Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userVarieties of contextuality based on complexion, quantum probabilities, and structural non-embeddability
55
0
0.0
(
0
)
Authors
Karl Svozil
Ask ChatGPT about the research
No Arabic abstract
Contextuality can either be synthetically defined in terms of outcome conditionality on the measurement conditions, or in terms of non-classical probability distributions. Another logico-algebraic strong form of contextuality characterizes collections of quantum observables that have no faithfully embedding into (extended) Boolean algebras. Any of these forms indicate a classical in- or underdetermination that can be termed value indefinite, and formalized by partial functions of theoretical computer sciences. he term contextual by indeterminate or value indefinite in the spirit of partial functions of theoretical computer sciences.
rate research
Read More
Quantum non-Gaussian states represent an important class of highly non-classical states whose preparation requires quantum operations or measurements beyond the class of Gaussian operations and statistical mixing. Here we derive criteria for certification of quantum non-Gaussianity based on probability of vacuum in the original quantum state and a state transmitted through a lossy channel with transmittance T. We prove that the criteria hold for arbitrary multimode states, which is important for their applicability in experiments with broadband sources and single-photon detectors. Interestingly, our approach allows to detect quantum non-Gaussianity using only one photodetector instead of complex multiplexed photon detection schemes, at the cost of increased experimental time. We also formulate a quantum non-Gaussianity criterion based on the vacuum probability and mean photon number of the state and we show that this criterion is closely related to the criteria based on pair of vacuum probabilities. We illustrate the performance of the obtained criteria on the example of realistic imperfect single-photon states modeled as a mixture of vacuum and single-photon states with background Poissonian noise.
We show, under natural assumptions for qubit systems, that measurement-based quantum computations (MBQCs) which compute a non-linear Boolean function with high probability are contextual. The class of contextual MBQCs includes an example which is of practical interest and has a super-polynomial speedup over the best known classical algorithm, namely the quantum algorithm that solves the Discrete Log problem.
Contextuality is often referred to as a generalization of non-locality. In this work, using the hypergraph approach for contextuality we show how to associate a contextual scenario to a general k-partite non local game, and consider the reverse direction: how and when is it possible to represent a general contextuality scenario as a non local game. Using the notion of conditional contextuality, we show that it is possible to embed any contextual scenario in a two players non local game. We also discuss different equivalences of contextuality scenarios and show that the construction used in the proof is not optimal by giving a simpler bipartite non local game when the contextual scenario is a graph instead of a general hypergraph.
In this letter we generalize Spekkens notion of measurement non-contextuality (NC). We show that any non-contextual ontological model based on this notion of contextuality fails to explain the statistics of outcomes of a single carefully constructed POVM executed sequentially on a quantum system. The POVM essentially forms a single measurement device. The context of measurement arises from the different configurations in which the device can be used. We develop an inequality from the non-contextual ontic model, and construct corresponding quantum situations where the measurement outcomes from the device violate this NC inequality. Our work brings out the hitherto unexplored implications of contextuality for a single measurement device, and paves the way for further study of consequences of contextuality for sequential measurements.
A central result in the foundations of quantum mechanics is the Kochen-Specker theorem. In short, it states that quantum mechanics is in conflict with classical models in which the result of a measurement does not depend on which other compatible measurements are jointly performed. Here, compatible measurements are those that can be performed simultaneously or in any order without disturbance. This conflict is generically called quantum contextuality. In this article, we present an introduction to this subject and its current status. We review several proofs of the Kochen-Specker theorem and different notions of contextuality. We explain how to experimentally test some of these notions and discuss connections between contextuality and nonlocality or graph theory. Finally, we review some applications of contextuality in quantum information processing.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
