An uncertainty view on complementarity and a complementarity view on uncertainty

• URL: http://arxiv.org/abs/2007.05053v5
• Date: Fri, 4 Jun 2021 17:00:38 GMT
• Title: An uncertainty view on complementarity and a complementarity view on uncertainty
• Authors: Marcos L. W. Basso and Jonas Maziero
• Abstract summary: We obtain a complete complementarity relation for quantum uncertainty, classical uncertainty, and predictability. We show that Brukner-Zeilinger's invariant information quantifies both the wave and particle characters of a quanton.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Since the uncertainty about an observable of a system prepared in a quantum state is usually described by its variance, when the state is mixed, the variance is a hybrid of quantum and classical uncertainties. Besides that, complementarity relations are saturated only for pure, single-quanton, quantum states. For mixed states, the wave-particle quantifiers never saturate the complementarity relation and can even reach zero for a maximally mixed state. So, to fully characterize a quanton it is not sufficient to consider its wave-particle aspect; one has also to regard its correlations with other systems. In this paper, we discuss the relation between quantum correlations and local classical uncertainty measures, as well as the relation between quantum coherence and quantum uncertainty quantifiers. We obtain a complete complementarity relation for quantum uncertainty, classical uncertainty, and predictability. The total quantum uncertainty of a d-paths interferometer is shown to be equivalent to the Wigner-Yanase coherence and the corresponding classical uncertainty is shown to be a quantum correlation quantifier. The duality between complementarity and uncertainty is used to derive quantum correlations measures that complete the complementarity relations for $l_1$-norm and $l_2$-norm coherences. Besides, we show that Brukner-Zeilinger's invariant information quantifies both the wave and particle characters of a quanton and we obtain a sum uncertainty relation for the generalized Gell Mann's matrices.

Related papers

• The effects of detuning on entropic uncertainty bound and quantum correlations in dissipative environment [0.0]
  We will use the entropic uncertainty relation in the presence of quantum memory. The effects of the detuning between the transition frequency of a quantum memory and the center frequency of a cavity on entrpic uncertainty bound and quantum correlation between quantum memory and measured particle will be studied.
  arXiv  Detail & Related papers  (2024-01-18T08:04:53Z)
• 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)
• Asymmetry and tighter uncertainty relations for R\'enyi entropies via quantum-classical decompositions of resource measures [0.0]
  It is known that the variance and entropy of quantum observables decompose into intrinsically quantum and classical contributions. Here a general method of constructing quantum-classical decompositions of resources such as uncertainty is discussed.
  arXiv  Detail & Related papers  (2023-04-12T08:49:48Z)
• Quantifying measurement-induced quantum-to-classical crossover using an open-system entanglement measure [49.1574468325115]
  We study the entanglement of a single particle under continuous measurements. We find that the entanglement at intermediate time scales shows the same qualitative behavior as a function of the measurement strength.
  arXiv  Detail & Related papers  (2023-04-06T09:45:11Z)
• Physical interpretation of nonlocal quantum correlation through local description of subsystems [19.542805787744133]
  We propose the physical interpretation of nonlocal quantum correlation between two systems. Different nonlocal quantum correlations can be discriminated from a single uncertainty relation derived under local hidden state (LHS)-LHS model only.
  arXiv  Detail & Related papers  (2022-10-01T10:13:40Z)
• Uncertainty of quantum channels via modified generalized variance and modified generalized Wigner-Yanase-Dyson skew information [4.73944507784056]
  Uncertainty relation is a fundamental issue in quantum mechanics and quantum information theory. We identify the total and quantum uncertainty of quantum channels. We discuss how to measure the total/quantum uncertainty of quantum channels for pure states.
  arXiv  Detail & Related papers  (2022-08-14T05:29:14Z)
• Quantum nonreciprocal interactions via dissipative gauge symmetry [18.218574433422535]
  One-way nonreciprocal interactions between two quantum systems are typically described by a cascaded quantum master equation. We present a new approach for obtaining nonreciprocal quantum interactions that is completely distinct from cascaded quantum systems.
  arXiv  Detail & Related papers  (2022-03-17T15:34:40Z)
• Quantum uncertainty as classical uncertainty of real-deterministic variables constructed from complex weak values and a global random variable [0.0]
  We construct a class of real-deterministic c-valued variables out of the weak values obtained via a non-perturbing weak measurement of quantum operators. We show that this class of c-valued physical quantities'' provides a real-deterministic contextual hidden variable model for the quantum expectation value of a certain class of operators.
  arXiv  Detail & Related papers  (2021-06-21T22:43:26Z)
• 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)
• Entanglement Monotones from Complementarity Relations [0.0]
  Bohr's complementarity and Schr"odinger's entanglement are prominent physical characters of quantum systems. For any complete complementarity relation involving predictability and visibility measures that satisfy the criteria established in the literature, these corresponding quantum correlations are entanglement monotones.
  arXiv  Detail & Related papers  (2020-12-28T20:08:21Z)
• Entropic Uncertainty Relations and the Quantum-to-Classical transition [77.34726150561087]
  We aim to shed some light on the quantum-to-classical transition as seen through the analysis of uncertainty relations. We employ entropic uncertainty relations to show that it is only by the inclusion of imprecision in our model of macroscopic measurements that we can prepare a system with two simultaneously well-defined quantities.
  arXiv  Detail & Related papers  (2020-03-04T14:01:17Z)

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.