Related papers: Generalized Kochen-Specker Theorem
We show that the value of a general two-prover quantum game cannot be computed by a semi-definite program ofvpolynomial size (unless P=NP), a method that has been successful in more restricted quantum games. More precisely, we show that…
By probabilistic means, the concept of contextuality is extended so that it can be used in non-ideal situations. An inequality is presented, which at least in principle enables a test to discard non-contextual hidden-variable models at low…
Quantum theory combines density matrices, Born probabilities, tensor-product composites, positive-operator-valued measures (POVMs), and quantum channels. In a finite-dimensional causal operational theory, we prove that two postulates…
Kochen-Specker (KS) theorem lies at the heart of the foundations of quantum mechanics. It establishes impossibility of explaining predictions of quantum theory by any noncontextual ontological model. Spekkens generalized the notion of KS…
A recent claim by Meyer, Kent and Clifton (MKC), that their models ``nullify'' the Kochen-Specker theorem, has attracted much comment. In this paper we present a new counter-argument, based on the fact that a classical measurement reveals,…
Hidden variables theories for quantum mechanics are usually assumed to satisfy the KS condition. The Bell-Kochen-Specker theorem then shows that these theories are necessarily contextual. But the KS condition can be criticized from an…
Quantum contextuality supports quantum computation and communication. One of its main vehicles is hypergraphs. The most elaborated are the Kochen-Specker ones, but there is also another class of contextual sets that are not of this kind.…
In this paper we attempt to discuss what has Kochen-Specker (KS) theorem to say about physical invariance and quantum individuality. In particular, we will discuss the impossibility of making reference to objective physical properties…
A generalized quantum distribution function is introduced. The corresponding ordering rule for non-commuting operators is given in terms of a single parameter. The origin of this parameter is in the extended canonical transformations that…
GHZ paradoxes are presented for all even numbers of qubits from four up. They are obtained from proofs of the Kochen-Specker (KS) theorem by showing how the assumption of noncontextuality can be justified on the basis of locality. The…
This article delves into the concept of quantum contextuality, specifically focusing on proofs of the Kochen-Specker theorem obtained by assigning Pauli observables to hypergraph vertices satisfying a given commutation relation. The…
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…
Feynman's sum-over-histories formulation of quantum mechanics is reviewed as an independent statement of quantum theory in spacetime form. It is different from the usual Schr\"odinger-Heisenberg formulation that utilizes states on spacelike…
Pusey, Barrett, and Rudolph introduce a new no-go theorem for hidden-variables models of quantum theory. We make precise the class of models targeted and construct equivalent models that evade the theorem. The theorem requires assumptions…
Quantum-proof randomness extractors are an important building block for classical and quantum cryptography as well as device independent randomness amplification and expansion. Furthermore they are also a useful tool in quantum Shannon…
Every measurement determines a single value as its outcome, and yet quantum mechanics predicts it only probabilistically. The Kochen-Specker theorem and Bell's inequality are often considered to reject a realist view but favor a skeptical…
I will propose that the reality to which the quantum formalism implicitly refers is a kind of generalized history, the word history having here the same meaning as in the phrase sum-over-histories. This proposal confers a certain…
The question of a hidden variable interpretation of quantum contextuality in the Mermin-Peres square is considered. The Kochen-Specker theorem implies that quantum mechanics may be interpreted as a contextual hidden variable theory. It is…
We present a toy theory that is based on a simple principle: the number of questions about the physical state of a system that are answered must always be equal to the number that are unanswered in a state of maximal knowledge. A wide…
In a recent paper the notion of {\em quantum perceptron} has been introduced in connection with projection operators. Here we extend this idea, using these kind of operators to produce a {\em clustering machine}, i.e. a framework which…