Abstract Heisenberg’s original uncertainty relation is related to measurement effect, which is different from the preparation uncertainty relation. However, it has been shown that Heisenberg’s error disturbance uncertainty relation is not valid in some cases. We experimentally test the error-tradeoff uncertainty relation by using a continuous-variable Gaussian Einstein–Podolsky–Rosen (EPR)-entangled state. Based on the quantum correlation between the two entangled optical beams, the errors on amplitude and phase quadratures of one EPR optical beam coming from joint measurement are estimated, respectively, which are used to verify the error–tradeoff relation. Especially, the error–tradeoff relation for error-free measurement of one observable is verified in our experiment. We also verify the error–tradeoff relations for nonzero errors and mixed state by introducing loss on one EPR beam. Our experimental results demonstrate that Heisenberg’s error–tradeoff relation is violated in some cases for a continuous-variable system, while the Ozawa’s and Branciard’s relations are valid.Abstract Heisenberg’s original uncertainty relation is related to measurement effect, which is different from the preparation uncertainty relation. However, it has been shown that Heisenberg’s error disturbance uncertainty relation is not valid in some cases. We experimentally test the error-tradeoff uncertainty relation by using a continuous-variable Gaussian Einstein–Podolsky–Rosen (EPR)-entangled state. Based on the quantum correlation between the two entangled optical beams, the errors on amplitude and phase quadratures of one EPR optical beam coming from joint measurement are estimated, respectively, which are used to verify the error–tradeoff relation. Especially, the error–tradeoff relation for error-free measurement of one observable is verified in our experiment. We also verify the error–tradeoff relations for nonzero errors and mixed state by introducing loss on one EPR beam. Our experimental results demonstrate that Heisenberg’s error–tradeoff relation is violated in some cases for a continuous-variable system, while the Ozawa’s and Branciard’s relations are valid.

arXiv:1905.05632npj Quantum InformationAug 8, 201916 citations

BEYOND HEISENBERG'S UNCERTAINTY RELATIONS

World Scientific series in contemporary chemical physicsDec 1, 20020 citations

Violation of Heisenberg’s Uncertainty Principle

Koji Nagata, Tadao Nakamura

Recently, violation of Heisenberg's uncertainty relation in spin measurements is discussed [J.Erhart et al., Nature Physics 8, 185 (2012)] and [G.Sulyok et al., Phys.Rev. A 88, 022110 (2013)].We derive the optimal limitation of Heisenberg's uncertainty principle in a specific two-level system (e.g., electron spin, photon polarizations, and so on).Some physical situation is that we would measure x σ and y σ , simultaneously.The optimality is certified by the Bloch sphere.We show that a violation of Heisenberg's uncertainty principle means a violation of the Bloch sphere in the specific case.Thus, the above experiments show a violation of the Bloch sphere when we use ±1 as measurement outcome.This conclusion agrees with recent researches [K.Recently, violation of Heisenberg's uncertainty relation in spin measurements is discussed [J.Erhart et al., Nature Physics 8, 185 (2012)] and [G.Sulyok et al., Phys.Rev. A 88, 022110 (2013)].We derive the optimal limitation of Heisenberg's uncertainty principle in a specific two-level system (e.g., electron spin, photon polarizations, and so on).Some physical situation is that we would measure x σ and y σ , simultaneously.The optimality is certified by the Bloch sphere.We show that a violation of Heisenberg's uncertainty principle means a violation of the Bloch sphere in the specific case.Thus, the above experiments show a violation of the Bloch sphere when we use ±1 as measurement outcome.This conclusion agrees with recent researches [K.

OALibJan 1, 201510 citations

The Heisenberg Uncertainty Relations

R. Shankar

Springer eBooksJan 1, 19951 citation

Inferred-variance uncertainty relations in the presence of quantum entanglement

Shrobona Bagchi, Chandan Datta, Pankaj Agrawal

Uncertainty relations play a significant role in drawing a line between classical physics and quantum physics. Since the introduction by Heisenberg, these relations have been considerably explored. However, the effect of quantum entanglement on uncertainty relations was not probed. Berta et al. [Nat. Phys. 6, 659 (2010)] removed this gap by deriving a conditional-entropic uncertainty relation in the presence of quantum entanglement. In the same spirit, using inferred-variance, we formulate uncertainty relations in the presence of entanglement for general two-qubit systems and arbitrary observables. We derive lower bounds for the sum and product inferred-variance uncertainty relations. Strikingly, we can write the lower bounds of these inferred-variance uncertainty relations in terms of measures of entanglement of two-qubit states, as characterized by concurrence, or $G$ function. The presence of entanglement in the lower bound of inferred-variance uncertainty relation is quite distinctive. We also explore the violation of local uncertainty relations in this context and an interference experiment. Furthermore, we discuss possible applications of these uncertainty relations.Uncertainty relations play a significant role in drawing a line between classical physics and quantum physics. Since the introduction by Heisenberg, these relations have been considerably explored. However, the effect of quantum entanglement on uncertainty relations was not probed. Berta et al. [Nat. Phys. 6, 659 (2010)] removed this gap by deriving a conditional-entropic uncertainty relation in the presence of quantum entanglement. In the same spirit, using inferred-variance, we formulate uncertainty relations in the presence of entanglement for general two-qubit systems and arbitrary observables. We derive lower bounds for the sum and product inferred-variance uncertainty relations. Strikingly, we can write the lower bounds of these inferred-variance uncertainty relations in terms of measures of entanglement of two-qubit states, as characterized by concurrence, or $G$ function. The presence of entanglement in the lower bound of inferred-variance uncertainty relation is quite distinctive. We also explore the violation of local uncertainty relations in this context and an interference experiment. Furthermore, we discuss possible applications of these uncertainty relations.

arXiv:1909.11486Physical Review AAug 3, 20225 citations

G

function. The presence of entanglement in the lower bound of inferred-variance uncertainty relation is quite distinctive. We also explore the violation of local uncertainty relations in this context and an interference experiment. Furthermore, we discuss possible applications of these uncertainty relations.