Incompatibility in restricted operational theories: connecting contextuality and steering

• URL: http://arxiv.org/abs/2112.10596v1
• Date: Thu, 16 Dec 2021 10:53:48 GMT
• Title: Incompatibility in restricted operational theories: connecting contextuality and steering
• Authors: Martin Pl\'avala
• Abstract summary: We show that for a class of bipartite states the steerability of the state by given set of measurements is equivalent to non-existence of preparation noncontextual hidden variable model. The connection between steering and contextuality is provided by the concept of incompatibility in restricted theories.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We investigate the connection between steering and contextuality in general probabilistic theories. We show that for a class of bipartite states the steerability of the state by given set of measurements is equivalent to non-existence of preparation noncontextual hidden variable model for certain restricted theory constructed from the given state and measurements. The connection between steering and contextuality is provided by the concept of incompatibility in restricted theories, which we also investigate.

Related papers

• Minimal operational theories: classical theories with quantum features [41.94295877935867]
  We show that almost all minimal theories with conditioning satisfy two quantum no-go theorems. As a relevant example, we construct a minimal toy-theory with conditioning where all systems are classical.
  arXiv  Detail & Related papers  (2024-08-02T16:24:09Z)
• Measurement incompatibility is strictly stronger than disturbance [44.99833362998488]
  Heisenberg argued that measurements irreversibly alter the state of the system on which they are acting, causing an irreducible disturbance on subsequent measurements. This article shows that measurement incompatibility is indeed a sufficient condition for irreversibility of measurement disturbance. However, we exhibit a toy theory, termed the minimal classical theory (MCT), that is a counterexample for the converse implication.
  arXiv  Detail & Related papers  (2023-05-26T13:47:00Z)
• A Measure-Theoretic Axiomatisation of Causality [55.6970314129444]
  We argue in favour of taking Kolmogorov's measure-theoretic axiomatisation of probability as the starting point towards an axiomatisation of causality. Our proposed framework is rigorously grounded in measure theory, but it also sheds light on long-standing limitations of existing frameworks.
  arXiv  Detail & Related papers  (2023-05-19T13:15:48Z)
• Separability, Contextuality, and the Quantum Frame Problem [0.0]
  We study the relationship between assumptions of state separability and both preparation and measurement contextuality. We show how contextuality is generically induced in state preparation and measurement by basis choice, thermodynamic exchange, and the imposition of a priori causal models.
  arXiv  Detail & Related papers  (2023-04-19T23:32:19Z)
• Unifying different notions of quantum incompatibility into a strict hierarchy of resource theories of communication [60.18814584837969]
  We introduce the notion of q-compatibility, which unifies different notions of POVMs, channels, and instruments incompatibility. We are able to pinpoint exactly what each notion of incompatibility consists of, in terms of information-theoretic resources.
  arXiv  Detail & Related papers  (2022-11-16T21:33:31Z)
• Contextuality as a Precondition for Quantum Entanglement [0.0]
  We prove that entanglement in a nonlocal scenario can arise only if there is preparation and measurement contextuality. As a direct consequence, our result allows us to translate any inequality for testing preparation and measurement contextuality into an entanglement test.
  arXiv  Detail & Related papers  (2022-09-20T18:36:34Z)
• What is nonclassical about uncertainty relations? [0.0]
  Uncertainty relations express limits on the extent to which the outcomes of distinct measurements on a single state can be made jointly predictable. We show that for a class of theories satisfying a particular symmetry property, the functional form of this predictability tradeoff is constrained by noncontextuality to be below a linear curve.
  arXiv  Detail & Related papers  (2022-07-24T17:19:47Z)
• Incompatibility of observables, channels and instruments in information theories [68.8204255655161]
  We study the notion of compatibility for tests of an operational probabilistic theory. We show that a theory admits of incompatible tests if and only if some information cannot be extracted without disturbance.
  arXiv  Detail & Related papers  (2022-04-17T08:44:29Z)
• Correlations constrained by composite measurements [1.539147548025619]
  How to understand the set of admissible correlations in nature is one outstanding open problem in the core of the foundations of quantum theory. We show that demanding that a theory exhibits a composite measurement imposes a hierarchy of constraints on the structure of its sets of states and effects. In particular, we show that in certain situations this assumption has surprisingly strong consequences, namely, that Tsirelson's bound can be recovered.
  arXiv  Detail & Related papers  (2020-09-10T17:05:19Z)
• Developing Constrained Neural Units Over Time [81.19349325749037]
  This paper focuses on an alternative way of defining Neural Networks, that is different from the majority of existing approaches. The structure of the neural architecture is defined by means of a special class of constraints that are extended also to the interaction with data. The proposed theory is cast into the time domain, in which data are presented to the network in an ordered manner.
  arXiv  Detail & Related papers  (2020-09-01T09:07:25Z)
• Constraint relation between steerability and concurrence for two-qubit states [6.687934752525343]
  Entanglement and steering are used to describe quantum inseparabilities. A natural question arises concerning how much territory steerability occupies entanglement for a general two-qubit entangled state. We investigate the constraint relation between steerability and concurrence by using two kinds of evolutionary states and randomly generated two-qubit states.
  arXiv  Detail & Related papers  (2020-07-18T05:29:44Z)

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.