Classical and Quantum Effect Algebras
Stan Gudder
In this article, we only consider finite effect algebras. We define the concepts of classical and quantum effect algebras and show that an effect algebra is classical if and on…
Finite (quantum) effect algebras
Stan Gudder, Teiko Heinosaari
We investigate finite effect algebras and their classification. We show that an effect algebra with elements has at least and at most nontrivial defined su…
Quantum Transition Probabilities
Stan Gudder
Transition probabilities are an important and useful tool in quantum mechanics. However, in their present form, they are limited in scope and only apply to pure quantum states. In…
Interval Effect Algebras and Holevo Instruments
Stan Gudder
This article begins with a study of convex effect-state spaces. We point out that such spaces are equivalent to interval effect algebras that generate an ordered linear space and p…
Quantum Channel Conditioning and Measurement Models
Stan Gudder
If and are finite-dimensional Hilbert spaces, a channel from to is a completely positive, linear map that takes the set of states $\mathcal{S}…
Four Related Combinatorial Problems
Stan Gudder
This pedagogical article solves an interesting problem in quantum measure theory. Although a quantum measure is a generalization of an ordinary probability measure, need no…
A Theory of Quantum Instruments
Stanley Gudder
Until recently, a quantum instrument was defined to be a completely positive operation-valued measure from the set of states on a Hilbert space to itself. In the last few years, th…
Conditional Effects, Observables and Instruments
Stanley Gudder
We begin with a study of operations and the effects they measure. We define the probability that an effect occurs when the system is in a state by . If $P_ρ…
Spooky Action at a Distance
Stan Gudder
This article studies quantum mechanical entanglement. We begin by illustrating why entanglement implies action at a distance. We then introduce a simple criterion for determining w…
A Theory of Entanglement
Stanley Gudder
This article presents the basis of a theory of entanglement. We begin with a classical theory of entangled discrete measures in Section~1. Section~2 treats quantum mechanics and di…
Wigner functions for curved spaces I: On hyperboloids
Miguel Angel Alonso, George S. Pogosyan, Kurt Bernardo Wolf
We propose a Wigner quasiprobability distribution function for Hamiltonian systems in spaces of constant curvature --in this paper on hyperboloids--, which returns the correct marg…