October 25, 2016
Published by Stephan Sponar
# Entanglement

occupies a peculiar position in quantum theory. It occurs in quantum systems that consist of space-like separated parts or—more generally—in systems whose observables belong to disjoint Hilbert spaces. The latter is the case for instance for spin, path and energy degree of freedom in the **s***ingle-neutron systems *in terms of or *bipartite* and *tripartite* entanglement. Apart from Bell’s theorem, there exists a second powerful argument against the possibility of extending QM into a more complete theory, namely the *Kochen–Specker (KS)* theorem. Th KS theorem sets certain constraints on classes of hidden variable theories, which try to explain the apparent randomness of quantum mechanics as a deterministic model featuring hidden states.

September 22, 2016
Published by Stephan Sponar
The remarkable discovery made by ** John S. Bell**, namely that quantum mechanics cannot be counterfactual (definiteness of results prior to measurement) and local (physical objects are only influenced by its immediate surroundings) gave rise to a number of experiments probing the foundations quantum mechanics. We prepare our neutrons in a spin-path entangled state and measure correlations that arise between observables of otherwise independent degrees of freedom in the single neutron system in order to validate the presence of entanglement.

September 21, 2016
Published by Stephan Sponar
**Greenberger–Horne–Zeilinger** (GHZ) and **W states** represent two very different kinds of tripartite entanglement. We prepare entanglement between the spin, path, and (total) energy degrees of freedom, in a single-neutron system. We implemented a triply entangled GHZ–like states, as well as W states, and coherently manipulated relative phases of two-level quantum subsystems.

October 20, 2015
Published by Stephan Sponar
The **Kochen-Specker (KS) Theorem** sets constrains on hidden-variable theories which try to explain the randomness of quantum mechanics in terms of a as a deterministic theory. We perform experimental tests of the Kochen-Specker theorem based on an inequality derived from the **Peres-Mermin** proof, using spin-path (momentum) entanglement in a single neutron system. A Bell-like state was generated, and three expectation values were determined. The observed violation clearly shows that quantum mechanical predictions cannot be reproduced by noncontextual hidden- variable theories.