Related papers: A Topological Study of Contextuality and Modality …
In the paper it is argued that the Kochen-Specker theorem necessitates a conclusion that for a quantum system it is possible to find a set of projection operators which is not truth-value bivalent; that is, a bivalent truth-value assignment…
The presence of contextuality in quantum theory was first highlighted by Bell, Kochen and Specker, who discovered that for quantum systems of three or more dimensions, measurements cannot be viewed as revealing pre-existing properties of…
A new theory-independent noncontextuality inequality is presented [Phys. Rev. Lett. 115, 110403 (2015)] based on Kochen-Specker (KS) set without imposing the assumption of determinism. By proposing novel noncontextuality inequalities, we…
When a measurement is compatible with each of two other measurements that are incompatible with one another, these define distinct contexts for the given measurement. The Kochen-Specker theorem rules out models of quantum theory that…
A generalized Kochen-Specker theorem is proved. It is shown that there exist sets of $n$ projection operators, representing $n$ yes-no questions about a quantum system, such that none of the $2^n$ possible answers is compatible with sum…
In this thesis we explore the questions of what should be considered a "classical" theory, and which aspects of quantum theory cannot be captured by any theory that respects our intuition of classicality. This exploration is divided in two…
This note presents a concise and non-polemical comparison of several major interpretations of quantum mechanics, with a particular emphasis on the distinction between FAPP-solutions ("For All Practical Purposes'') versus ontological…
Contextuality is one of the fundamental deviations of quantum mechanics from classical physics. The Kochen-Specker (KS) theorem shows that non-contextual classical physics with hidden variables is inconsistent with the predictions of…
Two notions of nonclassicality that have been investigated intensively are: (i) negativity, that is, the need to posit negative values when representing quantum states by quasiprobability distributions such as the Wigner representation, and…
We present a systematic, constructive analysis of Kochen-Specker contextuality, emphasizing the foundational importance of complete orthogonal bases (contexts). First, in three dimensions, we generate a complete inventory of 165 rays and…
So far, most of the literature on (quantum) contextuality and the Kochen-Specker theorem seems either to concern particular examples of contextuality, or be considered as quantum logic. Here, we develop a general formalism for contextuality…
A proof of the Kochen-Specker theorem for a single two-level system is presented. It employs five eight-element positive operator-valued measures and a simple algebraic reasoning based on the geometry of the dodecahedron.
Amplitudes are the major logical object in Quantum Theory. Despite this fact they presents no physical reality and in consequence only observables can be experimetally checked. We discuss the possibility of a theory of Quantum Probabilities…
The interpretation of quantum mechanics has been a problem since its founding days. A large contribution to the discussion of possible interpretations of quantum mechanics is given by the so-called impossibility proofs for hidden variable…
There are two powerful arguments against the possibility of extending quantum mechanics, the violation of Bell inequalities and the Kochen-Specker theorem, but the connection between the two remains confused. Following the distinctive…
Recently a new impulse has been given to the experimental investigation of contextuality. In this paper we show that for a widely used definition of contextuality there can be no decisive experiment on the existence of contextuality. To…
Structures that demonstrate nonclassicality are of foundational interest in quantum mechanics, and can also be seen as resources for numerous applications in quantum information processing - particularly in the Hilbert space of $N$ qubits.…
Topos quantum mechanics, developed by Isham et. al., creates a topos of presheaves over the poset V(N) of abelian von Neumann subalgebras of the von Neumann algebra N of bounded operators associated to a physical system, and established…
For a hidden variable theory to be indistinguishable from quantum theory for finite precision measurements, it is enough that its predictions agree for some measurement within the range of precision. Meyer has recently pointed out that the…
Nonlinear modifications of quantum theory are considered potential candidates for the theory of quantum gravity, with the intuitive argument that since Einstein field equations are nonlinear, quantum gravity should be nonlinear as well.…