title: Error-tradeoff and error-disturbance relations for incompatible quantum measurements.
abstract: Heisenberg's uncertainty principle is one of the main tenets of quantum theory. Nevertheless, and despite its fundamental importance for our understanding of quantum foundations, there has been some confusion in its interpretation: Although Heisenberg's first argument was that the measurement of one observable on a quantum state necessarily disturbs another incompatible observable, standard uncertainty relations typically bound the indeterminacy of the outcomes when either one or the other observable is measured. In this paper, we quantify precisely Heisenberg's intuition. Even if two incompatible observables cannot be measured together, one can still approximate their joint measurement, at the price of introducing some errors with respect to the ideal measurement of each of them. We present a tight relation characterizing the optimal tradeoff between the error on one observable vs. the error on the other. As a particular case, our approach allows us to characterize the disturbance of an observable induced by the approximate measurement of another one; we also derive a stronger error-disturbance relation for this scenario.
authors.affiliation: Centre for Engineered Quantum Systems and School of Mathematics and Physics, The University of Queensland, St. Lucia, QLD 4072, Australia. c.branciard@physics.uq.edu.au
authors.forename: Cyril
authors.initials: C
authors.lastname: Branciard
mesh_terms: D008956:Models, Chemical; D011789:Quantum Theory; D012107:Research Design; D035501:Uncertainty
references.citation: Phys Rev Lett. 1988 Jun 13;60(24):2447-2449
references.pmid: 10038356
references.citation: Phys Rev Lett. 2012 Sep 7;109(10):100404
references.pmid: 23005268