Since the seminal paper published by Albert Einstein, Boris Podolski and Nathan Rosen in 1935, and the famous series of papers published by Erwin Schrödinger in the years 1935 and 1936, entanglement has occupied a central position in quantum physics. This peculiar phenomenon has posed formidable challenges to several generations of physicists. In fact, it took about 30 years since the 1935 papers for the first mathematical consequence of this property to be demonstrated by John S. Bell and a...
Since the seminal paper published by Albert Einstein, Boris Podolski and Nathan Rosen in 1935, and the famous series of papers published by Erwin Schrödinger in the years 1935 and 1936, entanglement has occupied a central position in quantum physics. This peculiar phenomenon has posed formidable challenges to several generations of physicists. In fact, it took about 30 years since the 1935 papers for the first mathematical consequence of this property to be demonstrated by John S. Bell and a...
The famously controversial 1935 paper by Einstein, Podolsky, and Rosen (EPR) took aim at the heart of the flourishing field of quantum mechanics. The paper provoked responses from the leading theoretical physicists of the day, and brought entanglement and nonlocality to the forefront of discussion. This book looks back at the seminal year in which the EPR paper was published and explores the intense debate it unleashed. These conversations in print and in private correspondence offer significant insight into the minds of pioneering quantum physicists including Niels Bohr, Erwin Schrödinger and Albert Einstein himself. Offering the most complete collection of sources to date – many published or translated here for the first time – this text brings a rich new context to this pivotal moment in physics history. Both researchers and students in the history and philosophy of science, and enthusiasts alike, will find this book illuminating.
How it all began In 1935, a decade after the invention of quantum theory by Heisenberg (1925) and Schrödinger (1926), three papers appeared, setting the stage for a new concept, quantum entanglement. The previous decade had already seen momentous discussions on the meaning of the new theory, for example by Niels Bohr (see his contribution to Albert Einstein: Philosopher-Scientist in Further reading); but these new papers opened up the gates for a new, very deep philosophical debate about the nature of reality, about the role of knowledge, and about their relation. Since the 1970s, it has become possible for experimenters to observe entanglement directly in the laboratory and thus test the counter-intuitive predictions of quantum mechanics whose confirmation today is beyond reasonable doubt. Since the 1990s, the conceptual and experimental developments have led to new concepts in information technology, including such topics as quantum cryptography, quantum teleportation, and quantum computation, in which entanglement plays a key role. In the first of the three papers, Einstein, Podolsky, and Rosen (EPR) realized that, if two particles had interacted in their past, their properties will remain connected in the future in a novel way, namely, observation on one determines the quantum state of the other, no matter how far away. Their conclusion was that quantum mechanics is incomplete and they expressed their belief that a more complete theory may be found. Niels Bohr replied that the two systems may never be considered independent of each other, and observation on one changes the possible predictions on the other. Finally, Erwin Schrödinger, in the paper which also proposed his famous cat paradox, coined the term “entanglement” (in German Verschränkung ) for the new situation and he called it “not one, but the essential trait of the new theory, the one which forces a complete departure from all classical concepts.”
In 1935, Albert Einstein, Boris Podolsky and Nathan Rosen (EPR) published a thought experiment that is entirely correct, has been demonstrated in real experiments, and is now the most famous in quantum physics. Their pioneering work described, for the first time, quantum correlations and can be regarded as a very early glimpse into today's 'deep' quantum technologies, by which I mean those that enhance functionality by making use of quantum correlations. However, their work also contains a paradox that Erwin Schroedinger had already recognised as such in 1935 and which has since been cemented by the so-called Bell experiments. Here, I am now able to pinpoint the origin of the paradox within the chain of reasoning, which ultimately resolves the paradox.
Entanglement, according to the Austrian physicist Erwin Schrödinger the Essence of Quantum Mechanics, has been known for a long time now to be the source of a number of paradoxical and counterintuitive phenomena. Of those the most remarkable one is usually called non-locality and it is at the heart of the Einstein-Podolsky-Rosen Paradox and of the fact that Quantum Mechanics violates Bell’s inequalities. Recent years saw an emergence of novel ideas in entanglement of three or more particles. Most recently it turned out that entanglement is an important concept in the development of quantum communication, quantum cryptography and quantum computation. First explicit experimental realizations with two or more photons include quantum dense coding and quantum teleportation.
In Section 2.4 we learned that a composite quantum system, composed of two subsystems A and B , is associated with a tensor product space HA ? HB . Composite quantum systems have already played an important role in many instances in this text, especially in open systems and measurement models. In this chapter we dive deeper into tensor product spaces, discovering some strange implications of the quantum theory of composite quantum systems. As a result of its tensor product structure, quantum theory has embedded into it the phenomenon of entanglement , which is often seen as the foremost quantum feature. As early as in 1935 it puzzled Erwin Schrödinger, who introduced the German term Verschränkung [127] and Albert Einstein, who, together with Boris Podolski and Nathan Rosen, used the specific example of an entangled state to argue that quantum theory is incomplete [58]. In the 1960s John Bell demonstrated that the consequences of entanglement are incompatible with the Einstein– Podolsky–Rosen model of local realism [11], [12]. In recent years entanglement has been recognized as the resource for quantum information processing. Nowadays entanglement theory is a highly developed subject, and we can present only the mathematical basics. For the reader with a deeper interest in entanglement we recommend the recent reviews by Horodecki et al . [80] and Plenio et al . [118], which also cover the quantum information aspects of entanglement. To simplify our discussion we will assume that the Hilbert spaces are finite dimensional.
Expository paper providing a historical survey of the gradual transformation of the "philosophical discussions" between Bohr, Einstein and Schrödinger on foundational issues in quantum mechanics into a quantitative prediction of a new quantum effect, its experimental verification and its proposed (and loudly advertised) applications. The basic idea of the 1935 paper of Einstein-Podolsky-Rosen (EPR) was reformulated by David Bohm for a finite dimensional spin system. This allowed John Bell to derive his inequalities that separate the prediction of quantum entanglement from its possible classical interpretation. We reproduce here their later (1971) version, reviewing on the way the generalization (and mathematical derivation) of Heisenberg's uncertainty relations (due to Weyl and Schrödinger) needed for the passage from EPR to Bell. We also provide an improved derivation of the quantum theoretic violation of Bell's inequalities. Soon after the experimental confirmation of the quantum entanglement (culminating with the work of Alain Aspect) it was Feynman who made public the idea of a quantum computer based on the observed effect.