Sequences of projective measurements in generalized probabilistic models
@article{Kleinmann2014SequencesOP, title={Sequences of projective measurements in generalized probabilistic models}, author={Matthias Kleinmann}, journal={Journal of Physics A: Mathematical and Theoretical}, year={2014}, volume={47} }
We define a simple rule that allows us to describe sequences of projective measurements for a broad class of generalized probabilistic models. This class embraces quantum mechanics and classical probability theory, but, for example, also the hypothetical Popescu–Rohrlich box. For quantum mechanics, the definition yields the established Lüders rule, which is the standard rule for updating the quantum state after a measurement. For the general case, it can be seen as being the least disturbing or…
19 Citations
Probabilistic theories and reconstructions of quantum theory
- Physics
- 2021
These lecture notes provide a basic introduction to the framework of generalized probabilistic theories (GPTs) and a sketch of a reconstruction of quantum theory (QT) from simple operational principles and a summary of the principles of Tomographic Locality, Continuous Reversibility, and the Subspace Axiom.
Probabilistic Theories and Reconstructions of Quantum Theory (Les Houches 2019 lecture notes).
- Physics
- 2020
These lecture notes provide a basic introduction to the framework of generalized probabilistic theories (GPTs) and a sketch of a reconstruction of quantum theory (QT) from simple…
Memory cost of temporal correlations
- PhilosophyNew Journal of Physics
- 2019
A possible notion of nonclassicality for single systems can be defined on the basis of the notion of memory cost of classically simulating probabilities observed in a temporal sequence of…
Bridging the gap between general probabilistic theories and the device-independent framework for nonlocality and contextuality
- PhysicsInf. Comput.
- 2016
Quantum correlations from simple assumptions
- Computer SciencePhysical Review A
- 2019
The correlations that are possible according to quantum theory are equal to those possible under the assumptions that there is a nonempty set of correlations for every Bell and Kochen-Specker contextuality scenario and a statistically independent realization of any two KS experiments.
Generalized Bell nonlocality and Kochen-Specker contextuality are equivalent in quantum theory
- Physics
- 2019
Bell nonlocality and Kochen-Specker (KS) contextuality are logically independent concepts and fuel completely different quantum protocols. Puzzlingly, in quantum theory both concepts seem to be…
Tracking the Dynamics of an Ideal Quantum Measurement.
- PhysicsPhysical review letters
- 2020
By taking tomographic snapshots during the detection process, it is shown that the process develops in agreement with the model of an ideal quantum measurement with an average fidelity of 94%.
Bell Non-locality and Kochen–Specker Contextuality: How are They Connected?
- Computer Science
- 2020
This work shows that, in quantum theory, every matrix of quantum Bell non-local correlations can be mapped to an identical matrix of KS contextual correlations produced in a scenario with identical relations of compatibility but where measurements are ideal and no space-like separation is required.
Quantum Simulation Logic, Oracles, and the Quantum Advantage
- Computer ScienceEntropy
- 2019
This work investigates in detail the role that oracles play for the advantage of quantum algorithms by using a simulation framework, Quantum Simulation Logic (QSL), to construct oracles and algorithms that solve some problems with the same success probability and number of queries as the quantum algorithms.
Simple Explanation of the Quantum Limits of Genuine n-Body Nonlocality.
- PhysicsPhysical review letters
- 2015
It is shown that, for any n≥2, the exclusivity principle, as derived from axioms about sharp measurements, and a technical assumption give the exact bounds predicted by quantum theory.
References
SHOWING 1-10 OF 32 REFERENCES
Information processing in generalized probabilistic theories
- Physics
- 2005
A framework in which a variety of probabilistic theories can be defined, including classical and quantum theories, and many others, is introduced, and a tensor product rule for combining separate systems can be derived.
Typical local measurements in generalized probabilistic theories: emergence of quantum bipartite correlations.
- PhysicsPhysical review letters
- 2013
It is found that if only a subset of typical local measurements can be made then all the bipartite correlations produced in a GPT can be simulated to a high degree of accuracy by quantum mechanics.
Quantum mechanics as quantum measure theory
- Physics
- 1994
The additivity of classical probabilities is only the first in a hierarchy of possible sum rules, each of which implies its successor. The first and most restrictive sum rule of the hierarchy yields…
Conditional Probability, Three-Slit Experiments, and the Jordan Algebra Structure of Quantum Mechanics
- Mathematics
- 2012
Most quantum logics do not allow for a reasonable calculus of conditional probability. However, those ones which do so provide a very general and rich mathematical structure, including
classical…
State-independent experimental test of quantum contextuality
- PhysicsNature
- 2009
The question of whether quantum phenomena can be explained by classical models with hidden variables is the subject of a long-lasting debate. In 1964, Bell showed that certain types of classical…
Three Slit Experiments and the Structure of Quantum Theory
- Physics
- 2011
In spite of the interference manifested in the double-slit experiment, quantum theory predicts that a measure of interference defined by Sorkin and involving various outcome probabilities from an…
Information Processing in Convex Operational Theories
- PhysicsElectron. Notes Theor. Comput. Sci.
- 2011
Quantum measuring processes of continuous observables
- Mathematics
- 1984
The purpose of this paper is to provide a basis of theory of measurements of continuous observables. We generalize von Neumann’s description of measuring processes of discrete quantum observables in…
Generalizations of Boxworld
- Physics
- 2012
Boxworld is a toy theory that can generate extremal nonlocal correlations known as PR boxes. These have been well established as an important tool to examine general nonlocal correlations, even…