Related papers: Complete Quantum Relational Hoare Logics from Opti…

A holistic extension of classical propositional logic is introduced in the framework of quantum computation with mixed states. The concepts of tautology and contradiction are investigated in this extensions. A special family of quantum…

We present a logical separability analysis for a functional quantum computation language. This logic is inspired by previous works on logical analysis of aliasing for imperative functional programs. Both analyses share similarities notably…

The quantum harmonic oscillator is one of the most fundamental objects in physics. We consider the case where it is extended to an arbitrary number modes and includes all possible terms that are bilinear in the annihilation and creation…

We consider the problem of how to verify the security of probabilistic oblivious algorithms formally and systematically. Unfortunately, prior program logics fail to support a number of complexities that feature in the semantics and…

This paper gives a formulation of quantum logic in the abstract algebraic setting laid out by Dunn and Hardegree (2001). On this basis, it provides a comparative analysis of viable quantum logical bivalent semantics and their classical…

Distributed quantum systems and especially the Quantum Internet have the ever-increasing potential to fully demonstrate the power of quantum computation. This is particularly true given that developing a general-purpose quantum computer is…

We develop a sound and complete equational theory for the functional quantum programming language QML. The soundness and completeness of the theory are with respect to the previously-developed denotational semantics of QML. The completeness…

We consider categorical logic on the category of Hilbert spaces. More generally, in fact, any pre-Hilbert category suffices. We characterise closed subobjects, and prove that they form orthomodular lattices. This shows that quantum logic is…

We introduce propositional team-based logics expressively complete for (quasi) downward and (quasi) upward closed properties in a syntactically dual way, by using variants of the inclusion atom. In particular, the variants of the primitive…

We propose a probabilistic Hoare logic aHL based on the union bound, a tool from basic probability theory. While the union bound is simple, it is an extremely common tool for analyzing randomized algorithms. In formal verification terms,…

We investigate an unsuspected connection between logical connectives with non-harmonious deduction rules, such as Prior's tonk, and quantum computing. We argue that these connectives model the information-erasure, the non-reversibility, and…

Optimal Transport (OT) has fueled machine learning (ML) across many domains. When paired data measurements $(\boldsymbol{\mu}, \boldsymbol{\nu})$ are coupled to covariates, a challenging conditional distribution learning setting arises.…

The predictions that quantum theory makes about the outcomes of measurements are generally probabilistic. This has raised the question whether quantum theory can be considered complete, or whether there could exist alternative theories that…

We present a logical calculus for reasoning about information flow in quantum programs. In particular we introduce a dynamic logic that is capable of dealing with quantum measurements, unitary evolutions and entanglements in compound…

Using recent results in topos theory, two systems of higher-order logic are shown to be complete with respect to sheaf models over topological spaces---so-called ``topological semantics''. The first is classical higher-order logic, with…

A semantic embedding of (constant domain) quantified conditional logic in classical higher-order logic is presented.

Consider many instances of an arbitrary quadripartite pure state of four quantum systems ABCD. Alice holds the AC part of each state, Bob holds B, while D represents all other parties correlated with ABC. Alice is required to redistribute…

We investigate the formal semantics of a simple imperative language that has both classical and quantum constructs. More specifically, we provide an operational semantics, a denotational semantics and two Hoare-style proof systems: an…

While there is a long tradition of reasoning about (non)termination in program analysis, specialized logics are typically needed to give different termination criteria. This includes partial correctness, where termination is not guaranteed,…

Dedicated to Tony Hoare. In a paper published in 1972 Hoare articulated the fundamental notions of hiding invariants and simulations. Hiding: invariants on encapsulated data representations need not be mentioned in specifications that…