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Stronger uncertainty relations for all incompatible observables.

Lorenzo Maccone1, Arun K Pati2

  • 1Dipartimento Fisica and INFN Sez. Pavia, University of Pavia, via Bassi 6, I-27100 Pavia, Italy.

Physical Review Letters
|January 24, 2015
PubMed
Summary
This summary is machine-generated.

We introduce stronger uncertainty relations that capture incompatible observables. These new relations provide a nontrivial lower bound for the sum of variances, unlike the standard Heisenberg-Robertson relation.

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Area of Science:

  • Quantum mechanics
  • Quantum information theory

Background:

  • The Heisenberg-Robertson uncertainty relation sets a lower bound on the product of variances for two observables.
  • This relation can be trivial, failing to capture observable incompatibility when the lower bound is zero.

Purpose of the Study:

  • To develop stronger uncertainty relations that reliably detect incompatible observables.
  • To establish uncertainty relations based on the sum of variances.

Main Methods:

  • Derivation of two new uncertainty relations.
  • Analysis of the lower bound of the sum of variances.

Main Results:

  • The proposed uncertainty relations guarantee a nontrivial lower bound for the sum of variances.
  • This nontrivial bound is present specifically when observables are incompatible for a given quantum state.

Conclusions:

  • The new uncertainty relations offer a more robust measure of observable incompatibility in quantum systems.
  • These relations enhance our understanding of fundamental limitations in quantum state preparation and measurement.