Physics

Insolubility from No-Signalling
This paper improves on the result in my (Bacciagaluppi in Eur. J. Philos. Sci. 3: 87–100, 2013), showing that within the framework of the unitary Schrödinger equation it is impossible to reproduce the phenomenological description of quantum mechanical measurements (in particular the collapse of the state of the measured system) by assuming a suitable mixed initial state of the apparatus. The...


State Determination and Sufficiency of Observables
Informational completeness and the possibility of state distinction and determination are among the more important issues of quantum statistics. We use spectral and semispectral (POV) measures to analyse these questions. For a given W∗-algebra and a family of normal states on it we investigate the relation between sufficiency in Petz’s sense of a W∗-subalgebra generated by a spectral meas...
Logical Approach for Two-Valued States on Quantum Systems
In this paper we develop a logical system associated to two-valued states on orthomodular lattices. An completeness theorem with respect to a variety of orthomodular lattices enriched with an unary operation that represents two-valued states is given.


Quantum Sufficiency in the Operator Algebra Framework
The paper is devoted to the investigation of the notion of sufficiency in quantum statistics. Three kinds of this notion are considered: plain sufficiency (called simply: sufficiency), Petz’s sufficiency, and Umegaki’s sufficiency. The problem of the existence and structure of the minimal sufficient subalgebra is analyzed in some detail, conditions yielding equivalence of the three modes of...
Orthomodular Posets Related to Z2-Valued States
We study orthocomplemented posets (certain quantum logics) that possess an abundance of Z2-valued states. We first discuss their basic properties and, by means of examples, we illuminate intrinsic qualities of these orthocomplemented posets. We then address the problem of axiomatizability of our class of posets—a question that appears natural from the algebraic point of view. In the last sect...


Quantum Key Distribution in Large Scale Quantum Network Assisted by Classical Routing Information
Recently, small-scale Quantum Key Distribution (QKD) networks have been demonstrated and continuously operated in field environment. However, nodes of these QKD networks are less than 10 nodes. When the scale and structure of these networks becomes large and complex, such networks will subject to problem of intractable routing selection and limited transmission distance. We present a novel quan...
Strengthening Effect Algebras in a Logical Perspective: Heyting-Wajsberg Algebras
Heyting effect algebras are lattice-ordered pseudoboolean effect algebras endowed with a pseudocomplementation that maps on the center (i.e. Boolean elements). They are the algebraic counterpart of an extension of both Łukasiewicz many-valued logic and intuitionistic logic. We show that Heyting effect algebras are termwise equivalent to Heyting-Wajsberg algebras where the two different logical...

Transformations on Density Operators That Leave the Holevo Bound Invariant
For a given probability distribution λ1,…,λm we determine the structure of all such maps defined on a dense subset of density operators which leave the Holevo bound invariant i.e. which satisfy $$SBiggl(sum_{k=1}^m lambda_k phi(rho_k)Biggr)- sum_{k=1}^m lambda_k Sbigl(phi (rho_k)bigr)= SBiggl(sum _{k=1}^m lambda_k rho_kBiggr)- sum_{k=1}^m lambda_k S(rho_k) $$ for all possible collections ρ...
Unscrambling the Quantum Omelette
Based on recent theorems about quantum value-indefiniteness it is conjectured that many issues of “Born’s quantum mechanics” can be overcome by supposing that only a single pure state exists; and that the quantum evolution permutes this state.

Classes of Invariant Subspaces for Some Operator Algebras
New results showing connections between structural properties of von Neumann algebras and order theoretic properties of structures of invariant subspaces given by them are proved. We show that for any properly infinite von Neumann algebra M there is an affiliated subspace ({mathcal{L}} ) such that all important subspace classes living on ({mathcal{L}} ) are different. Moreover, we show that ({m...
Obstacles on the Way Toward an Entropic Uncertainty Relation
Deutsch’s entropic uncertainty relation is examined by using two experiments in which the spin of a single spin-half particle is detected after passing through two Stern-Gerlach apparatuses in two successive times. Two experiments differ only in the angle settings of the Stern-Gerlach apparatuses. In the general case where the angles are arbitrarily arranged, Deutsch’s inequality is violate...

Tense Operators on Spaces of Numerical Events
Spaces of numerical events were introduced for the sake to establish a propositional logic of physical phenomena. Since physical phenomena are variable in time, it is a natural task to develop temporal logic for this description. Hence we adopt the concept of tense operators used in classical propositional logic and in several sorts of non-classical one (e. g. Lukasiewicz many-valued logic, in...
A Structure of BCI-Algebras
Commutative BCI-algebras can be considered as semilattices whose sections are equipped with certain involutions. A similar view can be applied to commutative BCK-algebras. However, for general BCK-algebras a certain construction was settled by the author and J. Kühr (Miskolc Math. Notes 8:11–21, 2007) showing that they can be considered as structures essentially weaker than semilattices but ...
N-Perfect and (mathbb{Q})-Perfect Pseudo Effect Algebras
An n-perfect pseudo effect algebra means that it can be decomposed into n+1 comparable slices. We show that such a pseudo effect algebra satisfying a Riesz Decomposition Property type corresponds to the lexicographic product of a cyclic group (frac{1}{n}mathbb{Z}) with some po-group. The analogous result will be proved for strong (mathbb{Q})-perfect pseudo effect algebras....
Nanotechnology knowledge diffusion: measuring the impact of the research networking and a strategy for improvement
Given the global increase in public funding for nanotechnology research and development, it is even more important to support projects with promising return on investment. A main return is the benefit to other researchers and to the entire field through knowledge diffusion, invention, and innovation. The social network of researchers is one of the channels through which this happens. This study...