Related papers: Measurements and confluence in quantum lambda calc…
In this work we investigate how to quantify the coherence of quantum measurements. First, we establish a resource theoretical framework to address the coherence of measurement and show that any statistical distance can be adopted to define…
The quantum properties of quantum measurements are indispensable resources in quantum information processing and have drawn extensive research interest. The conventional approach to reveal the quantum properties relies on the reconstruction…
We present a new method for describing quantum measurements in relativistic systems that applies (i) to any QFT and for any field-detector coupling, (ii) to the measurement of any observable, and (iii) to arbitrary size, shape and motion of…
We study measurements of the unitary generalization of Pauli operators. First, an analytical (constructive) solution to the eigenproblem of these operators is presented. Next, in the case of two subsystems, the Schmidt form of the…
A quantum measurement is logically reversible if the premeasurement density operator of the measured system can be calculated from the postmeasurement density operator and from the outcome of the measurement. This paper analyzes why many…
The problem of measurement in quantum mechanics is reanalyzed within a general, strictly probabilistic framework (without reduction postulate). Based on a novel comprehensive definition of measurement the natural emergence of objective…
Finding a physically consistent approach to modelling interactions between classical and quantum systems is a highly nontrivial task. While many proposals based on various mathematical formalisms have been made, most of these efforts run…
Particle-style token machines are a way to interpret proofs and programs, when the latter are written following the principles of linear logic. In this paper, we show that token machines also make sense when the programs at hand are those…
Measurement is a fundamental operation in quantum computing and has many important use cases in quantum algorithms. This article provides a comprehensive overview of the basic measurement operations in quantum computing and represents a…
Generally, the measurement process consists in coupling a system to a detector that can give a continuous output. However, it may be interesting to use as a detector a system with a discrete spectrum, especially in view of applications to…
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…
This paper introduces a formal metalanguage called the lambda-q calculus for the specification of quantum programming languages. This metalanguage is an extension of the lambda calculus, which provides a formal setting for the specification…
We present a linearity theorem for a proof language of intuitionistic multiplicative additive linear logic, incorporating addition and scalar multiplication. The proofs in this language are linear in the algebraic sense. This work is part…
The rapid progress in quantum computing (QC) and machine learning (ML) has attracted growing attention, prompting extensive research into quantum machine learning (QML) algorithms to solve diverse and complex problems. Designing…
We provide a computational definition of the notions of vector space and bilinear functions. We use this result to introduce a minimal language combining higher-order computation and linear algebra. This language extends the Lambda-calculus…
Interest in problems of statistical inference connected to measurements of quantum systems has recently increased substantially, in step with dramatic new developments in experimental techniques for studying small quantum systems.…
Quantifying coherence is an essential endeavor for both quantum mechanical foundations and quantum technologies. We present a bona fide measure of quantum coherence by utilizing the Tsallis relative operator $(\alpha, \beta)$-entropy. We…
We provide an overview of a canonical formalism that describes mixed quantum-classical systems in terms of statistical ensembles on configuration space, and discuss applications to measurement theory. It is shown that the formalism allows a…
Quotients and comprehension are fundamental mathematical constructions that can be described via adjunctions in categorical logic. This paper reveals that quotients and comprehension are related to measurement, not only in quantum logic,…
Quantum metrology offers an enhanced performance in experiments such as gravitational wave-detection, magnetometry or atomic clocks frequency calibration. The enhancement, however, requires a delicate tuning of relevant quantum features…