Limitations imposed by complementarity
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Limitations imposed by complementarity F. E. S. Steinhoff1,2
· M. C. de Oliveira3
Received: 16 May 2020 / Accepted: 14 September 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract Complementarity is one of the main features of quantum physics that radically departs from classical notions. Here we consider the limitations that this principle imposes due to the unpredictability of measurement outcomes of incompatible observables. For two-level systems, it is shown that any preparation violating complementarity enables the preparation of a non-signalling box violating Tsirelson’s bound. Moreover, these “beyond-quantum” objects could be used to distinguish a plethora of non-orthogonal quantum states and hence enable improved cloning protocols. For higher-dimensional systems the main ideas are sketched. Keywords Complementarity · Nonlocality · Distinguishability
1 Introduction The basic postulates and results of a physical theory are based on principles that are strongly supported by empirical evidence. The principle of conservation of energy, for example, is a major pillar in all areas of physics and implies deep limitations on human experience: it is impossible to construct a perpetual motion machine, or to outperform Carnot’s heat engine. General relativity theory is governed by the equivalence principle and by the bound on the maximal speed of interactions given by the speed of light. These and other celebrated principles are often not only simple to understand, but very precisely stated, giving profound intuitions on the laws of nature. In quantum theory, there is an ongoing search for one or more physical principles that could explain the bounds on quantum correlations. More precisely, even though quantum systems can surpass classical bounds of Bell-like inequalities, it is known
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F. E. S. Steinhoff [email protected]
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Faculdade de Engenharia, Universidade Federal de Mato Grosso, Várzea Grande 78060-900, Brazil
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Naturwissenschaftlich Technische Fakultät, Universität Siegen, 57068 Siegen, Germany
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Instituto de Física “Gleb Wataghin”, Universidade Estadual de Campinas, Campinas 3083-970, Brazil 0123456789().: V,-vol
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F. E. S. Steinhoff, M. C. de Oliveira
that there are limits to the violations of local realism attained by quantum objects. There exist theoretical constructions known as nonlocal boxes which can violate Belllike inequalities more than quantum systems, without violating the principle of nonsignalling or basic probability axioms. There are many different proposals of physical principles that try to explain such bounds on quantum correlations [1–5], but there is no general consensus on their success [6]. For quantum systems, a major law is the principle of complementarity, firstly noticed by Bohr [7,8], based on the observation that certainty in the measurement of a fixed physical property precludes certainty in the measurement of a complementary one. In the double-slit experiment, complementarity is quantitatively expressed by
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