Noise and Disturbance of Qubit Measurements: An Information-Theoretic Characterisation

Abstract

Information-theoretic definitions for the noise associated with a quantum measurement and the corresponding disturbance to the state of the system have recently been introduced [F. Buscemi et al., Phys. Rev. Lett. 112, 050401 (2014)]. These definitions are invariant under relabelling of measurement outcomes, and lend themselves readily to the formulation of state-independent uncertainty relations both for the joint estimate of observables (noise-noise relations) and the noise-disturbance tradeoff. Here we derive such relations for incompatible qubit observables, which we prove to be tight in the case of joint estimates, and present progress towards fully characterising the noise-disturbance tradeoff. In doing so, we show that the set of obtainable noise-noise values for such observables is convex, whereas the conjectured form for the set of obtainable noise-disturbance values is not. Furthermore, projective measurements are not optimal with respect to the joint-measurement noise or noise-disturbance tradeoffs. Interestingly, it seems that four-outcome measurements are needed in the former case, whereas three-outcome measurements are optimal in the latter.

arXiv commentMinor changes, corresponds to final published version. 14 pages, 5 figures

References in corpus (15)

• Universally valid reformulation of the Heisenberg uncertainty principle on noise and disturbance in measurement
• Quantum root-mean-square error and measurement uncertainty relations
• How well can one jointly measure two incompatible observables on a given quantum state?
• Prior information: how to circumvent the standard joint-measurement uncertainty relation
• Noise and disturbance in quantum measurements: an information-theoretic approach
• Translation of Lueders' "Uber die Zustandsanderung durch den Messprozess"
• Improved bounds in entropic uncertainty relations
• Certainty in Heisenberg's uncertainty principle: Revisiting definitions for estimation errors and disturbance
• Quantum measurements on finite dimensional systems: relabeling and mixing
• Informationally complete joint measurements on finite quantum systems
• Experimental test of entropic noise-disturbance uncertainty relations for spin-1/2 measurements
• Tight state-independent uncertainty relations for qubits
• State-Dependent Approach to Entropic Measurement-Disturbance Relations
• Measurement Uncertainty for Finite Quantum Observables
• Entropic uncertainty relations for successive generalized measurements

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• Neutron optical test of completeness of quantum root-mean-square errors
• Error-disturbance uncertainty relations in Faraday measurements
• Entropic Approach to Error-Disturbance Tradeoff in Quantum Measurements
• Entropic measurement uncertainty relations for all the infinite components of a spin vector