Quantum optics and classical optics have coexisted for nearly a century as two distinct, self-consistent descriptions of light. What influences there were between the two domains all tended to go in one direction, as concepts from classical optics were incorporated into quantum theory's early development. But it's becoming increasingly clear that a significant quantum presence exists in classical territory-and, in particular, that the quintessential quantum attribute, entanglement, can be seen, studied and exploited in classical optics. This blurring of the classical-quantum boundary has opened up a potential new direction for frontier work in optics.
Quantum optics and classical optics have coexisted for nearly a century as two distinct, self-consistent descriptions of light. What influences there were between the two domains all tended to go in one direction, as concepts from classical optics were incorporated into quantum theory's early development. But it's becoming increasingly clear that a significant quantum presence exists in classical territory-and, in particular, that the quintessential quantum attribute, entanglement, can be seen, studied and exploited in classical optics. This blurring of the classical-quantum boundary has opened up a potential new direction for frontier work in optics.
The study of light through the centuries has produced a number of theories and experiments. Newton advanced the corpuscular theory, building on the early Greek view of matter composed of atoms. Then Young essentially proved the wave nature of light through the interference experiments. Maxwell provided the firm theoretical basis for the wave nature. During the late 1800s and early 1900s, further experiments showed predictions based on a continuous wave led to the well-known ultraviolet catastrophe. Plank and Einstein originated and developed the notion of the photon as an elementary quantum of propagating electromagnetic (EM) energy. The first half of the 20th century saw the development of the field quantization and the quantum electrodynamics (QED). Feynmann labeled QED as ‘‘the best theory we have’’ to describe the matter-light interaction. The second half of the 20th century witnessed the development of the coherent and squeezed optical states attributable to Glauber and Yuen. The study of light and electromagnetic fields has a long history. This chapter explores the nature of light in terms of quantum optics.
Quantum optics and classical optics are linked in ways that are becoming apparent as a result of numerous recent detailed examinations of the relationships that elementary notions of optics have with each other. These elementary notions include interference, polarization, coherence, complementarity and entanglement. All of them are present in both quantum and classical optics. They have historic origins, and at least partly for this reason not all of them have quantitative definitions that are universally accepted. This makes further investigation into their engagement in optics very desirable. We pay particular attention to effects that arise from the mere co-existence of separately identifiable and readily available vector spaces. Exploitation of these vector-space relationships are shown to have unfamiliar theoretical implications and new options for observation. It is our goal to bring emerging quantum–classical links into wider view and to indicate directions in which forthcoming and future work will promote discussion and lead to unified understanding.
IntroductionPhysics has always had several different domains of application in on-going development, and physicists have always striven for unification among its different domains.Unification is usually achieved through development of so-called 'covering theories'.In the nineteenth century, the stunning example was Maxwell's Electrodynamics (MED), which unified electricity and magnetism as one domain of theory.Another major domain of theory then present was Newton's Mechanics (NM), which in the eighteenth century had really launched modern physics as a mathematical discipline.At the turn of the twentieth century, NM and MED were well in place, and were fulfilling many technologically important requirements.But there seemed to be an incompatibility between them.The problem concerned their invariance with respect to choice of reference frame: NM exhibited invariance if the allowed reference frames were all connected through Galilean transformations, whereas MED exhibited invariance if the allowed reference frames were all connected through Lorentz transformations.It looked as though one of these two theories must be more nearly correct than the other, but it was not clear which one was the better one.That problem seemed resolved with the advent of Einstein's Special Relativity Theory (SRT).SRT was believed to capture the true meaning of MED concerning the behavior of light signals, and SRT was certainly an endorsement of Lorentz transformation, so SRT was believed to offer the one possible revision of NM that could make mechanics fully consistent with MED.But meanwhile, new phenomena were being discovered at the micro scale of physics, and they often seemed inexplicable with any known theory, whether NM, SRT, or MED.These were phenomena suggesting quantization of light, quantized atomic states, atomic, molecular and crystal structures, radioactivity, etc.So at almost the same time as one problem seemed to be resolved, other problems were emerging.Since the earlier situation between NM and MED had demanded that Physics allow two seemingly discordant theories to co-exist until some good argument could replace one of them, the situation then presented by the new phenomena being discovered naturally invited the development of another potentially discordant theory: Quantum Mechanics (QM).The discovery of the photoelectric effect, and the introduction of the idea of the photon, initiated QM.Almost immediately, QM was developed to handle the Hydrogen atom, and the ground state thereof, the stability of which was thought to be impossible with MED.www.intechopen.
=1, which engages concurrence (C) and polarization (P). This relationship has revealed a striking connection between two seemingly unrelated measures. Indeed, while C quantifies entanglement, which is widely seen as a quantum information resource, P quantifies the amount of coherence between optical field components. We discuss the conditions under which C and P may be related to one another and show how the optical approach discloses entanglement as a resource that may be found in both the quantum and the classical domain. This is confirmed by a proposed Bell violation that can be exhibited using either quantum or classical light.
As quantum computing approaches the threshold where certain tasks demonstrably outpace their classical machines, the need for a precise, clear, consensus-driven definition of quantum advantage becomes essential. Rapid progress in the field has blurred this term across companies, architectures, and application domains. Here, we aim to articulate an operational definition for quantum advantage that is both platform-agnostic and empirically verifiable. Building on this framework, we highlight the algorithmic families most likely to achieve early advantage. Finally, we outline our vision for the near future, in which quantum computers enhance existing high-performance computing platforms, enabling new frontiers in chemistry, materials discovery, optimization, and beyond.
The similarities between quantum mechanics and paraxial optics were already well-known to the founding fathers of quantum mechanics; indeed knowledge of paraxial optics partly informed quantum mechanics as a wave theory. Likewise quantum mechanical methods have been employed to better understand optics, for example, to determine which optical transformations are in principle realisable and which not. Recently the notion of classical entanglement has been mooted, ushering in a new avenue to explore, perhaps bridging the classical-quantum divide. These developments have raised questions as to which quantum tasks could be implemented with classical light, taking advantage of the wealth of four centuries of experience in optics. In this article we review the similarities as well as differences between optics and quantum mechanics, providing a quantum notation for classical light. We review the evidence for cross-fertilisation between quantum mechanics and classical optics, in particular considering the issue of classical entanglement and its exploitation for quantum tasks. Our work provides a concise theoretical framework punctuated with relevant examples, and critically assesses the current state of the field and its limits.