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Variance-based uncertainty relation for incompatible observers

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Based on mixedness definition as $$M=1-\hbox {tr}\left( {\rho ^{2}}\right) $$M=1-trρ2, we obtain a new variance-based uncertainty equality along with an inequality for Hermitian operators of a single-qubit system. The obtained… Click to show full abstract

Based on mixedness definition as $$M=1-\hbox {tr}\left( {\rho ^{2}}\right) $$M=1-trρ2, we obtain a new variance-based uncertainty equality along with an inequality for Hermitian operators of a single-qubit system. The obtained uncertainty equality can be used as a measure of the system mixedness. A qubit system with feedback control is also exploited to demonstrate the new uncertainty.

Keywords: uncertainty; relation incompatible; based uncertainty; variance based; uncertainty relation

Journal Title: Quantum Information Processing
Year Published: 2017

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