Conditional probability framework for entanglement and its decoupling from tensor product structure

• URL: http://arxiv.org/abs/2205.11510v2
• Date: Sat, 30 Jul 2022 04:28:51 GMT
• Title: Conditional probability framework for entanglement and its decoupling from tensor product structure
• Authors: Irina Basieva and Andrei Khrennikov
• Abstract summary: In Schr"odinger's words, this is entanglement of knowledge which can be extracted via conditional measurements. We restrict considerations to perfect conditional correlations (PCC) induced by measurements. One of our aims is to decouple the notion of entanglement from the compound systems.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Our aim is to make a step towards clarification of foundations for the notion of entanglement (both physical and mathematical) by representing it in the conditional probability framework. In Schr\"odinger's words, this is entanglement of knowledge which can be extracted via conditional measurements. In particular, quantum probabilities are interpreted as conditional ones (as, e.g., by Ballentine). We restrict considerations to perfect conditional correlations (PCC) induced by measurements ("EPR entanglement"). Such entanglement is coupled to the pairs of observables with the projection type state update as the back action of measurement. In this way, we determine a special class of entangled states. One of our aims is to decouple the notion of entanglement from the compound systems. The rigid association of entanglement with the state of a few body systems stimulated its linking with quantum nonlocality ("spooky action at a distance"). However, already by Schr\"odinger entanglement was presented as knotting of knowledge (about statistics) for one observable A with knowledge about another observable B.

Related papers

• A computational test of quantum contextuality, and even simpler proofs of quantumness [43.25018099464869]
  We show that an arbitrary contextuality game can be compiled into an operational "test of contextuality" involving a single quantum device. Our work can be seen as using cryptography to enforce spatial separation within subsystems of a single quantum device.
  arXiv  Detail & Related papers  (2024-05-10T19:30:23Z)
• Kolmogorovian Censorship, Predictive Incompleteness, and the locality loophole in Bell experiments [0.0]
  Kolmogorovian Censorship stipulates that quantum probabilities can be identified with classical, Kolmogorovian probabilities. In a loophole-free Bell test, the remote random choices of measurements have the purpose to prevent this matching. We argue that predictive incompleteness is the correct quantum way to understand the violation of Bell's inequalities.
  arXiv  Detail & Related papers  (2024-05-06T06:20:54Z)
• Depolarizing Reference Devices in Generalized Probabilistic Theories [0.0]
  QBism is an interpretation of quantum theory which views quantum mechanics as standard probability theory supplemented with a few extra normative constraints. We show that, given any reference measurement, a set of post-measurement reference states can always be chosen to give its probability rule very form. What stands out for the QBist project from this analysis is that it is not only the pure form of the rule that must be understood normatively, but the constants within it as well.
  arXiv  Detail & Related papers  (2023-12-20T06:22:55Z)
• Measurement-Device-Independent Detection of Beyond-Quantum State [53.64687146666141]
  We propose a measurement-device-independent (MDI) test for beyond-quantum state detection. We discuss the importance of tomographic completeness of the input sets to the detection.
  arXiv  Detail & Related papers  (2023-12-11T06:40:13Z)
• Quantification of Entanglement and Coherence with Purity Detection [16.01598003770752]
  Entanglement and coherence are fundamental properties of quantum systems, promising to power near future quantum technologies. Here, we demonstrate quantitative bounds to operationally useful entanglement and coherence. Our research offers an efficient means of verifying large-scale quantum information processing.
  arXiv  Detail & Related papers  (2023-08-14T11:03:40Z)
• The measurement postulates of quantum mechanics are not redundant [0.0]
  Masanes, Galley and M"uller argue that the measurement postulates of non-relativistic quantum mechanics follow from the structural postulates. We refute their conclusion, giving explicit examples of non-quantum measurement and state update rules.
  arXiv  Detail & Related papers  (2023-07-12T14:30:36Z)
• Entanglement of observables: Quantum conditional probability approach [0.0]
  It is meaningless to speak about entanglement without pointing to the fixed observables A and B, so this is AB-entanglement. Dependence of quantum observables is formalized as non-coincidence of conditional probabilities.
  arXiv  Detail & Related papers  (2023-03-22T08:58:15Z)
• Branch-counting in the Everett Interpretation of quantum mechanics [0.0]
  Well-known branch-counting rule, for realistic models of measurements, fails this test. New rule hinges on the use of decoherence theory in defining branching structure.
  arXiv  Detail & Related papers  (2022-01-16T16:50:07Z)
• Quantum indistinguishability through exchangeable desirable gambles [69.62715388742298]
  Two particles are identical if all their intrinsic properties, such as spin and charge, are the same. Quantum mechanics is seen as a normative and algorithmic theory guiding an agent to assess her subjective beliefs represented as (coherent) sets of gambles. We show how sets of exchangeable observables (gambles) may be updated after a measurement and discuss the issue of defining entanglement for indistinguishable particle systems.
  arXiv  Detail & Related papers  (2021-05-10T13:11:59Z)
• Partitioning dysprosium's electronic spin to reveal entanglement in non-classical states [55.41644538483948]
  We report on an experimental study of entanglement in dysprosium's electronic spin. Our findings open up the possibility to engineer novel types of entangled atomic ensembles.
  arXiv  Detail & Related papers  (2021-04-29T15:02:22Z)
• Observers of quantum systems cannot agree to disagree [55.41644538483948]
  We ask whether agreement between observers can serve as a physical principle that must hold for any theory of the world. We construct examples of (postquantum) no-signaling boxes where observers can agree to disagree.
  arXiv  Detail & Related papers  (2021-02-17T19:00:04Z)

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.