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Rényi and Tsallis formulations of noise-disturbance trade-off relations

We address an information-theoretic approach to noise and disturbance in quantum measurements. Properties of corresponding probability distributions are characterized by means of both the Rényi and Tsallis entropies. Related information-theoretic measures of noise and disturbance are introduced. These definitions are based on the concept of conditional entropy. To motivate introduced measures, some important properties of the conditional Rényi and Tsallis entropies are discussed. There exist several formulations of entropic uncertainty relations for a pair of observables. Trade-off relations for noise and disturbance are derived on the base of known formulations of such a kind.

preprint2016arXivOpen access
Alexey E. Rastegin
quant-ph
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Alexey E. Rastegin

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