相关论文: Twelve-dimensional Pauli group contextuality

A theory of principal bundles possessing quantum structure groups and classical base manifolds is presented. Structural analysis of such quantum principal bundles is performed. A differential calculus is constructed, combining differential…

One could begin a study like the present one by simply postulating that our universe is four-dimensional. There are ample reasons for doing this. Experience, observation and experiment all point to the fact that we inhabit a…

Quantum theory is known to be nonlocal in the sense that separated parties can perform measurements on a shared quantum state to obtain correlated probability distributions, which cannot be achieved if the parties share only classical…

The paper is a brief informal introduction to C*-algebraic foundations of causal contextual subquantum theories. In particular, it is explained how the contextuality property (which is a necessary consistency condition of all causal…

We present and experimentally demonstrate a novel non-classical phenomenon, bi-contextuality, observed in quantum systems prepared by two independent sources. This discovery plays a key role in the developing framework of network…

We describe a scheme of quantum computation with magic states on qubits for which contextuality is a necessary resource possessed by the magic states. More generally, we establish contextuality as a necessary resource for all schemes of…

Classical realism demands that system properties exist independently of whether they are measured, while noncontextuality demands that the results of measurements do not depend on what other measurements are performed in conjunction with…

Contextuality is central to both the foundations of quantum theory and to the novel information processing tasks. Although it was recognized before Bell's nonlocality, despite some recent proposals, it still faces a fundamental problem: how…

Contextuality and nonlocality are non-classical properties exhibited by quantum statistics whose implications profoundly impact both foundations and applications of quantum theory. In this paper we provide some insights into logical…

Recently, Yu and Oh [Phys. Rev. Lett. 108, 030402 (2012)] have conjectured that the simplest set of vectors needed to prove state-independent contextuality on a qutrit requires 13 vectors. Here we first prove that a necessary and sufficient…

KS-contextuality is a crucial feature of quantum theory. Previous research demonstrated the vanishing of $N$-cycle KS-contextuality in setups where multiple independent observers measure sequentially on the same system, which we call Public…

Quantum contextuality, as proved by Kochen and Specker, and also by Bell, should manifest itself in any state in any system with more than two distinguishable states and recently has been experimentally verified on various physical systems.…

In this paper we study various convolution-type algebras associated with a locally compact quantum group from cohomological and geometrical points of view. The quantum group duality endows the space of trace class operators over a locally…

In the standard formulation of quantum mechanics, there exists an inherent feedback of the measurement setting on the elementary object under scrutiny. Thus one cannot assume that an 'element of reality' prexists to the measurement and, it…

Contextuality is a phenomenon at the heart of the quantum mechanical departure from classical behaviour, and has been recently identified as a resource in quantum computation. Experimental demonstration of contextuality is thus an important…

Looking for a quantum-mechanical implementation of duality, we formulate a relation between coherent states and complex-differentiable structures on classical phase space ${\cal C}$. A necessary and sufficient condition for the existence of…

One of the defining differences between classical and quantum systems is how measurements affect them. Here, we compare the approaches of contextuality and quantum discord in capturing quantum correlations in special classes of two-qubit…

Traditionally categorical data analysis (e.g. generalized linear models) works with simple, flat datasets akin to a single table in a database with no notion of missing data or conflicting versions. In contrast, modern data analysis must…

For differential calculi over certain right coideal subalgebras of quantum groups the notion of quantum tangent space is introduced. In generalization of a result by Woronowicz a one to one correspondence between quantum tangent spaces and…

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…