Lifting noncontextuality inequalities

• URL: http://arxiv.org/abs/2401.12349v2
• Date: Tue, 14 May 2024 15:05:26 GMT
• Title: Lifting noncontextuality inequalities
• Authors: Raman Choudhary, Rui Soares Barbosa, Adán Cabello,
• Abstract summary: All known noncontextuality inequalities corresponding to facets of noncontextual polytopes are either Bell inequalities or refer to cyclic or state-independent contextuality scenarios. We introduce a general method for lifting noncontextuality inequalities, deriving facets of noncontextual polytopes for more complex scenarios from known facets of simpler subscenarios. Our results shed light on the structure of noncontextuality polytopes and the relationship between such polytopes across different scenarios.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Kochen-Specker contextuality is a fundamental feature of quantum mechanics and a crucial resource for quantum computational advantage and reduction of communication complexity. Its presence is witnessed in empirical data by the violation of noncontextuality inequalities. However, all known noncontextuality inequalities corresponding to facets of noncontextual polytopes are either Bell inequalities or refer to cyclic or state-independent contextuality scenarios. We introduce a general method for lifting noncontextuality inequalities, deriving facets of noncontextual polytopes for more complex scenarios from known facets of simpler subscenarios. Concretely, starting from an arbitrary scenario, the addition of a new measurement or a new outcome preserves the facet-defining nature of any noncontextuality inequality. This extends the results of Pironio [J. Math. Phys. 46, 062112 (2005)] from Bell nonlocality scenarios to contextuality scenarios, unifying liftings of Bell and noncontextuality inequalities. Our method produces facet-defining noncontextuality inequalities in all scenarios with contextual correlations, and we present examples of facet-defining noncontextuality inequalities for scenarios where no examples were known. Our results shed light on the structure of noncontextuality polytopes and the relationship between such polytopes across different scenarios.

Related papers

• Optimal demonstration of generalized quantum contextuality [0.0]
  This work presents an alternative methodology for constructing a polytope that encompasses the actual noncontextual polytope. In particular, the facet inequalities of this polytope serve as necessary conditions for noncontextuality.
  arXiv  Detail & Related papers  (2024-06-13T13:40:30Z)
• Skews in the Phenomenon Space Hinder Generalization in Text-to-Image Generation [59.138470433237615]
  We introduce statistical metrics that quantify both the linguistic and visual skew of a dataset for relational learning. We show that systematically controlled metrics are strongly predictive of generalization performance. This work informs an important direction towards quality-enhancing the data diversity or balance to scaling up the absolute size.
  arXiv  Detail & Related papers  (2024-03-25T03:18:39Z)
• Similarity, Compression and Local Steps: Three Pillars of Efficient Communications for Distributed Variational Inequalities [91.12425544503395]
  Variational inequalities are used in various applications ranging from equilibrium search to adversarial learning. Most distributed approaches have a bottleneck - the cost of communications. The three main techniques to reduce the total number of communication rounds and the cost of one such round are the similarity of local functions, compression of transmitted information, and local updates. The methods presented in this paper have the best theoretical guarantees of communication complexity and are significantly ahead of other methods for distributed variational inequalities.
  arXiv  Detail & Related papers  (2023-02-15T12:11:27Z)
• Simple Primitives with Feasibility- and Contextuality-Dependence for Open-World Compositional Zero-shot Learning [86.5258816031722]
  The task of Compositional Zero-Shot Learning (CZSL) is to recognize images of novel state-object compositions that are absent during the training stage. Previous methods of learning compositional embedding have shown effectiveness in closed-world CZSL. In Open-World CZSL (OW-CZSL), their performance tends to degrade significantly due to the large cardinality of possible compositions.
  arXiv  Detail & Related papers  (2022-11-05T12:57:06Z)
• Textual Entailment Recognition with Semantic Features from Empirical Text Representation [60.31047947815282]
  A text entails a hypothesis if and only if the true value of the hypothesis follows the text. In this paper, we propose a novel approach to identifying the textual entailment relationship between text and hypothesis. We employ an element-wise Manhattan distance vector-based feature that can identify the semantic entailment relationship between the text-hypothesis pair.
  arXiv  Detail & Related papers  (2022-10-18T10:03:51Z)
• Inequalities witnessing coherence, nonlocality, and contextuality [0.0]
  Quantum coherence, nonlocality, and contextuality are key resources for quantum advantage in metrology, communication, and computation. We introduce a graph-based approach to derive classicality inequalities that bound local, non-contextual, and coherence-free models. Our approach generalizes recently proposed basis-independent coherence witnesses, and recovers all non-contextuality inequalities of the exclusivity graph approach.
  arXiv  Detail & Related papers  (2022-09-06T17:32:58Z)
• Using a resource theoretic perspective to witness and engineer quantum generalized contextuality for prepare-and-measure scenarios [0.0]
  We employ the resource theory of generalized contextuality as a tool for analyzing the structure of prepare-and-measure scenarios. We argue that this framework simplifies proofs of quantum contextuality in complex scenarios.
  arXiv  Detail & Related papers  (2021-02-20T23:06:03Z)
• On Possibilistic Conditions to Contextuality and Nonlocality [0.0]
  We provide some insights into logical contextuality and inequality-free proofs. We show the existence of possibilistic paradoxes whose occurrence is a necessary and sufficient condition for logical contextuality.
  arXiv  Detail & Related papers  (2020-11-08T23:52:40Z)
• Experimental certification of nonclassicality via phase-space inequalities [58.720142291102135]
  We present the first experimental implementation of the recently introduced phase-space inequalities for nonclassicality certification. We demonstrate the practicality and sensitivity of this approach by studying nonclassicality of a family of noisy and lossy quantum states of light.
  arXiv  Detail & Related papers  (2020-10-01T09:03:52Z)
• Contextuality scenarios arising from networks of stochastic processes [68.8204255655161]
  An empirical model is said contextual if its distributions cannot be obtained marginalizing a joint distribution over X. We present a different and classical source of contextual empirical models: the interaction among many processes. The statistical behavior of the network in the long run makes the empirical model generically contextual and even strongly contextual.
  arXiv  Detail & Related papers  (2020-06-22T16:57:52Z)
• Noncontextuality Inequalities from Antidistinguishability [0.0]
  We show that antidistinguishability can also be used to derive noncontextuality inequalities. The Yu-Oh 13 ray noncontextuality inequality can be re-derived and generalized as an instance of our antidistinguishability method.
  arXiv  Detail & Related papers  (2020-01-30T18:08:00Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.