# The Mathematical Language of Quantum Theory: From Uncertainty to Entanglement

@inproceedings{Heinosaari2012TheML, title={The Mathematical Language of Quantum Theory: From Uncertainty to Entanglement}, author={Teiko Heinosaari and M{\'a}rio Ziman}, year={2012} }

Introduction 1. Hilbert space refresher 2. States and effects 3. Observables 4. Operations and channels 5. Measurement models and instruments 6. Entanglement Bibliography Index.

#### 159 Citations

Quantum Entanglement: Spooky Action at a Distance

- Physics
- 2020

Quantum entanglement is an important resource in quantum information technologies. Here, we study and characterize in a precise mathematical language some of the weird and nonintuitive features of… Expand

Complete quantum measurements break entanglement

- Physics
- 2012

Abstract A complete measurement of a quantum observable (POVM) is a measurement of the maximally refined version of the POVM. Complete measurements give information on multiplicities of measurement… Expand

Effectuses in Categorical Quantum Foundations

- Computer Science, Physics
- ArXiv
- 2019

This thesis develops the theory of effectuses as a categorical axiomatic approach to quantum theory. It provides a comprehensive introduction to effectus theory and reveals its connections with… Expand

Complete quantum measurements break entanglement

- Physics
- 2012

Complete measurement of a quantum observable (POVM) is a measurement of the maximally refined version of the POVM. Complete measurements give information on multiplicities of measurement outcomes and… Expand

Relation between the state distinction power and disturbance in quantum measurements

- Physics, Mathematics
- Journal of Mathematical Physics
- 2019

The measurement of an informative observable strongly disturbs a quantum state. We examine the so-called information-disturbance relation by introducing order relations based on the state distinction… Expand

Fuzzy Approach for Toffoli Gate in Quantum Computation With Mixed States

- Mathematics
- 2014

In the framework of quantum computation with mixed states, a fuzzy representation based on continuous t -norms for Toffoli gate is introduced. In this representation, the incidence of nonseparability… Expand

Quantum instruments: I. Extreme instruments

- Physics
- 2013

The structure of completely positive quantum instruments is analyzed thoroughly. We characterize the extreme points of the convex set of instruments. The characterization holds also for nondiscrete… Expand

Holistic type extension for classical propositional logic in quantum computation

- Physics, Mathematics
- 2019

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… Expand

A Theory of Entanglement

- Computer Science, Mathematics
- Quanta
- 2020

The basis of a theory of entanglement for quantum states is presented, which begins with a classical theory of entangled discrete measures, then treats quantum mechanics and discusses the statistics of bounded operators on a Hilbert space in terms of context coefficients. Expand

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