We show that three fundamental information-theoretic constraints -- the impossibility of superluminal information transfer between two physical systems by performing measurements on one of them, the impossibility of broadcasting the information contained in an unknown physical state, and the impossibility of unconditionally secure bit commitment -- suffice to entail that the observables and state space of a physical theory are quantum-mechanical. We demonstrate the converse derivation in part, and consider the implications of alternative answers to a remaining open question about (...) nonlocality and bit commitment. (shrink)

The well-known proposal to consider the Lüders-von Neumann measurement as a non-classical extension of probability conditionalization is further developed. The major results include some new concepts like the different grades of compatibility, the objective conditional probabilities which are independent of the underlying state and stem from a certain purely algebraic relation between the events, and an axiomatic approach to quantum mechanics. The main axioms are certain postulates concerning the conditional probabilities and own intrinsic probabilistic interpretations from the very beginning. A (...) Jordan product is derived for the observables, and the consideration of composite systems leads to operator algebras on the Hilbert space over the complex numbers, which is the standard model of quantum mechanics. The paper gives an expository overview of the results presented in a series of recent papers by the author. For the first time, the complete approach is presented as a whole in a single paper. Moreover, since the mathematical proofs are already available in the original papers, the present paper can dispense with the mathematical details and maximum generality, thus addressing a wider audience of physicists, philosophers or quantum computer scientists. (shrink)

No-cloning theorem says that there is no unitary operation that makes perfect clones of non-orthogonal quantum states. The objective of the present paper is to examine whether an imperfect cloning operation exists or not in a C*-algebraic framework. We define a universal \ -imperfect cloning operation which tolerates a finite loss \ of fidelity in the cloned state, and show that an individual system’s algebra of observables is abelian if and only if there is a universal \ -imperfect cloning operation (...) in the case where the loss of fidelity is less than \ . Therefore in this case no universal \ -imperfect cloning operation is possible in algebraic quantum theory. (shrink)

The quantum mechanical no-cloning theorem for pure states is generalized and transfered to the quantum logics with a conditional probability calculus. This is, on the one hand, an extension of the classical probability calculus and, on the other hand, a mathematical generalization of the Lueders - von Neumann quantum measurement process. In the non-classical case, a very special type of conditional probability emerges, describing the probability for the transition from a past event to a future event independently of any underlying (...) state. This probability results from the algebraic structure of the quantum logic only and is invariant under algebraic morphisms, which is used to prove the generalized no-cloning theorem in a rather abstract, though simple and basic fashion without relying on a tensor product construction as required in other approaches. (shrink)