Certification of incompatible measurements using quantum steering

Stronger Error Disturbance Relations for Incompatible Quantum Measurements

We formulate three new error disturbance relations, one of which is free from explicit dependence upon intrinsic fluctuations of observables. The first error-disturbance relation is tighter than the one provided by the Branciard inequality and the Ozawa inequality for some initial states. Other two error disturbance relations provide a tighter bound to Ozawa’s error disturbance relation and one...

Error-tradeoff and error-disturbance relations for incompatible quantum measurements.

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 unc...

Quantum steering of Gaussian states via non-Gaussian measurements

Quantum steering-a strong correlation to be verified even when one party or its measuring device is fully untrusted-not only provides a profound insight into quantum physics but also offers a crucial basis for practical applications. For continuous-variable (CV) systems, Gaussian states among others have been extensively studied, however, mostly confined to Gaussian measurements. While the fulf...

Einstein-Podolsky-Rosen Steering and Quantum Steering Ellipsoids: Optimal Two-Qubit States and Projective Measurements

Quantum theory of incompatible observations

Quantum theory describes events on the most fundamental level currently available. The synthesis of information from mutually incompatible quantum measurements plays the key role in testing the structure of the theory. The purpose of this Letter is to show a unique relationship between quantum theory and the mathematical statistics used to obtain optimal information from incompatible observatio...