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John Bell and the Great Enterprise
Get PDFI outline Bell's vision of the "great enterprise" of science, and his view that conventional teachings about quantum mechanics constituted a betrayal of this enterprise. I describe a proposal of his to put the theory on a more satisfactory footing, and review the subsequent uses that have been made of one element of this proposal, namely Bell's transition probabilities regarded as fundamental physical processes.Quanta 2018; 7: 68–73
Quantum Mechanics and Global Determinism
Get PDFIt is proposed that certain features of quantum mechanics may be perspectival effects, which arise because experiments performed on locally accessible variables can only uncover a certain subset of the correlations exhibited by an underlying deterministic theory. This hypothesis is used to derive the no-signaling principle, thus resolving an open question regarding the apparently fine-tuned nature of quantum correlations. Some potential objections to this approach are then discussed and answered.Quanta 2018; 7: 40–53
A Quantum Implementation Model for Artificial Neural Networks
Get PDFThe learning process for multilayered neural networks with many nodes makes heavy demands on computational resources. In some neural network models, the learning formulas, such as the Widrow–Hoff formula, do not change the eigenvectors of the weight matrix while flatting the eigenvalues. In infinity, these iterative formulas result in terms formed by the principal components of the weight matrix, namely, the eigenvectors corresponding to the non-zero eigenvalues. In quantum computing, the phase estimation algorithm is known to provide speedups over the conventional algorithms for the eigenvalue-related problems. Combining the quantum amplitude amplification with the phase estimation algorithm, a quantum implementation model for artificial neural networks using the Widrow–Hoff learning rule is presented. The complexity of the model is found to be linear in the size of the weight matrix. This provides a quadratic improvement over the classical algorithms.Quanta 2018; 7: 7–18
An Invitation to Quantum Channels
Get PDFOpen quantum systems have become an active area of research, owing to its potential applications in many different fields ranging from computation to biology. Here, we review the formalism of dynamical maps used to represent the time evolution of open quantum systems and discuss the various representations and properties of the same, with many examples.Quanta 2018; 7: 54–67
Biphoton Interference in a Double-Slit Experiment
Get PDFA double-slit experiment with entangled photons is theoretically analyzed. It is shown that, under suitable conditions, two entangled photons of wavelength λ can behave like a biphoton of wavelength λ/2. The interference of these biphotons, passing through a double-slit can be obtained by detecting both photons of the pair at the same position. This is in agreement with the results of an earlier experiment. More interestingly, we show that even if the two entangled photons are separated by a polarizing beam splitter, they can still behave like a biphoton of wavelength λ/2. In this modified setup, the two separated photons passing through two different double-slits, surprisingly show an interference corresponding to a wavelength λ/2, instead of λ which is the wavelength of each photon. We point out two experiments that have been carried out in different contexts, which saw the effect predicted here without realizing this connection.Quanta 2018; 7: 1–6
Schrödinger's Cat: Where Does The Entanglement Come From?
No full textSchrödinger's cat is one of the most striking paradoxes of quantum mechanics that reveals the counterintuitive aspects of the microscopic world. Here, I discuss the paradox in the framework of quantum information. Using a quantum networks formalism, I analyse the information flow between the atom and the cat. This reveals that the atom and the cat are connected only through a classical information channel: the detector clicks → the poison is released → the cat is killed. No amount of local operations and classical communication can entangle the atom and the cat, which are initially in a separable state. This casts a new light on the paradox.Quanta 2017; 6: 57–60
Hanbury Brown–Twiss Effect with Wave Packets
Get PDFThe Hanbury Brown–Twiss (HBT) effect, at the quantum level, is essentially an interference of one particle with another, as opposed to interference of a particle with itself. Conventional treatments of identical particles encounter difficulties while dealing with entanglement. A recently introduced label-free approach to indistinguishable particles is described, and is used to analyze the HBT effect. Quantum wave-packets have been used to provide a better understanding of the quantum interpretation of the HBT effect. The effect is demonstrated for two independent particles governed by Bose–Einstein or Fermi–Dirac statistics. The HBT effect is also analyzed for pairs of entangled particles. Surprisingly, entanglement has almost no effect on the interference seen in the HBT effect. In the light of the results, an old quantum optics experiment is reanalyzed, and it is argued that the interference seen in that experiment is not a consequence of non-local correlations between the photons, as is commonly believed.Quanta 2017; 6: 61–69
Erwin Schrödinger and Quantum Wave Mechanics
Get PDFThe fathers of matrix quantum mechanics believed that the quantum particles are unanschaulich (unvisualizable) and that quantum particles pop into existence only when we measure them. Challenging the orthodoxy, in 1926 Erwin Schrödinger developed his wave equation that describes the quantum particles as a packet of quantum probability amplitudes evolving in space and time. Thus, Schrödinger visualized the unvisualizable and lifted the veil that has been obscuring the wonders of the quantum world.Quanta 2017; 6: 48–52
Quantum Mechanics and Liouville's Equation
Get PDFIn non-relativistic quantum mechanics, the absolute square of Schrödinger's wave function for a particle in a potential determines the probability of finding it either at a position or momentum at a given time. In classical mechanics the corresponding problem is determined by the solution of Liouville's equation for the probability density of finding the joint position and momentum of the particle at a given time. Integrating this classical solution over either one of these two variables can then be compared with the probability in quantum mechanics. For the special case that the force is a constant, it is shown analytically that for an initial Gaussian probability distribution, the solution of Liouville's integrated over momentum is equal to Schrödinger's probability function in coordinate space, provided the coordinate and momentum initial widths of this classical solution satisfy the minimal Heisenberg uncertainty relation. Likewise, integrating Lioville's solution over position is equal to Schrödinger's probability function in momentum space.Quanta 2017; 6: 53–56
Quantum Cryptography: Key Distribution and Beyond
Get PDFUniquely among the sciences, quantum cryptography has driven both foundational research as well as practical real-life applications. We review the progress of quantum cryptography in the last decade, covering quantum key distribution and other applications.Quanta 2017; 6: 1–47