Uncertainty relations from graph theory

• URL: http://arxiv.org/abs/2207.02197v4
• Date: Thu, 20 Jul 2023 09:43:25 GMT
• Title: Uncertainty relations from graph theory
• Abstract summary: Quantum measurements are inherently probabilistic and quantum theory often forbids to precisely predict the outcomes of simultaneous measurements. We derive uncertainty relations valid for any set of dichotomic observables. As applications, our results can be straightforwardly used to formulate entropic uncertainty relations, separability criteria and entanglement witnesses.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Quantum measurements are inherently probabilistic and quantum theory often forbids to precisely predict the outcomes of simultaneous measurements. This phenomenon is captured and quantified through uncertainty relations. Although studied since the inception of quantum theory, the problem of determining the possible expectation values of a collection of quantum measurements remains, in general, unsolved. By constructing a close connection between observables and graph theory, we derive uncertainty relations valid for any set of dichotomic observables. These relations are, in many cases, tight, and related to the size of the maximum clique of the associated graph. As applications, our results can be straightforwardly used to formulate entropic uncertainty relations, separability criteria and entanglement witnesses.

Related papers

• Quantum incompatibility of Born probabilities [0.0]
  We show that, when measurements are made relative to non-ideal quantum reference frames, the probabilities themselves become indefinite.<n>We propose a quantum-optical implementation of these relational measurements based on pulsed homodyne detection frequencies.<n>Our findings motivate an extension of the notion of the quantum state to regimes constrained by finite resources.
  arXiv  Detail & Related papers  (2026-07-13T18:00:05Z)
• Tighter entropic uncertainty relations in the presence of quantum memories for complete sets of mutually unbiased bases [25.094962102120178]
  We propose more stringent quantum-memory-assisted entropic uncertainty relations for complete sets of mutually unbiased bases in multipartite scenarios.<n>We present lower and upper bounds of the quantum uncertainties based on the complementarity of the observables, the purity of the measured state, the (conditional) von-Neumann entropies, the Holevo quantities and mutual information.
  arXiv  Detail & Related papers  (2026-04-05T06:23:10Z)
• A decision-theoretic approach to dealing with uncertainty in quantum mechanics [42.166654559515244]
  We provide a decision-theoretic framework for dealing with uncertainty in quantum mechanics. We show that measurements play the role of acts with an uncertain outcome. We discuss the mathematical implications of our findings.
  arXiv  Detail & Related papers  (2025-03-26T14:53:06Z)
• Tightening the entropic uncertainty relations with quantum memory in a multipartite scenario [17.30562902622871]
  We introduce a tripartite quantum-memory-assisted entropic uncertainty relation.<n>We extend the relation to encompass multiple measurements conducted within multipartite systems.
  arXiv  Detail & Related papers  (2025-01-06T09:09:34Z)
• Observing tight triple uncertainty relations in two-qubit systems [21.034105385856765]
  We demonstrate the uncertainty relations in two-qubit systems involving three physical components with the tight constant $2/sqrt3$. Our results provide a new insight into understanding the uncertainty relations with multiple observables and may motivate more innovative applications in quantum information science.
  arXiv  Detail & Related papers  (2024-10-08T11:24:24Z)
• Entropic uncertainty relations in Schwarzschild space-time [10.560954016047198]
  We propose a generalized entropic uncertainty relation for arbitrary multiple-observable in multipartite system. We discuss the proposed uncertainty relations and quantum coherence in the context of Schwarzschild space-time.
  arXiv  Detail & Related papers  (2024-07-18T02:26:21Z)
• 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)
• Dynamics Investigation of the quantum-control-assisted multipartite uncertainty relation in Heisenberg model with Dzyaloshinski-Moriya interaction [10.664589057582157]
  Zheng constructs a quantum-control-assisted multipartite variance-based uncertainty relation. We investigate the dynamics of the new uncertainty relation in the Heisenberg system with the Dzyaloshinski-Moriya interaction.
  arXiv  Detail & Related papers  (2023-08-25T12:11:42Z)
• 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)
• 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)
• Disturbance Enhanced Uncertainty Relations [2.075038010521211]
  We show that disturbance of one measurement to a subsequent measurement sets lower-bounds to uncertainty. The obtained relations, referred to as disturbance enhanced uncertainty relations, immediately find various applications in the field of quantum information. We anticipate that this new twist on uncertainty principle may shed new light on quantum foundations and may also inspire further applications in the field of quantum information.
  arXiv  Detail & Related papers  (2022-02-15T08:37:24Z)
• Quasiprobability fluctuation theorem behind the spread of quantum information [10.640597124563614]
  We theoretically uncover the quantum fluctuation theorem behind the informational inequality. The fluctuation theorem quantitatively predicts the statistics of the underlying quantum process. We experimentally apply an interference-based method to measure the amplitudes composing the quasiprobability.
  arXiv  Detail & Related papers  (2022-01-02T17:45:50Z)
• Tripartite quantum-memory-assisted entropic uncertainty relations for multiple measurements [0.0]
  We obtain tripartite quantum memory-assisted entropic uncertainty relations. We show that the lower bounds of these relations have three terms that depend on the complementarity of the observables.
  arXiv  Detail & Related papers  (2021-03-11T21:35:04Z)
• Preparation Uncertainty Implies Measurement Uncertainty in a Class of Generalized Probabilistic Theories [0.0]
  It is known for a pair of noncommutative observables that there is no state on which they take simultaneously definite values. Research has unveiled that they are not independent from but related with each other in a quantitative way. This study aims to reveal whether similar relations to quantum ones hold also in generalized probabilistic theories.
  arXiv  Detail & Related papers  (2020-06-03T08:06:48Z)
• 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.