Entanglement of two or more quantum objects is a process whereby the quantum mechanical wavefunctions describing these individual objects are manipulated to create a new, interwoven state comprising a superposition of the individual wavefunctions. In this entangled system, all of the objects are correlated, and measuring the state of just one of them gives information on all of the others. Such a property is useful both for probing fundamental questions in quantum mechanics and for developing quantum computers. As the number of objects entangled increases, the superposed state becomes more complex, but exponentially more powerful.
Entanglement of two or more quantum objects is a process whereby the quantum mechanical wavefunctions describing these individual objects are manipulated to create a new, interwoven state comprising a superposition of the individual wavefunctions. In this entangled system, all of the objects are correlated, and measuring the state of just one of them gives information on all of the others. Such a property is useful both for probing fundamental questions in quantum mechanics and for developing quantum computers. As the number of objects entangled increases, the superposed state becomes more complex, but exponentially more powerful.
After quantum particles have interacted, they generally remain in an entangled state and are correlated at a distance by quantum-mechanical links that can be used to transmit and process information in nonclassical ways. This implies programmable sequences of operations to generate and analyze the entanglement of complex systems. We have demonstrated such a procedure for two atoms and a single-photon cavity mode, engineering and analyzing a three-particle entangled state by a succession of controlled steps that address the particles individually. This entangling procedure can, in principle, operate on larger numbers of particles, opening new perspectives for fundamental tests of quantum theory.
One of the most intriguing features of quantum mechanics is the existence of entangled states. These states result from the superposition of individual quantum states in composite systems, such as a collection of particles, and cannot be expressed as a product of the individual states. The generation and manipulation of entangled states is fundamental to studies of the most basic aspects of quantum mechanics, and provides the basis of applications such as quantum computing, quantum communications and high-precision spectroscopy.
In this chapter, we will discuss the central topic in the current quantum optics studies, that is, entanglement. We focus mostly on the problem of creation of entanglement between two atoms and address the question how one could create multi-atom entangled states. The term entanglement, one of themost intriguing properties of multi-particle systems, was introduced by Schro¨dinger in his discussions of the foundations of quantum mechanics. It describes a multi-particle system that has the astonishing property that the results of a measurement on one particle cannot be specified independently of the results of measurements on the other particles. Although entangled systems can be physically separated, they can no longer be considered as independent, even when they are very far from one another. Entanglement is not only at the heart of the distinction between quantum and classical mechanics, but is now regarded to be a resource central to the development of quantum technologies ranging from quantum information, quantum cryptography, teleportation and quantum computation to atomic and molecular spectroscopy. These practical implementations all stem from the realization that we may control and manipulate quantum systems at the level of single atoms and photons to store information and transfer the information between distant systems in a controlled way and with high fidelity. This field of study is a relatively new one, and considerable research activity is taking place at present. The most active ones are the studies of practical schemes for creation of entanglement between trapped atoms or ions [91, 94].
After they have interacted, quantum particles generally behave as a single nonseparable entangled system. The concept of entanglement plays an essential role in quantum physics. We have performed entanglement experiments with Rydberg atoms and microwave photons in a cavity and tested quantum mechanics in situations of increasing complexity. Entanglement resulted either from a resonant exchange of energy between atoms and the cavity field or from dispersive energy shifts affecting atoms and photons when they were not resonant. With two entangled particles (two atoms or one atom and a photon), we have realized new versions of the Einstein-Podolsky-Rosen situation. The detection of one particle projected the other, at a distance, in a correlated state. This process could be viewed as an elementary measurement, one particle being a ``meter'' measuring the other. We have performed a ``quantum nondemolition'' measurement of a single photon, which we detected repeatedly without destroying it. Entanglement is also essential to understand decoherence, the process accounting for the classical appearance of the macroscopic world. A mesoscopic superposition of states (``Schr\"odinger cat'') gets rapidly entangled with its environment, losing its quantum coherence. We have prepared a Schr\"odinger cat made of a few photons and studied the dynamics of its decoherence, in an experiment which constitutes a glimpse at the quantum/classical boundary. We have also investigated entanglement as a resource for the processing of quantum information. By using quantum two-state systems (qubits) instead of classical bits of information, one can perform logical operations exploiting quantum interferences and taking advantage of the properties of entanglement. Manipulating as qubits atoms and photons in a cavity, we have operated a quantum gate and applied it to the generation of a complex three-particle entangled state. We finally discuss the perspectives opened by these experiments for further fundamental studies.
Quantum entanglement, a cornerstone of quantum mechanics, holds immense potential for revolutionizing computation. This paper explores the application of quantum entanglement to expand state computation, aiming to develop novel methods for solving complex problems with enhanced computational power. We outline a core mechanism leveraging entanglement to generate and manipulate extended quantum states, culminating in the derivation of physical properties through this process. The research focuses on utilizing entanglement's inherent non-classical properties to overcome limitations of conventional quantum algorithms. This work presents a fundamentally new approach to quantum state computation, offering a pathway towards potentially transformative advancements in quantum information processing.
Present-day computers work on the principles of classical mechanics. Imagine a coin in the classical regime. When we toss the coin, it can take up either of these two states: “head” (H) or “tail” (T). However, in a quantum world, a coin, or rather a quantum one, can exist in both the states “head” and “tail” simultaneously. This property of quantum mechanical objects—existing in multiple states simultaneously—is known as superposition . Similarly, quantum mechanical objects can exhibit a much stronger correlation than their classical counterparts through the phenomenon of entanglement . Using entanglement, two or more quantum particles can be linked in perfect unison, even when they are placed at opposite ends of the universe. Quantum computing harnesses and exploits the laws of quantum mechanics, especially superposition, entanglement, and interference, to process information. An important idea in quantum computing is to collapse a probability distribution toward specific measurement states. Quantum interference is a by-product of quantum superposition, and it helps bias quantum measurement toward specific quantum states.