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Quantum entanglement in the double slit experiment with qubit which-path detectors

Johannes Kirchner

Published Jan 1, 2015• 0 citations
OpenAlex

Abstract

After reviewing basic concepts and tools in order to quantify entanglement, a theoretical set up is proposed, which is based on the double slit experiment and the Mach-Zehnder interferometer. A particle, which is in a superposition of two paths, can interfere with a qubit on each path before it is scattered by a beam splitter and measured by two separate detectors. After a detailed investigation, it can be shown that it is possible to induce entanglement to the qubits via post-selection. This means that the measurement does not induce entanglement, but can be used to select the entangled qubits after a number of iterations. A remarkable result is, that this works independently from the probability of interaction between the particle and the qubits, which could turn out be very beneficial in a possible realization of the set up.

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Cambridge University Press eBooks•Mar 25, 2010•0 citations
After reviewing basic concepts and tools in order to quantify entanglement, a theoretical set up is proposed, which is based on the double slit experiment and the Mach-Zehnder interferometer. A particle, which is in a superposition of two paths, can interfere with a qubit on each path before it is scattered by a beam splitter and measured by two separate detectors. After a detailed investigation, it can be shown that it is possible to induce entanglement to the qubits via post-selection. This means that the measurement does not induce entanglement, but can be used to select the entangled qubits after a number of iterations. A remarkable result is, that this works independently from the probability of interaction between the particle and the qubits, which could turn out be very beneficial in a possible realization of the set up.
Abstract The Mach–Zehnder interferometer experiment described earlier shows why and how quantum mechanics is different from classical mechanics. A photon sent through a beam splitter behaves like a particle when it is observed by only one of the two detectors. When two beam splitters are used, the photon “interferes with itself” and behaves like a wave. This is the so-called wave-particle duality of quantum mechanics which leads to quantum entanglement. This chapter discusses quantum superpositions when two or more particles are present. Understanding and analysing entanglement is one of the most interesting directions in the field of quantum information. First, a historical background of quantum entanglement is given, followed by a discussion on Bell's inequalities, separable states that do not violate Bell's inequalities, pure states that violate Bell's inequalities, mixed states that do not violate Bell's inequalities, and entanglement in second quantisation.
It is generally believed that the “mystery” behind understanding Quantum Mechanics (QM) and the global drives to construct quantum computers using “Entanglement”, can be understood from how the two-beam superposition effect (SE) emerges out of a 2-slit, and a Mach-Zehnder Interferometer (MZI). This chapter rehabilitates the classical analyses of these two superposition effects, while exploiting functional asymmetries, either deliberately introduced or intrinsic in the two-beam apparatuses. We are using mathematical formalism already well-established in classical optics since 1800’s, but with the extra emphasis that any final data generation requires some real physical interaction between the detector and the two light signals simultaneously stimulating the detecting molecules. This critical step of physical interaction process is not explicitly underscored by either the classical or the quantum physics. However, the asymmetry, either in the propagation or in the interaction process, is utilized to bring out the contradictions with the QM interpretations. For the 2-slit system, we deliberately introduce asymmetry on one of the slits. For MZI, the asymmetry is already built into the classical reflection property of a typical beams splitter.
Double-double-slit thought experiment provides profound insight on interference of quantum entangled particles. This paper presents a detailed experimental realisation of quantum double-double-slit thought experiment with momentum entangled photons and theoretical analysis of the experiment. Experiment is configured in such a way that photons are path entangled and each photon can reveal the which-slit path information of the other photon. As a consequence, single photon interference is suppressed. However, two-photon interference pattern appears if locations of detection of photons are correlated without revealing the which-slit path information. It is also shown experimentally and theoretically that two-photon quantum interference disappears when the which-slit path of a photon in the double-double-slit is detected.
Over the past several decades, single photon-based path interference in double-slit experiment has been well demonstrated for the particle nature of photons satisfying complementarity theory, where the quantum mechanical interpretation of the single photon interference fringe is given by Born rule for complex amplitudes in measurements. Unlike most conventional methods using entangled photon pairs, here, a classical coherent light source is directly applied for the proof of the same self-interference phenomenon. Instead of double slits, we use a Mach-Zehnder interferometer as usual, where the resulting self-interference fringe of coherent single photons is exactly the same as that of the coherent photon ensemble of the laser, demonstrating that the classical coherence based on the wave nature is rooted in the single photon self-interference. This unexpected result seems to contradict our common understanding of decoherence phenomena caused by multi-wave interference among bandwidth distributed photons in coherence optics.
A 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.
The photon in the interferometer This chapter introduces many of the ideas of quantum theory by exploring three specific “case studies” of quantum systems. Each is an example of a qubit , a generic name for the simplest type of quantum system. The concepts we develop will be incorporated into a rigorous mathematical framework in the next chapter. Our business here is to provide some intuition about why that mathematical framework is reasonable and appropriate for dealing with the quantum facts of life. Interferometers In Section 1.2 we discussed the two-slit interference experiment with a single photon. In that experiment, the partial waves of probability amplitude were spread throughout the entire region of space beyond the two slits. It is much easier to analyze the situation in an interferometer , an optical apparatus in which the light is restricted to a finite number of discrete beams . The beams may be guided from one point to another, split apart or recombined as needed, and when two beams are recombined into one, the result may show interference effects. At the end of the interferometer, one or more sensors can measure the intensity of various beams. (A beam is just a possible path for the light, so there is nothing paradoxical in talking about a beam of zero intensity.) Figure 2.1 shows the layout of a Mach–Zehnder interferometer , which is an example of this kind of apparatus.