Uncertainty-disturbance relations are derived showing uncertainty prerequisites and upper-bounds disturbance, with applications to estimating quantum resources for rank-one projective measurements.
Uncertainty-Complementarity Balance as a General Constraint on Non-locality
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abstract
We propose an uncertainty-complementarity balance relation and build quantitative connections among non-locality, complementarity, and uncertainty. Our balance relation, which is formulated in a theory-independent manner, states that for two measurements performed sequentially, the complementarity demonstrated in the first measurement in terms of disturbance is no greater than the uncertainty of the first measurement. Quantum theory respects our balance relation, from which the Tsirelson bound can be derived, up to an inessential assumption. In the simplest Bell scenario, we show that the bound of Clauser-Horne-Shimony-Holt inequality for a general non-local theory can be expressed as a function of the balance strength, a constance for the given theory. As an application, we derive the balance strength as well as the nonlocal bound of Popescu-Rohrlich box. Our results shed light on quantitative connections among three fundamental concepts, i.e., uncertainty, complementarity and non-locality.
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UNVERDICTED 2representative citing papers
The 'no disturbance without uncertainty' principle constrains non-signaling correlations to recover quantum ones in cases including Tsirelson's bound, tight bounds on noisy super-nonlocal boxes, and exclusion of certain almost-quantum correlations.
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Uncertainty-disturbance relations and applications
Uncertainty-disturbance relations are derived showing uncertainty prerequisites and upper-bounds disturbance, with applications to estimating quantum resources for rank-one projective measurements.
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No Disturbance Without Uncertainty as a Physical Principle
The 'no disturbance without uncertainty' principle constrains non-signaling correlations to recover quantum ones in cases including Tsirelson's bound, tight bounds on noisy super-nonlocal boxes, and exclusion of certain almost-quantum correlations.