Related papers: A Quantum Interpretation of Bunched Logic for Quan…
We show that the bipartite separability of a pure qubit state hinges critically on the combinatorial structure of its computational-basis support. Using Boolean cube geometry, we introduce a taxonomy that distinguishes support-guaranteed…
We present a logic for reasoning about pairs of interactive quantum programs - quantum relational Hoare logic (qRHL). This logic follows the spirit of probabilistic relational Hoare logic (Barthe et al. 2009) and allows us to formulate how…
Matching logic is a logical framework for specifying and reasoning about programs using pattern matching semantics. A pattern is made up of a number of structural components and constraints. Structural components are syntactically matched,…
We present a formalism for encoding the logical basis of a qubit into subspaces of multiple physical levels. The need for this multilevel encoding arises naturally in situations where the speed of quantum operations exceeds the limits…
Quantum computing is a growing field where the information is processed by two-levels quantum states known as qubits. Current physical realizations of qubits require a careful calibration, composed by different experiments, due to noise and…
This paper introduces a novel type theory and logic for probabilistic reasoning. Its logic is quantitative, with fuzzy predicates. It includes normalisation and conditioning of states. This conditioning uses a key aspect that distinguishes…
We introduce algebraic sets in the complex projective spaces for the mixed states in bipartite quantum systems as their invariants under local unitary operations. The algebraic sets of the mixed state have to be the union of the linear…
Experiments in cognitive science and decision theory show that the ways in which people combine concepts and make decisions cannot be described by classical logic and probability theory. This has serious implications for applied disciplines…
Mixed state quantum computation can perform certain tasks which are believed to be efficiently intractable on a classical computer. For a specific model of mixed state quantum computation, namely, {\it deterministic quantum computation with…
The common-sense view of reality is expressed logically in Boolean subset logic (each element is either definitely in or not in a subset, i.e., either definitely has or does not have a property). But quantum mechanics does not agree with…
Quantum programs are notoriously difficult to code and verify due to unintuitive quantum knowledge associated with quantum programming. Automated tools relieving the tedium and errors associated with low-level quantum details would hence be…
A new physical implementation for quantum computation is proposed. The vibrational modes of molecules are used to encode qubit systems. Global quantum logic gates are realized using shaped femtosecond laser pulses which are calculated…
We study the separability of permutationally symmetric quantum states. We show that for bipartite symmetric systems most of the relevant entanglement criteria coincide. However, we provide a method to generate examples of bound entangled…
We introduce Bifurcation Logic, BL, which combines a basic classical modality with separating conjunction * together with its naturally associated multiplicative implication, that is defined using the modal ordering. Specifically, a formula…
A projective quantum logic in terms of relative states is developed, emphasizing the importance of information transfer between a system under study and its environment. The need for accounting for the historical evolution of system is…
Stone-type duality theorems, which relate algebraic and relational/topological models, are important tools in logic because -- in addition to elegant abstraction -- they strengthen soundness and completeness to a categorical equivalence,…
We present an approach to program reasoning which inserts between a program and its verification conditions an additional layer, the denotation of the program expressed in a declarative form. The program is first translated into its…
Bialgebrae provide an abstract framework encompassing the semantics of different kinds of computational models. In this paper we propose a bialgebraic approach to the semantics of logic programming. Our methodology is to study logic…
In this paper, we present a Hoare-style logic for reasoning about quantum programs with classical variables. Our approach offers several improvements over previous work: (1) Enhanced expressivity of the programming language: Our logic…
Quantum computers use the quantum interference of different computational paths to enhance correct outcomes and suppress erroneous outcomes of computations. In effect, they follow the same logical paradigm as (multi-particle)…