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arXiv:1906.11807

No Disturbance Without Uncertainty as a Physical Principle

Liangliang Sun, Xiang Zhou, Sixia Yu

Published Jun 27, 2019• 2 citations
arXivHTMLPDF

Abstract

Finding physical principles lying behind quantum mechanics is essential to understand various quantum features, e.g., the quantum correlations, in a theory-independent manner. Here we propose such a principle, namely, no disturbance without uncertainty, stating that the disturbance caused by a measurement to a subsequent incompatible measurement is no larger than the uncertainty of the first measurement, equipped with suitable theory-independent measures for disturbance and uncertainty. When applied to local systems in a multipartite scenario, our principle imposes such a strong constraint on non-signaling correlations that quantum correlations can be recovered in many cases: i. it accounts for the Tsirelsons bound; ii. it provides the so far tightest boundary for a family of the noisy super-nonlocal box with 3 parameters, and iii. it rules out an almost quantum correlation from quantum correlations by which all the previous principles fail, as well as the celebrated quantum criterion due to Navascues, Pironio, and Acin. Our results pave the way to understand nonlocality exhibited in quantum correlations from local principles.

DOI
10.48550/arxiv.1906.11807

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Finding physical principles lying behind quantum mechanics is essential to understand various quantum features, e.g., the quantum correlations, in a theory-independent manner. Here we propose such a principle, namely, no disturbance without uncertainty, stating that the disturbance caused by a measurement to a subsequent incompatible measurement is no larger than the uncertainty of the first measurement, equipped with suitable theory-independent measures for disturbance and uncertainty. When applied to local systems in a multipartite scenario, our principle imposes such a strong constraint on non-signaling correlations that quantum correlations can be recovered in many cases: i. it accounts for the Tsirelsons bound; ii. it provides the so far tightest boundary for a family of the noisy super-nonlocal box with 3 parameters, and iii. it rules out an almost quantum correlation from quantum correlations by which all the previous principles fail, as well as the celebrated quantum criterion due to Navascues, Pironio, and Acin. Our results pave the way to understand nonlocality exhibited in quantum correlations from local principles.
One of the formulations of Heisenberg uncertainty principle, concerning so-called measurement uncertainty, states that the measurement of one observable modifies the statistics of the other. Here, we derive such a measurement uncertainty principle from two comprehensible assumptions: impossibility of instantaneous messaging at a distance (no-signaling), and violation of Bell inequalities (non-locality). The uncertainty is established for a pair of observables of one of two spatially separated systems that exhibit non-local correlations. To this end, we introduce a gentle form of measurement which acquires partial information about one of the observables. We then bound disturbance of the remaining observables by the amount of information gained from the gentle measurement, minus a correction depending on the degree of non-locality. The obtained quantitative expression resembles the quantum mechanical formulations, yet it is derived without the quantum formalism and complements the known qualitative effect of disturbance implied by non-locality and no-signaling.
We propose a new scheme to express the uncertainty principle in the form of inequality of the bipartite correlation functions for a given multipartite state, which provides an experimentally feasible and model-independent way to verify various uncertainty and measurement disturbance relations. By virtue of this scheme, the implementation of experimental measurement on the measurement disturbance relation to a variety of physical systems becomes practical. The inequality in turn, also imposes a constraint on the strength of correlation, i.e. it determines the maximum value of the correlation function for two-body system and a monogamy relation of the bipartite correlation functions for multipartite system.
Nonlocality is arguably one of the most fundamental and counterintuitive aspects of quantum theory. Nonlocal correlations could, however, be even more nonlocal than quantum theory allows, while still complying with basic physical principles such as no-signaling. So why is quantum mechanics not as nonlocal as it could be? Are there other physical or information-theoretic principles which prohibit this? So far, the proposed answers to this question have been only partially successful, partly because they are lacking genuinely multipartite formulations. In Fritz et al. [Nat. Commun. 4, 2263 (2013)], we introduced the principle of local orthogonality (LO), an intrinsically multipartite principle which is satisfied by quantum mechanics but is violated by nonphysical correlations. Here we further explore the LO principle, presenting additional results and explaining some of its subtleties. In particular, we show that the set of no-signaling boxes satisfying LO is closed under wirings, present a classification of all LO inequalities in certain scenarios, show that all extremal tripartite boxes with two binary measurements per party violate LO, and explain the connection between LO inequalities and unextendible product bases.
The notion of nonlocality implicitly implies there might be some kind of spooky action at a distance in nature, however, the validity of quantum mechanics has been well tested up to now. In this work it is argued that the notion of nonlocality is physically improper, the basic principle of locality in nature is well respected by quantum mechanics, namely, the uncertainty principle. We show that the quantum bound on the Clauser, Horne, Shimony, and Holt (CHSH) inequality can be recovered from the uncertainty relation in a multipartite setting. We further argue that the super-quantum correlation demonstrated by the nonlocal box is not physically comparable with the quantum one. The origin of the quantum structure of nature still remains to be explained, some post-quantum theory which is more complete in some sense than quantum mechanics is possible and might not necessarily be a hidden variable theory.
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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.