A Universal Formulation of Uncertainty Relation for Error and Disturbance

• URL: http://arxiv.org/abs/2004.06099v2
• Date: Wed, 18 Oct 2023 17:55:07 GMT
• Title: A Universal Formulation of Uncertainty Relation for Error and Disturbance
• Authors: Jaeha Lee and Izumi Tsutsui
• Abstract summary: We present a universal formulation of uncertainty relation valid for any conceivable quantum measurement. Owing to its simplicity and operational tangibility, our general relation is also experimentally verifiable.
• Score: 0.9479435599284545
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We present a universal formulation of uncertainty relation valid for any conceivable quantum measurement and the resultant observation (observer) effect of statistical nature. Owing to its simplicity and operational tangibility, our general relation is also experimentally verifiable. Our relation violates the traditional na{\"i}ve bound $\hbar/2$ for the position-momentum measurement while respecting Heisenberg's original philosophy of the uncertainty principle. Our error-disturbance relation admits a parallel formulation to our relation for errors, which also embraces the standard Kennard--Robertson (Schr{\"o}dinger) relation as a special case; this attains a unified picture of the three orthodox realms of uncertainty regarding quantum indeterminacy, measurement, and observation effect within a single framework.

Related papers

• 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)
• Gaussian Formalism: Concrete Realization of Joint Measurement for Heisenberg's Uncertainty Relation for Errors [0.0]
  We show that our joint measurement smoothly interpolates between the projective measurements of position and momentum. We obtain the Lee-Tsutsui (LT) error and the refined Lee error for the position-momentum measurement.
  arXiv  Detail & Related papers  (2024-03-28T14:10:48Z)
• 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)
• Realization of algorithmic identification of cause and effect in quantum correlations [13.164461672508711]
  A quantum perspective of correlations holds the promise of overcoming the limitation by Reichenbach's principle. We have devised an algorithm capable of identifying any two-qubit statistical correlations generated by the two basic causal structures under an observational scenario. Our result paves the way for studying quantum causality in general settings.
  arXiv  Detail & Related papers  (2023-04-20T10:06:38Z)
• A Consistent Estimator for Confounding Strength [21.443297599122058]
  We derive the behavior of the confounding strength estimator by Janzing and Sch"olkopf. We then use tools from random matrix theory to derive an adapted, consistent estimator.
  arXiv  Detail & Related papers  (2022-11-03T15:34:33Z)
• A Universal Formulation of Uncertainty Relation for Error-Disturbance and Local Representability of Quantum Observables [1.696974372855528]
  A universal formulation of the quantum uncertainty regarding quantum indeterminacy, quantum measurement, and its inevitable observer effect is presented. The framework assures that the resultant general relations admit natural operational interpretations and characterisations.
  arXiv  Detail & Related papers  (2022-04-25T17:44:21Z)
• A Universal Formulation of Uncertainty Relation for Errors under Local Representability [1.696974372855528]
  A universal formulation of uncertainty relations for quantum measurements is presented. Owing to the simplicity and operational tangibility of the framework, the resultant general relations admit natural operational interpretations and characterisations.
  arXiv  Detail & Related papers  (2022-03-15T18:50:13Z)
• Experimentally ruling out joint reality based on operational completeness [20.56996045100972]
  We report a device-independent experiment to confirm that the joint reality of two observables on a single two-level system is incompatible with the assumption of operational completeness. Our results push the fundamental limit to delineate the quantum-classical boundary and pave the way for exploring relevant problems in other scenarios.
  arXiv  Detail & Related papers  (2022-03-10T08:58:28Z)
• Experimental test of the majorization uncertainty relation with mixed states [6.613272059966484]
  The uncertainty relation lies at the heart of quantum theory and behaves as a non-classical constraint on the indeterminacies of incompatible observables in a system. In this work we test the novel majorization uncertainty relations of three incompatible observables using a series of mixed states with adjustable mixing degrees.
  arXiv  Detail & Related papers  (2021-04-07T01:18:32Z)
• Geometric Formulation of Universally Valid Uncertainty Relation for Error [1.696974372855528]
  We present a new geometric formulation of uncertainty relation valid for any quantum measurements of statistical nature. Owing to its simplicity and tangibility, our relation is universally valid and experimentally viable.
  arXiv  Detail & Related papers  (2020-02-10T18:31:54Z)

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.