Related papers: Confluence Results for a Quantum Lambda Calculus w…
This paper demonstrates how to add a measurement operator to quantum lambda-calculi. A proof of the consistency of the semantics is given through a proof of confluence presented in a sufficiently general way to allow this technique to be…
We present a new and formal coinductive proof of confluence and normalisation of B\"ohm reduction in infinitary lambda calculus. The proof is simpler than previous proofs of this result. The technique of the proof is new, i.e., it is not…
Driven by the interest of reasoning about probabilistic programming languages, we set out to study a notion of unicity of normal forms for them. To provide a tractable proof method for it, we define a property of distribution confluence…
The classical lambda calculus may be regarded both as a programming language and as a formal algebraic system for reasoning about computation. It provides a computational model equivalent to the Turing machine, and continues to be of…
In measurement-based quantum computing (MBQC), computation is carried out by a sequence of measurements and corrections on an entangled state. Flow, and related concepts, are powerful techniques for characterising the dependence of the…
The linear-algebraic lambda-calculus and the algebraic lambda-calculus are untyped lambda-calculi extended with arbitrary linear combinations of terms. The former presents the axioms of linear algebra in the form of a rewrite system, while…
In measurement-based quantum computing (MBQC), computation is carried out by a sequence of measurements and corrections on an entangled state. Flow, and related concepts, are powerful techniques for characterising the dependence of the…
We study an untyped lambda calculus with quantum data and classical control. This work stems from previous proposals by Selinger and Valiron and by Van Tonder. We focus on syntax and expressiveness, rather than (denotational) semantics. We…
On the topic of probabilistic rewriting, there are several works studying both termination and confluence of different systems. While working with a lambda calculus modelling quantum computation, we found a system with probabilistic…
Quantum measurement is a class of quantum channels that sends quantum states to classical states. We set up resource theories of quantum coherence and quantum entanglement for quantum measurements and find relations between them. For this,…
The measurement postulate of quantum theory stands in conflict with the laws of thermodynamics and has evoked debate regarding what actually constitutes a measurement. With the help of modern quantum statistical mechanics, we take the first…
When applied on some particular quantum entangled states, measurements are universal for quantum computing. In particular, despite the fondamental probabilistic evolution of quantum measurements, any unitary evolution can be simulated by a…
This note contains the complete mathematical proof of the main Theorem of the paper "How continuous measurements in finite dimension are actually discrete" (quant-ph/0702068), thus showing that in finite dimension any measurement with…
Quantum measurements are noncontextual, with outcomes independent of which other commuting observables are measured at the same time, when consistently analyzed using principles of Hilbert space quantum mechanics rather than classical…
The objective of this paper is to develop a functional programming language for quantum computers. We develop a lambda calculus for the classical control model, following the first author's work on quantum flow-charts. We define a…
The claim that there is an inconsistency of quantum-classical dynamics [1] is investigated. We point out that a consistent formulation of quantum and classical dynamics which can be used to describe quantum measurement processes is already…
We introduce Lambda-SX, a typed quantum lambda-calculus that supports multiple measurement bases. By tracking duplicability relative to arbitrary bases within the type system, Lambda-SX enables more flexible control and compositional…
Quantum coherence is an essential ingredient in quantum information processing and plays a central role in emergent fields such as nanoscale thermodynamics and quantum biology. However, our understanding and quantitative characterization of…
Before the availability of large scale fault-tolerant quantum devices, one has to find ways to make the most of current noisy intermediate-scale quantum devices. One possibility is to seek smaller repetitive hybrid quantum-classical tasks…
Measurement-based quantum computing (MBQC) is a universal model for quantum computation. The combinatorial characterisation of determinism in this model, powered by measurements, and hence, fundamentally probabilistic, is the cornerstone of…