4.2 Complementarity, Completeness, and Einstein’s Local Realism

William Demopoulos

Gina Maria Schwarz

Marcos L. W. Basso, Jonas Maziero

Abstract Wave-particle duality is an essential character of quantum systems. In the last few years, much progress has been made towards formally quantifying these quantum features. The properties of the quantum density matrix were shown to lead to duality inequalities for single-quanton mixed states and to triality identities, also known as complete complementarity relations (CCRs), for two-quanton pure states. In this article, we establish connections between CCRs and Einstein-Podolsky-Rosen (ir)realism, as formalized by Bilobran and Angelo (see Bilobran A. L. O. and Angelo R. M., EPL , 112 (2015) 40005). Besides, we show that, for tripartite pure states , CCRs can be applied to obtain the system-environment entanglement of formation, , through the local information of a system A and its classical correlation with an auxiliary system B . Moreover, we discuss CCRs in the context of the emergence of the pointer basis in the decoherence process identified via the constancy of system-apparatus classical correlations. We also obtain CCRs for purified mixed bipartite quantum-classical states. In addition, we derive CCRs for mixed-bipartite two-qudit quantum states and discuss its interpretations.

Jeffrey Bub

Leemon McHenry

In his book, Nature Loves to Hide, Shimon Malin provides a wonderfully lucid and fascinating account of the development of quantum mechanics in the twentieth century and argues that the baffling puzzles of the quantum world can be understood in terms of Whitehead's process metaphysics. 1 Malin thus joins an ever-growing number of physicists who see in Whitehead's theories a useful framework for understanding contemporary physics, including for example, Henry Stapp, Timothy Eastman, Lawrence Fagg, Basil Hiley and David Finkelstein.Nature Loves to Hide is divided into three parts: "e Quandary," "From a Universe of Objects to a Universe of Experiences," and "Physics and the One."Malin also includes three appendices on the relativity of simultaneity, the proof of Bell's inequalities, and interpretations of quantum theory (i.e., quantum ontologies)."e Quandary" examines the debate between Niels Bohr and Albert Einstein regarding the completeness of quantum mechanics.Einstein believed that quantum mechanics violates both local realism and determinism and therefore fails as a complete, fundamental theory of nature while Bohr held that quantum mechanics was complete regardless of its violations.Bohr's radical thesis was that a single model cannot adequately describe the atomic and subatomic realms.His complementarity framework of wave/particle applies to different conditions, but even here Bohr is not describing nature itself, but rather what we can know about nature.Malin distinguishes between Einstein's ontic approach and Bohr's epistemic approach (39).e latter, which became the orthodox "Copenhagen Interpretation," is often described as pragmatic or instrumentalist since quantum theory is to be viewed as merely a set of rules for calculating correlations among observations.As the Einstein-Bohr controversy continued through their disciples, John Bell demonstrated in 1964 that the issue was not merely philosophical but rather scientific when his theorem led to an experiment that proved nature violates local realism.At this round, Bohr wins, Einstein loses.Malin understands "the quandary" to be the fact that local realism must be abandoned even if it is the "eminently reasonable" world-view to which we continue to cling.Physics (post Bell's theorem) has suffered a type of "schizophrenia" since physicists adhere to Bohr's view as the orthodox interpretation of quantum mechanics, yet, at the same time, rely on Einstein's paradigm at some fundamental level.Malin's

Guang-Liang Li

As we all know, Einstein disagreed with Born's probabilistic interpretation of wave-functions, which collapse abruptly once measurements are performed on the corresponding systems. In the Einstein-Bohr debate, Einstein considered quantum mechanics incomplete. Inspired by Einstein, Bell and his followers intended to complete quantum mechanics within the framework of local realism. Regrettably, deterministic correlations in Einstein's local-realist description of the world are mistaken for "nonlocal-interactions" (non-locality) in the world described by Bell's theorem, which leads to the questionable interpretation of the experimental results obtained by testing Bell inequalities. This article introduces a new principle, the general principle of measurements, which is proved as a mathematical theorem and allows quantum mechanics to be completed within the framework of local realism while keeping the axiomatic definition of a general Hilbert space essentially unchanged. Using disjunction ("or") as the logical relation between orthonormal vectors spanning a given Hilbert space, the completed quantum theory precludes inexplicable collapses of wave-functions and is intuitively comprehensible, thus alleviating much difficulty in understanding quantum mechanics. Among various world views, Einstein's local-realist world view is correct.