Entanglement as a semantic resource

The characteristic holistic features of the quantum theoretic formalism and the intriguing notion of entanglement can be applied to a field that is far from microphysics: logical semantics. Quantum computational logics are new forms of quantum logic that have been suggested by the theory of quantum logical gates in quantum computation. In the standard semantics of these logics, sentences denote quantum information quantities: systems of qubits (quregisters) or, more generally, mixtures of quregisters (qumixes), while logical connectives are interpreted as special quantum logical gates (which have a characteristic reversible and dynamic behavior). In this framework, states of knowledge may be entangled, in such a way that our information about the whole determines our information about the parts; and the procedure cannot be, generally, inverted. In spite of its appealing properties, the standard version of the quantum computational semantics is strongly "Hilbert-space dependent". This certainly represents a shortcoming for all applications, where real and complex numbers do not generally play any significant role (as happens, for instance, in the case of natural and of artistic languages). We propose an abstract version of quantum computational semantics, where abstract qumixes, quregisters and registers are identified with some special objects (not necessarily living in a Hilbert space), while gates are reversible functions that transform qumixes into qumixes. In this framework, one can give an abstract definition of the notions of superposition and of entangled pieces of information, quite independently of any numerical values. We investigate three different forms of abstract holistic quantum computational logic

A quantum computational semantics for epistemic logical operators. Part I: epistemic structures

Some critical open problems of epistemic logics can be investigated in the framework of a quantum computational approach. The basic idea is to interpret sentences like “Alice knows that Bob does not understand that π is irrational” as pieces of quantum information (generally represented by density operators of convenient Hilbert spaces). Logical epistemic operators (to understand, to know. . .) are dealt with as (generally irreversible) quantum operations, which are, in a sense, similar to measurement-procedures. This approach permits us to model some characteristic epistemic processes, that concern both human and artificial intelligence. For instance, the operation of “memorizing and retrieving information” can be formally represented, in this framework, by using a quantum teleportation phenomenon

A first-order epistemic quantum computational semantics with relativistic-like epistemic effects

Quantum computation has suggested new forms of quantum logic, called quantum computational logics. In these logics well-formed formulas are supposed to denote pieces of quantum information: possible pure states of quantum systems that can store the information in question. At the same time, the logical connectives are interpreted as quantum logical gates: unitary operators that process quantum information in a reversible way, giving rise to quantum circuits. Quantum computational logics have been mainly studied as sentential logics (whose alphabet consists of atomic sentences and of logical connectives). In this article we propose a semantic characterization for a first-order epistemic quantum computational logic, whose language can express sentences like "Alice knows that everybody knows that she is pretty". One can prove that (unlike the case of logical connectives) both quantifiers and epistemic operators cannot be generally represented as (reversible) quantum logical gates. The "act of knowing" and the use of universal (or existential) assertions seem to involve some irreversible "theoretic jumps", which are similar to quantum measurements. Since all epistemic agents are characterized by specific epistemic domains (which contain all pieces of information accessible to them), the unrealistic phenomenon of logical omniscience is here avoided: knowing a given sentence does not imply knowing all its logical consequences

Conjugatable water-soluble Pt(ii) and Pd(ii) porphyrin complexes: Novel nano- and molecular probes for optical oxygen tension measurement in tissue engineering

Measurement of oxygen tension in compressed collagen sheets was performed using matrix-embedded optical oxygen sensors based on platinum(II) and palladium(II) porphyrins supported on polyacrylamide nanoparticles. Bespoke, fully water-soluble, mono-functionalised Pt(II) and Pd(II) porphyrin complexes designed for conjugation under mild conditions were obtained using microwave-assisted metallation. The new sensors display a linear response (1/τ vs. O₂) to varying oxygen tension over a biologically relevant range (7.0 × 10⁻⁴ to 2.7 × 10⁻¹ mM) in aqueous solutions; a behaviour that is maintained following conjugation to polyacrylamide nanoparticles, and following embedding of the nanosensors in compressed collagen sheets, paving the way to innovative approaches for real-time resolution of oxygen gradients throughout 3D matrices useful for tissue regeneration

Epistemic quantum computational structures in a Hilbert-space environment

Some critical open problems of epistemic logics can be investigated in the framework of a quantum computational approach. The basic idea is to interpret sentences like “Alice knows that Bob does not understand that π is irrational” as pieces of quantum information (generally represented by density operators of convenient Hilbert spaces). Logical epistemic operators (to understand, to know ...) are dealt with as (generally irreversible) quantum operations, which are, in a sense, similar to measurement-procedures. This approach permits us to model some characteristic epistemic processes, that concern both human and artificial intelligence. For instance, the operation of “memorizing and retrieving information” can be formally represented, in this framework, by using a quantum teleportation phenomenon

Quantum information, cognition, and music

Parallelism represents an essential aspect of human mind/brain activities. One can recognize some common features between psychological parallelism and the characteristic parallel structures that arise in quantum theory and in quantum computation. The article is devoted to a discussion of the following questions: 1. a comparison between classical probabilistic Turing machines and quantum Turing machines. 2. possible applications of the quantum computational semantics to cognitive problems. 3. parallelism in music

A quantum logical and geometrical approach to the study of improper mixtures

We study improper mixtures from a quantum logical and geometrical point of view. Taking into account the fact that improper mixtures do not admit an ignorance interpretation and must be considered as states in their own right, we do not follow the standard approach which considers improper mixtures as measures over the algebra of projections. Instead of it, we use the convex set of states in order to construct a new lattice whose atoms are all physical states: pure states and improper mixtures. This is done in order to overcome one of the problems which appear in the standard quantum logical formalism, namely, that for a subsystem of a larger system in an entangled state, the conjunction of all actual properties of the subsystem does not yield its actual state. In fact, its state is an improper mixture and cannot be represented in the von Neumann lattice as a minimal property which determines all other properties as is the case for pure states or classical systems. The new lattice also contains all propositions of the von Neumann lattice. We argue that this extension expresses in an algebraic form the fact that -alike the classical case- quantum interactions produce non trivial correlations between the systems. Finally, we study the maps which can be defined between the extended lattice of a compound system and the lattices of its subsystems.Comment: submitted to the Journal of Mathematical Physic

Flexible synthesis of cationic peptide-porphyrin derivatives for light-triggered drug delivery and photodynamic therapy

Efficient syntheses of cell-penetrating peptide-porphyrin conjugates are described using a variety of bioconjugation chemistries. This provides a flexible means to convert essentially hydrophobic tetrapyrolle photosensitisers into amphiphilic derivatives which are well-suited for use in light-triggered drug delivery by photochemical internalisation (PCI) and targeted photodynamic therapy (PDT)

A representation theorem for MV-algebras

An {\em MV-pair} is a pair $(B,G)$ where $B$ is a Boolean algebra and $G$ is a subgroup of the automorphism group of $B$ satisfying certain conditions. Let $\sim_G$ be the equivalence relation on $B$ naturally associated with $G$. We prove that for every MV-pair $(B,G)$, the effect algebra $B/\sim_G$ is an MV- effect algebra. Moreover, for every MV-effect algebra $M$ there is an MV-pair $(B,G)$ such that $M$ is isomorphic to $B/\sim_G$