Improved Error-Tradeoff and Error-Disturbance Relations

Abstract

Heisenberg's uncertainty principle is quantified by error-disturbance tradeoff relations, which have been tested experimentally in various scenarios. Here we shall report improved new versions of various error-disturbance tradeoff relations by decomposing the measurement errors into two different components, namely, operator bias and fuzziness. Our improved uncertainty relations reveal the tradeoffs between these two components of errors, and imply various conditionally valid error-tradeoff relations for the unbiased and projective measurements. We also design a quantum circuit to measure the two components of the error and disturbance.

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• Error-Disturbance Trade-off in Sequential Quantum Measurements
• Experimental test of error-tradeoff uncertainty relation using a continuous-variable entangled state
• Generalized-mean Cramér-Rao Bounds for Multiparameter Quantum Metrology
• Simultaneous Measurement of Multiple Incompatible Observables and Tradeoff in Multiparameter Quantum Estimation
• Error-Disturbance Relation in Stern-Gerlach Measurements
• Error-disturbance relations for finite dimensional systems
• Heisenberg Uncertainty Relation Revisited
• Uncertainty-disturbance relations and applications
• Experimental Joint Estimation of Phase and Phase Diffusion via Deterministic Bell Measurements
• Minimal Trade-off and Optimal Measurement for Multiparameter Quantum Estimation