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Contextual Deterministic Quantum Mechanics

Roy, S M

Published Aug 19, 1999• 4 citations
OpenAlex

Abstract

We present a simple proof of quantum contextuality for a spinless particle with a one dimensional configuration space. We then discuss how the maximally realistic deterministic quantum mechanics recently constructed by this author and V. Singh can be applied to different contexts.

Related papers

CONTEXTUAL DETERMINISTIC QUANTUM MECHANICS

S. M. ROY

We present a simple proof of quantum contextuality for a spinless particle with a one-dimensional configuration space. We then discuss how the maximally realistic deterministic quantum mechanics recently constructed by this author and V. Singh can be applied to different contexts.

arXiv:quant-ph/9908062•International Journal of Modern Physics B•Aug 10, 2000•3 citations

Kochen-Specker Configurations from Grids on Dual Quadrics

Giuseppe Favacchio

We develop a geometric framework for constructing and organizing Kochen--Specker configurations in real four-dimensional space. The construction uses finite grids on pairs of smooth quadrics related by Euclidean polarity. Their incidence geometry directly produces orthogonal measurement contexts and parity proofs of quantum contextuality, yielding infinite families of configurations and a geometric interpretation and extension of a previously known cyclic construction. For a distinguished subfamily, the same geometry admits a canonical completion determined by secant lines. The first two instances of this completion recover the exceptional root configurations of types $F_4$ and $H_4$, while the smallest case also recovers the Cabello configuration and its embedding in the Peres configuration. Thus several prominent four-dimensional contextual configurations, previously obtained from different constructions, arise from a single projective-geometric mechanism.

math.AGCross-listedarXiv:2608.25008•Aug 27, 2026•0 citations

Facets of contextual realism in quantum mechanics

A. K. Pan, Dipankar Home, Dipankar Home +2 more

In recent times, there is an upsurge of interest in demonstrating the quantum contextuality. In this proceedings, we explore the two different forms of arguments that have been used for showing the contextual character of quantum mechanics. First line of study concerns the violations of the noncontextual realist models by quantum mechanics, where second line of study that is qualitatively distinct from the earlier one, demonstrates the contextuality within the formalism of quantum mechanics.

AIP conference proceedings•Jan 1, 2011•0 citations

Quantum theory allows for absolute maximal contextuality

Bárbara Amaral, Marcelo Terra Cunha, Adán Cabello

Contextuality is believed to be a fundamental property of quantum theory. On investigating how large it can be, instances are shown wherein quantum theory achieves the maximum conceivable value of a certain contextuality quantifier.

arXiv:1507.03142•Physical Review A•Dec 16, 2015•23 citations

Large violations in Kochen Specker contextuality and their applications

Ravishankar Ramanathan, Yuan Liu, Paweł Horodecki

Abstract It is of interest to study how contextual quantum mechanics is, in terms of the violation of Kochen Specker state-independent and state-dependent non-contextuality inequalities. We present state-independent non-contextuality inequalities with large violations, in particular, we exploit a connection between Kochen–Specker proofs and pseudo-telepathy games to show KS proofs in Hilbert spaces of dimension d ⩾ 217 with the ratio of quantum value to classical bias being O ( d / log d ) . We study the properties of this KS set and show applications of the large violation. It has been recently shown that Kochen–Specker proofs always consist of substructures of state-dependent contextuality proofs called 01-gadgets. We show a one-to-one connection between 01-gadgets in C d and Hardy paradoxes for the maximally entangled state in C d ⊗ C d . We use this connection to construct large violation 01-gadgets between arbitrary vectors in C d , as well as novel Hardy paradoxes for the maximally entangled state in C d ⊗ C d , and give applications of these constructions. As a technical result, we show that the minimum dimension of the faithful orthogonal representation of a graph in R d is not a graph monotone, a result that may be of independent interest.

arXiv:2106.15954•New Journal of Physics•Nov 17, 2021•3 citations

Is Quantum Mechanics Deterministic or Non-deterministic?

Kees van Hee, Kees van Berkel

Lecture notes in computer science•Jan 1, 2026•0 citations
We develop a geometric framework for constructing and organizing Kochen--Specker configurations in real four-dimensional space. The construction uses finite grids on pairs of smooth quadrics related by Euclidean polarity. Their incidence geometry directly produces orthogonal measurement contexts and parity proofs of quantum contextuality, yielding infinite families of configurations and a geometric interpretation and extension of a previously known cyclic construction. For a distinguished subfamily, the same geometry admits a canonical completion determined by secant lines. The first two instances of this completion recover the exceptional root configurations of types F4F_4F4​ and H4H_4H4​, while the smallest case also recovers the Cabello configuration and its embedding in the Peres configuration. Thus several prominent four-dimensional contextual configurations, previously obtained from different constructions, arise from a single projective-geometric mechanism.
Abstract It is of interest to study how contextual quantum mechanics is, in terms of the violation of Kochen Specker state-independent and state-dependent non-contextuality inequalities. We present state-independent non-contextuality inequalities with large violations, in particular, we exploit a connection between Kochen–Specker proofs and pseudo-telepathy games to show KS proofs in Hilbert spaces of dimension d ⩾ 217 with the ratio of quantum value to classical bias being O ( d / log d ) . We study the properties of this KS set and show applications of the large violation. It has been recently shown that Kochen–Specker proofs always consist of substructures of state-dependent contextuality proofs called 01-gadgets. We show a one-to-one connection between 01-gadgets in C d and Hardy paradoxes for the maximally entangled state in C d ⊗ C d . We use this connection to construct large violation 01-gadgets between arbitrary vectors in C d , as well as novel Hardy paradoxes for the maximally entangled state in C d ⊗ C d , and give applications of these constructions. As a technical result, we show that the minimum dimension of the faithful orthogonal representation of a graph in R d is not a graph monotone, a result that may be of independent interest.