The stories about teleportation did sound to me like a horrible monster that was growing while walking through the cities. Everyone who knew that Walter and I were opposed to the idea of instantaneous influences at a distance told us that quantum teleportation was now proven and that it demonstrated clearly the existence of influences at a distance. My usual response was that quantum theory had some very great successes with predicting the precise energies of electrons in atoms. The experiments relating to quantum information such as the EPRB-type experiments and the so-called teleportation did not agreewith quantum theorywith such precision but only approximately. Furthermore, asmentioned, I soon convinced myself that the idea of quantum teleportation assumes that Bell is correct and influences at a distance do exist.We thus have another logical circle. Quantum teleportation is only then something remarkable if influences at a distance are assumed to exist on the basis of Bell’s work to start with. Experiments are explained using this assumption and then, because of a very approximate agreement of the experiments with the quantum predictions, it is claimed that teleportation has been proven. Here are the actual facts startingwith the concept of a quantum computer.
The stories about teleportation did sound to me like a horrible monster that was growing while walking through the cities. Everyone who knew that Walter and I were opposed to the idea of instantaneous influences at a distance told us that quantum teleportation was now proven and that it demonstrated clearly the existence of influences at a distance. My usual response was that quantum theory had some very great successes with predicting the precise energies of electrons in atoms. The experiments relating to quantum information such as the EPRB-type experiments and the so-called teleportation did not agreewith quantum theorywith such precision but only approximately. Furthermore, asmentioned, I soon convinced myself that the idea of quantum teleportation assumes that Bell is correct and influences at a distance do exist.We thus have another logical circle. Quantum teleportation is only then something remarkable if influences at a distance are assumed to exist on the basis of Bell’s work to start with. Experiments are explained using this assumption and then, because of a very approximate agreement of the experiments with the quantum predictions, it is claimed that teleportation has been proven. Here are the actual facts startingwith the concept of a quantum computer.
I was very enthusiastic about our findings and wanted to publish them in a prestigious journal. I knew that this was not going to be easy, because neither Walter nor I were known experts in this particular area of mathematical physics, and any referee who saw that we tried to refute Bell would probably have a negative reaction to it. This is why I called my friend Federico Capasso and asked him to help. I had known Federico since many years. He was one of the top researchers at Bell Laboratories and now professor of applied physics at Harvard. Federico and I had hadmany spirited discussions about research topics and had become very good friends. Federico’s research area is solid state physics. He is a great expert in the area of light detectors, including the photodetectors that are used in the EPRB experiments, and he is the “father” of the quantum cascade laser. He knew about EPRB experiments and the Bell theorem. He also knew that I would not be calling him if I was not convinced about having important results. After presenting my case, I asked Federicowhether hewould, as amember of the National Academy of Sciences, sponsor a paper for PNAS, the proceedings of this National Academy and a very prestigious journal. I was at that time not yet a member of the academy myself. Any member of the academy could communicate annually a small number of papers to PNAS, determine the referees, and be involved in the publication process in the role of a guest editor. If the referee reports were good, such a paper would be printed with very high probability. For academymembers, this was a wonderful way to publish their own research and also to sponsor deserving research of young scientists as well as research on somewhat risky but highly interesting topics.
This work is the result of the research which I started independently late in the 60s in Russia and since August 1992 have proceeded with abroad. The subject of the research was initially chosen to be Systems Theory, because it seemed rather close to the theory of communications, the then field of my occupation, on the one hand, and because it sounded intriguing enough and worth attempting at, on the other. But there was no idea of how and where to start the research, and it was decided to begin with the simplest type of system – a linear system.
The first step proved rather successful: there was found quite an elegant solution of the problem, imagined by myself, of determining the functional complexity of linear systems by their characteristics. That work was published in the 1969, No.2, issue of the Transactions of the Research Institute of Radio (Moscow) where I worked then. Although it was unclear how to proceed with that result, there was a vague indication in it to some connection between the abstract theory of linear systems and statistical physics, which seemed promising.
To make that puzzle out, I set off to supplement my knowledge of theoretical physics, and soon the above indication became more articulate: there is indeed some deep connection between the problem of the synthesis of linear systems and quantum mechanics. Intrigued by that clue, I attempted for several years to apply the solutions of Schroedinger’s-like equations, with the potential determined by characteristics of the system, to its synthesis. However, the results were unsatisfactory: something essential was missing in comprehending both the objects of theoretical physic and linear systems.
The solution came suddenly from where nobody could have expected it - from philosophy. Looking once through Hegel’s works, I was struck by a strangely close analogy between the conceptions of duality in dialectical logic and particle physics. That revelation triggered another stage of self-education, this time in dialectical philosophy. As a result, there arose conviction that Hegel's dialectical logic is actually the
general theory of systems sought for, but the philosopher’s peculiar way of thinking and the extremely abstract language of that his work made its interpretation in scientific terms almost impossible, with the exception of some most simple cases. So I had no choice but to endeavor my own interpretation of the dialectical logic, on the one hand, and, simultaneously, a revision of some theories and principles of theoretical physics in accordance with that logic, on the other hand, which eventually resulted in the theory expounded in this book. The first rough results, such as the existence of ether, its composition and the phenomenon of spontaneous generation of neutrons in it, were achieved early in the 80s, but it took me about fifteen years more to complete this research in a sufficiently adequate and convincing form.
The academic research into entanglement nicely illustrates the interplay between fundamental science and applications, and the need to foster both aspects to advance either one. For instance, the possibility to distribute entangled photons over tens or even hundreds of kilometers is fascinating because it confirms the quantum predictions over large distances, while quantum theory is often presented to apply to the very small (see Figure 1). On the other hand, entanglement enables quantum key distribution (QKD) [1]. This most advanced application of quantum information processing allows one to distribute cryptographic keys in a provably secure manner. For this, one merely has to measure the two halves of an entangled pair of photons. Surprisingly, and being of both fundamental and practical interest, the use of entanglement removes even the necessity for trusting most equipment used for the measurements [5]. Furthermore, entanglement serves as a resource for quantum teleportation (see Figure 2) [1]. In turn, this provides a tool for extending quantum key distribution to arbitrarily large distances and building large-scale networks that connect future quantum computers and atomic clocks [6]. In the following, we describe the counter-intuitive properties of entangled particles as well as a few recent experiments that address fundamental and applied aspects of quantum teleportation. While a lot of work is being done using different quantum systems, including trapped ions, color centers in diamond, quantum dots, and superconducting circuits, we will restrict ourselves to experiments involving photons due to their suitability for building future quantum networks.
Introduction When I was a student I had much difficulty with quantum mechanics. It was comforting to find that even Einstein had had such difficulties for a long time. Indeed they had led him to the heretical conclusion that something was missing in the theory: ‘I am, in fact, rather firmly convinced that the essentially statistical character of contemporary quantum theory is solely to be ascribed to the fact that this (theory) operates with an incomplete description of physical systems.’ More explicitly, in ‘a complete physical description, the statistical quantum theory would … take an approximately analogous position to the statistical mechanics within the framework of classical mechanics …’. Einstein did not seem to know that this possibility, of peaceful coexistence between quantum statistical predictions and a more complete theoretical description, had been disposed of with great rigour by J. von Neumann. I myself did not know von Neumann's demonstration at first hand, for at that time it was available only in German, which I could not read. However I knew of it from the beautiful book by Born, Natural Philosophy of Cause and Chance , which was in fact one of the highlights of my physics education. Discussing how physics might develop Born wrote: ‘I expect … that we shall have to sacrifice some current ideas and to use still more abstract methods. However these are only opinions.