Bohr's Complementarity Principle Research Articles

Heisenberg's uncertainty principle, Bohr's complementarity principle, and the Copenhagen interpretation

The atomic absorption and emission process that uses noninstantaneous electronic transitions of the atomic electron (i.e., electric charge), the tangent reference system, the property of speed instantaneity, and the conservation laws leads to a violation of Heisenberg's uncertainty principle, and it is maintained in the atomic absorption and emission process discontinuity that is conserved as the emitted photon's (i.e., electromagnetic radiation's) discontinuity. This leads to a falsification of Bohr's complementary principle that aligns with Einstein's 1909 falsification of it. The violation of Heisenberg's uncertainty principle and falsification of Bohr's complementarity principle falsify the Copenhagen interpretation, because it requires Heisenberg's uncertainty principle not to be violated and Bohr's complementarity principle not to be falsified.

Using double slit experiment based on Bohr complementarity principle to transmit information without media transmission from the information source to destination

This paper proposes information transmission without media transmission from the information source to destination based on Bohr complementarity principle. When a single photon passes through Young’s double-slit, its particle degree characteristics increase with the path distinguishability increasing. After single photon passes through double-slit, the photons propagation route is divided into two regions, the source region and the destination region. Keep the path distinguishability in the destination region unchanged. Distinguish or not distinguish the path information in the source region. The distribution of photons on each region will be different after single photons pass through double-slit. Use the laser trigger signal on the front optical path to confirm whether the photons detected at the destination region are valid photons, rather than photon information of the source region. Count the percentage of photons falling in the destination region in the photons passing through the double-slit, by pre-synchronizing to make particle degree characteristics of each photon similar in each period of time. This percentage can reveal the photon path distinguishability of the source region. The interference visibility of the fringe formed by valid photons detected at the destination region can achieve the target too.

Characterization of two-particle interference by complementarity

Bohr's complementarity principle is quantitatively formulated in terms of the distinguishability of various paths a quanton can take and the measure of the interference it produces. This phenomenon results from the interference of single-quanton amplitudes for various paths. The distinguishability of paths puts a bound on the sharpness of the interference the quanton can produce. However, there exist other kinds of quantum phenomena where interference of two-particle amplitudes results in a two-particle interference, if the particles are indistinguishable. The Hong-Ou-Mandel (HOM) effect and the Hanbury-Brown-Twiss (HBT) effect are two well-known examples. However, two-particle interference is not as easy to define as its single-particle counterpart, and the realization that it involves interference of two-particle amplitudes came much later. In this work, a duality relation, between the particle distinguishability and the visibility of two-particle interference, is derived. The distinguishability of the two particles, arising from some internal degree of freedom, puts a bound on the sharpness of the two-particle interference they can produce, in a HOM or HBT kind of experiment. It is argued that the existence of this kind of complementarity can be used to characterize two-particle interference, which in turn leads one to the conclusion that the HOM and the HBT effects are equivalent in essence and may be treated as a single two-particle-interference phenonmenon.

Fidelity-disturbance-entropy tradeoff in quantum channels

Quantum channels are indispensable instruments for transmitting, extracting, and processing information. According to the spirit of the Bohr complementarity principle and the Heisenberg uncertainty principle, one expects that there are intrinsic tradeoff relations between state disturbance and information gain for any channel, which indeed have been widely studied and characterized from various angles. In this work, we investigate this issue from the perspective of information conservation. More specifically, we divide the information associated with a channel into three categories: transmitted information (quantified by operation fidelity), disturbance (quantified by the Hilbert-Schmidt norm), and extracted information (quantified by the increase of Tsallis-2 entropy), which are all derived naturally from a channel with direct physical motivations. We reveal basic properties of these three information-theoretic quantities and establish a triality relation between them. As applications, we apply these quantities to shed insights into the Mach-Zehnder interferometry and several prototypical channels.

Experimental tests of the density matrix's property-based complementarity relations

Bohr's complementarity principle is of fundamental historic and conceptual importance for Quantum Mechanics (QM), and states that, with a given experimental apparatus configuration, one can observe either the wave-like or the particle-like character of a quantum system, but not both. However, it was eventually realized that these dual behaviors can both manifest partially in the same experimental setup, and, using ad hoc proposed measures for the wave and particle aspects of the quanton, complementarity relations were proposed limiting how strong these manifestations can be. Recently, a formalism was developed and quantifiers for the particleness and waveness of a quantum system were derived from the mathematical structure of QM entailed in the density matrix's basic properties ($\rho\ge 0$, $\mathrm{Tr}\rho=1$). In this article, using IBM Quantum Experience quantum computers, we perform experimental tests of these complementarity relations applied to a particular class of one-qubit quantum states and also for random quantum states of one, two, and three qubits.

Evidence of the entanglement constraint on wave-particle duality using the IBM Q quantum computer

We experimentally verify the link existing between entanglement and the amount of wave-particle duality in a bipartite quantum system, with superconducting qubits in the IBM Q quantum computer. We consider both pure and mixed states, and study the influence of state purity on the observation of the complementarity "triality" relation of Jakob and Bergou. This work confirms the quantitative completion of local Bohr's complementarity principle by the nonlocal quantum entanglement typical of a truly bipartite quantum system.

Wave-particle duality using the Compton effect

Thought experiments based on the double-slit interferometer had a crucial role to develop ideas concerning the wave-particle duality and the Bohr's complementarity principle. Ideally, a slit with a sufficiently low mass recoils due to the passage of the photon. This motion denounces the path taken by the light and suppresses any attempt to observe an interference pattern. In real life, however, available which-way information in such a setup is significantly impaired by the typical magnitudes of photons and slits, making the verification of the effect almost impossible. Here, we extend this discussion by applying similar ideas to the Mach-Zehnder interferometer. That is, we study the consequences of the beam-splitter recoil, during the passage of the photon, over the interference pattern produced by the device. Unlike the double-slit experiment, this recoil can now be encoded in the wavelength of the photon itself, which, in principle, is more easily accessed. Fortuitously, the model used to describe the interaction between the idealized beam-splitter and the photon clearly indicates that an interferometer based on Compton's effect could be build to study wave-particle duality. We follow this hint, finding realistic experimental parameters needed to observe the trade-off between wave and corpuscular behaviors in such a modified interferometer.

Super-overdistribution

Conjoint recognition studies have revealed that episodic memory is subadditive over mutually exclusive reality states (e.g., old vs. new), which is known as overdistribution. Because overdistribution violates the additive law of probability, it has stimulated the development of quantum memory models, which implement the distinction between verbatim and gist traces of experience. Recent versions of those models treat verbatim and gist memory as incompatible knowledge states that obey the Bohr complementarity principle, which specifies that these states can only be accessed sequentially. An extreme form of subadditivity, super-overdistribution, falls out of this incompatibility assumption, and we report the first evidence of it. Super-overdistribution occurs when it is easier to remember that items belong to a subordinate reality state than to remember that they belong to a superordinate state that contains it. Quantum memory models identify conditions under which this paradoxical phenomenon should occur and the classes of items that are more vs. less likely to exhibit it. Super-overdistribution was detected in three lines of research and, as expected, was more pronounced for some classes of items than for others.

Get Rid of Nonlocality from Quantum Physics.

This paper is aimed to dissociate nonlocality from quantum theory. We demonstrate that the tests on violation of the Bell type inequalities are simply statistical tests of local incompatibility of observables. In fact, these are tests on violation of the Bohr complementarity principle. Thus, the attempts to couple experimental violations of the Bell type inequalities with “quantum nonlocality” is really misleading. These violations are explained in the quantum theory as exhibitions of incompatibility of observables for a single quantum system, e.g., the spin projections for a single electron or the polarization projections for a single photon. Of course, one can go beyond quantum theory with the hidden variables models (as was suggested by Bell) and then discuss their possible nonlocal features. However, conventional quantum theory is local.

Coherence and complementarity in state-channel interaction

While Bohr's complementarity principle constitutes a bedrock of quantum mechanics with profound implications, coherence, as a defining feature of the quantum realm originating from the superposition principle, pervades almost every quantum consideration. By exploiting the algebraic and geometric structure of state-channel interaction, we show that an information-theoretic measure of coherence and a quantitative symmetry-asymmetry complementarity emerge naturally from the formalism of quantum mechanics. This is achieved by decomposing the state-channel interaction into a symmetric part and an asymmetric part, which satisfy a conservation relation. The symmetric part is represented by the symmetric Jordan product, and the asymmetric part is synthesized by the skew-symmetric Lie product. The latter further leads to a significant extension of the celebrated Wigner--Yanase skew information, and has an operational interpretation as quantum coherence of a state with respect to a channel. This not only presents a basic and alternative framework for addressing complementarity, but also puts the study of coherence in a broad context involving channels. Fundamental properties of the symmetry-asymmetry complementarity are revealed, and applications and implications are illustrated via several prototypical channels as well as the Mach--Zehnder interferometry, in which the fringe visibility is linked to symmetry and the which-path is linked to asymmetry.

Experimental demonstration of wave-particle duality relation based on coherence measure.

Wave-particle duality is a typical example of Bohr's complementarity principle that plays a significant role in quantum mechanics. Previous studies used the visibility of an interference pattern to quantify the wave property and used path information to quantify the particle property. However, coherence is the core and basis of the interference phenomenon. If we could use coherence to characterize the wave property, the understanding of wave-particle duality would be strengthened. A recent theoretical work [ Phys. Rev. Lett.116, 160406 (2016)] found two relations between quantum coherence and path information. Here, we demonstrate the new measure of wave-particle duality based on two kinds of coherence measures quantitatively for the first time. The wave property, quantified by the coherence in the l1-norm measure and the relative entropy measure, can be obtained via tomography of the target state, which is encoded in the path degree of freedom of the photons. The particle property, quantified by the path information, can be obtained via the discrimination of detector states, which is encoded in the polarization degree of freedom of the photons. Our work may deepen people's understanding of coherence and provide a new perspective regarding wave-particle duality.

Quantum delayed-choice experiment with a single neutral atom.

We present a proposal to implement a quantum delayed-choice (QDC) experiment with a single neutral atom, such as a rubidium or cesium atom. In our proposal, a Ramsey interferometer is adopted to observe the wave-like or particle-like behaviors of a single atom depending on the existence or absence of the second π/2-rotation. A quantum-controlled π/2-rotation on target atom is realized through a Rydberg-Rydberg interaction by another ancilla atom. It shows that a heavy neutral atom can also have a morphing behavior between the particle and the wave. The realization of the QDC experiment with such heavy neutral atoms not only is significant to understand the Bohr's complementarity principle in matter-wave and matter-particle domains but also has great potential on the quantum information process with neutral atoms.

Experimental test of Bohr's complementarity principle with single neutral atoms

An experimental test of quantum complementarity principle based on single neutral atom trapped in a blue detuned bottle trap was here performed. A Ramsey interferometer was used to assess the wavelike behavior or particle-like behavior with second $\pi/2$-rotation on or off. The wavelike behavior or particle-like behavior is characterized by the visibility $V$ of the interference or the predictability $P$ of which-path information, respectively. The measured results fulfill the complementarity relation $P^2+V^2\leq1$. Imbalance losses were deliberately introduced to the stem and find the complementarity relation is then formally "violated." All the experimental results can be completely explained theoretically by quantum mechanics without considering the interference between wave and particle behaviors. This observation complements existing information concerning the BCP based on wave-particle duality of massive quantum.

Critique of Quantum Optical Experimental Refutations of Bohr’s Principle of Complementarity, of the Wootters–Zurek Principle of Complementarity, and of the Particle–Wave Duality Relation

I argue that quantum optical experiments that purport to refute Bohr's principle of complementarity (BPC) fail in their aim. Some of these experiments try to refute complementarity by refuting the so called particle-wave duality relations, which evolved from the Wootters-Zureck reformulation of BPC (WZPC). I therefore consider it important for my forgoing arguments to first recall the essential tenets of BPC, and to clearly separate BPC from WZPC, which I will argue is a direct contradiction of BPC. This leads to a need to consider the meaning of particle-wave duality relations and to question their fundamental status. I further argue (albeit, in opposition to BPC) that particle and wave complementary concepts are on a different footing than other pairs of complementary concepts.

Duality of quantum coherence and path distinguishability

We derive a generalized wave-particle duality relation for arbitrary multipath quantum interference phenomena. Beyond the conventional notion of the wave nature of a quantum system, i.e., the interference fringe visibility, we introduce a quantifier as the normalized quantum coherence, recently defined in the framework of quantum information theory. To witness the particle nature, we quantify the path distinguishability or the which-path information based on unambiguous quantum state discrimination. Then, the Bohr complementarity principle for multipath quantum interference can be stated as a duality relation between the quantum coherence and the path distinguishability. For two-path interference, the quantum coherence is identical to the interference fringe visibility, and the relation reduces to the well-known complementarity relation. The duality relation continues to hold in the case where mixedness is introduced due to possible decoherence effects.

Can Yin-Yang Guide Chinese Indigenous Management Research?

In this article, I argue that it is misleading to dichotomize the West as being either/or and the East as being both/and. The West has thought dialectically since ancient Greece. I offer a typology to compare and contrast three dialectical or non-either/or logical systems or ways of thinking: Chinese Yin-Yang philosophy, Hegel's dialectic, and Niels Bohr's complementarity principle, as well as Aristotle's formal (either/or) logic. I show that the four logical systems have differences and similarities and show that Westerners can and do think dialectically. I also argue that Chinese Yin-Yang philosophy, while useful and powerful in some situations, is not always superior to the other logical systems and philosophies. My purpose is to alert Chinese management scholars to the dangers of overconfidence and to stimulate discussion and debate on the true value of Yin-Yang in particular and the promotion of Chinese indigenous management research in general. To that end, I present my opinion on the merits and drawbacks of Yin-Yang and posit that it may inspire but cannot guide Chinese indigenous management research because Chinese philosophy lacks a well-defined methodology and operationalizable methods.

Revisiting Bohr's principle of complementarity with a quantum device

Bohr's principle of complementarity (BPC) is the cornerstone of quantum mechanics. According to this principle, the total wavelike and particlelike information of a particle is limited by the Englert-Greenberger (EG) duality relation. Here, by introducing a quantum detecting device into the experiment, we find that the limit of the EG duality relation is exceeded because of the interference between the wave and particle properties of the photon. A generalized EG duality relation is further developed. Our work provides a generalization of BPC and gives new insights into quantum mechanics.

Experimental analysis of the quantum complementarity principle

One of the milestones of quantum mechanics is Bohr's complementarity principle. It states that a single quantum can exhibit a particle-like \emph{or} a wave-like behaviour, but never both at the same time. These are mutually exclusive and complementary aspects of the quantum system. This means that we need distinct experimental arrangements in order to measure the particle or the wave nature of a physical system. One of the most known representations of this principle is the single-photon Mach-Zehnder interferometer. When the interferometer is closed an interference pattern is observed (wave aspect of the quantum) while if it is open, the quantum behaves like a particle. Here, using a molecular quantum information processor and employing nuclear magnetic resonant (NMR) techniques, we analyze the quantum version of this principle by means of an interferometer that is in a quantum superposition of being closed and open, and confirm that we can indeed measure both aspects of the system with the same experimental apparatus. More specifically, we observe with a single apparatus the interference between the particle and the wave aspects of a quantum system.

Causalidade e teoria quântica

O desenvolvimento da teoria quântica, na primeira metade do século passado, acendeu um debate acalorado entre filósofos e físicos sobre a natureza das leis físicas e, em especial, sobre a validade do princípio de causalidade. Tendo em vista a teoria de Planck sobre a radiação, a interpretação probabilista de Max Born, as relações de incerteza de Heisenberg e o princípio de complementaridade de Bohr, muitos físicos colocaram em dúvida a causalidade clássica, cuja legitimidade parecia a princípio não mais estar assegurada no domínio quântico. O objetivo deste artigo é apresentar e discutir as diferentes posições em torno desse debate. Serão analisados, além dos argumentos levantados pelos intérpretes de Copenhague, aqueles sustentados por neopositivistas e neokantianos. Procuraremos mostrar que, a despeito dos antagonismos filosóficos, a posição adotada por Schlick nesse debate parece estar mais próxima de Cassirer do que de seu colaborador Reichenbach.

Modified Two-Slit Experiments and Complementarity

Some modified two-slit interference experiments claim to demonstrate a violation of Bohr's complementarity principle. A typical such experiment is theoretically analyzed using wave-packet dynamics. The flaw in the analysis of such experiments is pointed out and it is demonstrated that they do not violate complementarity. In addition, it is quite generally proved that if the state of a particle is such that the modulus square of the wave-function yields an interference pattern, then it necessarily loses which-path information.