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Quantum Sensing and Nano Electronics and Photonics

A new perspective on causality, locality, and duality in entangled quantum nano systems

Sarma N. Gullapalli

Published Feb 1, 2019• 1 citation
Publisher

Abstract

Interference with or without entanglement has been recognized as a key resource for quantum computing and quantum communications systems, as for example discussed by Nielsen and Chuang1 and numerous other works. Multiple paths between sources and detectors require an understanding of the underpinning wave-particle duality issue in the interference effects. Recently a new axiom (particle and its wave function φ(r, t) cannot be coincident or co-located at space-time point (rk, tk) unless φ(r, t) = δ(r-rk, t-tk) the Dirac delta function) has been suggested2 and justified, which explains duality without Niels Bohr’s complementarity principle, thus eliminating the role of the observer, avoiding complicated “which way” (welcher-weg) considerations and observer subjectivity. This greatly simplifies analysis and design of multi-path quantum systems and restores objectivity. The same paper also suggested in the context of entanglement new concepts of (a) “total causality” that includes entanglement as a cause to locally and causally explain “action at a distance”, and (b) “partial causality” that excludes entanglement as a cause and thereby introduces the perception of strange phenomena of non-locality, retro-causality and quantum erasure, which are nevertheless very important. This paper reviews and then applies the axiom to bring much needed clarity to certain confusing and much debated aspects of developments in non-interaction measurements, counterfactual communications and quantum computers. These potential clarifications and simplifications of analysis and design of multi path systems may help developers of future quantum communication and quantum computer systems.

DOI
10.1117/12.2506801

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Interference with or without entanglement has been recognized as a key resource for quantum computing and quantum communications systems, as for example discussed by Nielsen and Chuang1 and numerous other works. Multiple paths between sources and detectors require an understanding of the underpinning wave-particle duality issue in the interference effects. Recently a new axiom (particle and its wave function φ(r, t) cannot be coincident or co-located at space-time point (rk, tk) unless φ(r, t) = δ(r-rk, t-tk) the Dirac delta function) has been suggested2 and justified, which explains duality without Niels Bohr’s complementarity principle, thus eliminating the role of the observer, avoiding complicated “which way” (welcher-weg) considerations and observer subjectivity. This greatly simplifies analysis and design of multi-path quantum systems and restores objectivity. The same paper also suggested in the context of entanglement new concepts of (a) “total causality” that includes entanglement as a cause to locally and causally explain “action at a distance”, and (b) “partial causality” that excludes entanglement as a cause and thereby introduces the perception of strange phenomena of non-locality, retro-causality and quantum erasure, which are nevertheless very important. This paper reviews and then applies the axiom to bring much needed clarity to certain confusing and much debated aspects of developments in non-interaction measurements, counterfactual communications and quantum computers. These potential clarifications and simplifications of analysis and design of multi path systems may help developers of future quantum communication and quantum computer systems.
An Axiom is presented and justified which (a) Explains duality in interference without complementarity or “which way” (welcher-weg) observation (b) Shows the equivalence: Coherence and alignment ≡ Interference ≡ No “which way” observation; No coherence or alignment ≡ No interference ≡ “which way” observation (c) Explains Wheeler’s delayed choice thought experiment (d) Explains results of experimental implementations of Wheeler’s experiment which show retro-causality with and without entanglement (e) Explains non-local action at a distance, and (f) Rephrases Albert Einstein’s unanswered question “Is quantum mechanics complete?” at a more fundamental level than just duality and non-locality. The explanation given does not require that the particle (photon) somehow “know” about the test setup or “which way” observation or change its behavior from particle to wave and vice versa as required by currently accepted explanation based on Niels Bohr’s complementarity principle. No new assumptions are made, only a new complete interpretation of probability which is already a fundamental assumption of quantum mechanics.
Early on, Albert Einstein and Niels Bohr heatedly debated wave-particle duality. To explain duality Bohr postulated his principle of complementarity, which is now widely accepted, but has mystifying metaphysical implications. Albert Einstein disagreed. Richard Feynman called it the “only mystery�? in quantum mechanics. Ingenious experiments including those using entanglement have confirmed Bohr’s complementarity. In this paper a new Duality Theorem is presented with proof which explains duality with particle always remaining particle and wave always remaining wave throughout, without using wave-particle complementarity or “which way�? (welcher-weg) observation. We explain results of reported experiments by showing the equivalence: Coherence and alignment ≡ Interference ≡ No “which way�? observation; No coherence or alignment ≡ No interference ≡ “which way�? observation That is, complementarity is redundant; conventional criteria of alignment and coherence alone suffice for interference. Our explanation does not require that photon somehow “know�? about the test setup or “which way�? observation and change its behavior from particle to wave and vice versa. No new assumptions are made, only new reasoning. In the context of entanglement we also help explain non-local action at a distance, and rephrase Albert Einstein’s unanswered question “Is quantum mechanics complete?�? at a more fundamental level.
Ninety years ago in 1927, at an international congress in Como, Italy, Niels Bohr gave an address which is recognized as the first instance in which the term "complementarity", as a physical concept, was spoken publicly [1], revealing Bohr's own thinking about Louis de Broglie's "duality". Bohr had very slowly accepted duality as a principle of physics: close observation of any quantum object will reveal either wave-like or particle-like behavior, one or the other of two fundamental and complementary features. Little disagreement exists today about complementarity's importance and broad applicability in quantum science. Book-length scholarly examinations even provide speculations about the relevance of complementarity in fields as different from physics as biology, psychology and social anthropology, connections which were apparently of interest to Bohr himself (see Jammer [2], Murdoch [3] and Whitaker [4]). Confusion evident in Como following his talk was not eliminated by Bohr's article [1], and complementarity has been subjected to nine decades of repeated examination ever since with no agreed resolution. Semi-popular treatments [5] as well as expert examinations [6-9] show that the topic cannot be avoided, and complementarity retains its central place in the interpretation of quantum mechanics. However, recent approaches by our group [10-13] and others [14-20] to the underlying notion of coherence now allow us to present a universal formulation of complementarity that may signal the end to the confusion. We demonstrate a new relationship that constrains the behavior of an electromagnetic field (quantum or classical) in the fundamental context of two-slit experiments. We show that entanglement is the ingredient needed to complete Bohr's formulation of complementarity, debated for decades because of its incompleteness.
Wave-particle duality is a bizarre feature at the heart of quantum mechanics which refers to the mutually exclusive dual attributes of quantum objects as the wave and the particle. Quantum eraser presents a counterintuitive aspect of the wave-particle duality. In this paper, we show that quantum eraser can be quantitatively understood in terms of the recently developed duality-entanglement relation. In other words, we show that wave-particle-entanglement triality captures all the physics of the quantum erasure. We find that a controllable partial erasure of the which-path information is attainable, enabling the partial recovery of the quantum interference and extending the scope of the conventional quantum eraser protocols.
Introduction Our concern in this chapter is locality in quantum mechanics (QM). Locality is a heuristic physics principle based on the following propositions. No Action-at-a-Distance All the evidence points to the principle that physical actions, taken within restricted (localized) regions of space and time by observers or other agencies such as systems under observation (SUOs), do not cause instantly observable effects on other SUOs at large distances. This does not apply to mathematical/ metaphysical concepts such as quantum wave functions or correlations, as these are conceptual objects (Scarani et al., 2000). Statements about instantaneous wave function collapse are vacuous (have no empirical significance) and are therefore not an issue of significance in physics. Such statements are an issue to theorists who objectivize wave functions, as in Hidden Variables (HV) theory. Action-at-a-distance is generally regarded as anathema by most physicists. For example, Newton's law of universal gravitation is well known for mathematically encoding action-at-a-distance. There is direct evidence, however, in the form of a letter written by Newton to Bentley, that Newton believed that gravity acting “at a distance through a vacuum without the mediation of anything else” was an absurdity (Newton, 2006). The no action-at-a-distance principle is encoded in quantized detector networks (QDN) by the requirement that labstate preparation and consequent signal detection never occur at the same stage. Causal Transmission All physically observable consequences of local actions taken by an observer or SUO are transmitted by identifiable physical processes, such as electromagnetic waves or neutrinos. There is no such thing as magic or action-at-a-distance . In QDN this proposition is taken into account implicitly in the labstate outcome amplitudes at each stage, as these model how information is propagated from stage to stage. When necessary, the information void can be modeled as if there were fields and/or particles propagating through it, giving scope for different mathematical models, such as Euclidean space, curved spacetime, noncommuting spacetimes, and so on. The structure of the information void is essentially a discussion of whatever modules have to be taken into account between labstate preparation and signal detection.
By moving to the context of relativistic space-time structure, this chapter completes the argument of Chapter 4 that we can use quantum theory locally to explain correlations that violate Bell inequalities with no instantaneous action at a distance. Chance here must be relativized not just to time but to a space-time point, so that an event may have more than one chance at the same time—it may even be certain relative to one space-time point but ‘at the same time’ completely uncertain relative to another. This renders Bell’s principle of Local Causality either inapplicable or intuitively unmotivated. Counterfactual dependence between the outcomes of measurements on systems assigned an entangled state is not causal since neither outcome is subject to intervention: but it may still be appealed to in a non-causal explanation of one in terms of the other.