Related papers: Complete Quantum Relational Hoare Logics from Opti…

Lawvere showed that generalised metric spaces are categories enriched over $[0, \infty]$, the quantale of the positive extended reals. The statement of enrichment is a quantitative analogue of being a preorder. Towards seeking a logic for…

We initiate the study of parallel quantum programming by defining the operational and denotational semantics of parallel quantum programs. The technical contributions of this paper include: (1) find a series of useful proof rules for…

Inspired by the trend on unifying theories of programming, this paper shows how the algebraic treatment of standard data dependency theory equips relational data with functional types and an associated type system which is useful for type…

We study optimal perfect distinguishability between a unitary and a general quantum operation. In 2-dimensional case we provide a simple sufficient and necessary condition for sequential perfect distinguishability and an analytical formula…

Thanks to the rapid progress and growing complexity of quantum algorithms, correctness of quantum programs has become a major concern. Pioneering research over the past years has proposed various approaches to formally verify quantum…

We establish two complementarity relations for the relative entropy of coherence in quantum information processing, i.e., quantum dense coding and teleportation. We first give an uncertaintylike expression relating local quantum coherence…

Finding a denotational semantics for higher order quantum computation is a long-standing problem in the semantics of quantum programming languages. Most past approaches to this problem fell short in one way or another, either limiting the…

We ask whether the operational quantum description is complete at the level of preparations: can the empirically accessible properties of a finite preparation set be reproduced exactly by a hidden-variable description, or must every such…

We discuss an algebraic approach to propositional logic with side effects. To this end, we use Hoare's conditional [1985], which is a ternary connective comparable to if-then-else. Starting from McCarthy's notion of sequential evaluation…

The notion of perfect correlations between arbitrary observables, or more generally arbitrary POVMs, is introduced in the standard formulation of quantum mechanics, and characterized by several well-established statistical conditions. The…

This paper investigates the logical strength of completeness theorems for modal propositional logic within second-order arithmetic. We demonstrate that the weak completeness theorem for modal propositional logic is provable in…

Hoare-style verification provides a principled foundation for reasoning about the correctness of quantum programs, but existing approaches do not allow fully automatic verification. While automata-based verification scales well when…

Predictions for measurement outcomes in physical theories are usually computed by combining two distinct notions: a state, describing the physical system, and an observable, describing the measurement which is performed. In quantum theory,…

Quantum theory brings into question the compatibility of the twin desiderata of exact knowability of the present state of the physical world and perfect predictability of its future states. Bohr's coordination-causality complementarity…

We analyze a class of quantum operations based on a geometrical representation of $d-$level quantum system (or qudit for short). A sufficient and necessary condition of complete positivity, expressed in terms of the quantum Fourier…

This paper obtains a completeness result for inequational reasoning with applicative terms without variables in a setting where the intended semantic models are the full structures, the full type hierarchies over preorders for the base…

Many security- and performance-critical domains, such as cryptography, rely on low-level verification to minimize the trusted computing surface and allow code to be written directly in assembly. However, verifying assembly code against a…

Algebraic logic studies algebraic theories related to proposition and first-order logic. A new algebraic approach to first-order logic is sketched in this paper. We introduce the notion of a quantifier theory, which is a functor from the…

Left-sequential logics provide a means for reasoning about (closed) propositional terms with atomic propositions that may have side effects and that are evaluated sequentially from left to right. Such propositional terms are commonly used…

Previously, gradual verification has been developed using overapproximating logics such as Hoare logic. We show that the static verification component of gradual verification is also connected to underapproximating logics like incorrectness…