Lack of understanding of the ideas of quantum physics leads to the fact that the very word "quantum" begins to be perceived as a synonym for something mysterious, incomprehensible, and even doubtful. The arising errors sometimes lead to inadequate media coverage of the development of quantum technologies, as the case with the ignorant reaction of the press in June 2016 to the statement of the Russian authorities about the prospects of quantum teleportation, which some media presented as teleportation from science fiction. Such misunderstandings can impede the formation of the necessary trust in quantum technologies on the part of the business community, politicians and the public. In part, the reason for this state of the art may be the insufficient attention of physicists themselves to the development of popular scientific and pedagogical discourse, which makes it possible to correctly introduce the ideas of quantum mechanics into the context of general culture. For decades, physicists have flaunted the kind of esotericism of quantum mechanics. Journalists love to quote the classics of quantum physics: “Those who are not shocked when they first come across quantum theory cannot possibly have understood it” (Niels Bohr); “I think I can safely say that nobody understands quantum mechanics” (Richard Feynman); “Quantum mechanics is absolutely meaningless” (Roger Penrose) [1]. Indeed, for many quantum-scale phenomena, no analogues have yet been found in the everyday world, and they are difficult to express in our everyday language. As a result, the introduction to quantum mechanics begins with a description of the mathematical formalism, which becomes an obstacle for the untrained listener and is not suitable for popularization. Moreover, such an approach creates problems for physicists themselves: many of them, studying the mathematical formalism of quantum mechanics and being convinced in practice of its effectiveness, do not ask the question of how the founders of this science were able to go in the opposite direction and, starting from experience, find the required formalism. As a result, important problematic and heuristic aspects of the development of science may drop off even professional physicists’ radar. In view of the above, an important task is to find effective explanatory techniques that allow one to talk about quantum phenomena without resorting to mathematical apparatus and without abuse of doubtful metaphors. This article attempts to find such an approach to explaining quantum cryptography. The choice in its favor is determined by the fact that it is one of the most mature quantum technologies of the second generation, which is already beginning to generate a demand for technical specialists to set up and maintain secure quantum communication lines. This activity requires a general understanding of the ideas of quantum mechanics underlying the technology, but at the same time, it does not require full knowledge of the mathematical apparatus that is used in research and development. In accordance with this, the task was set to outline the principle of quantum cryptography without resorting to such abstract concepts as the state space of a quantum system, its bases and the choice between them in quantum measurement. In a popular scientific sense, the advantage of quantum cryptography is a simplicity for understanding. Our experience shows that its main points can be explained to students in about half an hour without extraordinary mental effort. It is also enigmatical and fascinating, since, on the one hand, it is associated with spy codes, and on the other hand, it provides protection based on the laws of nature. Methodologically, the positive aspect of quantum cryptography is valuable. Many fundamental premises of quantum physics are negative: the impossibility of making any measurement without affecting the system, the Heisenberg uncertainty principle, the nocloning theorem. At the same time, quantum cryptography, on the contrary, allows an absolutely secure distribution of the encryption key.
Lack of understanding of the ideas of quantum physics leads to the fact that the very word "quantum" begins to be perceived as a synonym for something mysterious, incomprehensible, and even doubtful. The arising errors sometimes lead to inadequate media coverage of the development of quantum technologies, as the case with the ignorant reaction of the press in June 2016 to the statement of the Russian authorities about the prospects of quantum teleportation, which some media presented as teleportation from science fiction. Such misunderstandings can impede the formation of the necessary trust in quantum technologies on the part of the business community, politicians and the public. In part, the reason for this state of the art may be the insufficient attention of physicists themselves to the development of popular scientific and pedagogical discourse, which makes it possible to correctly introduce the ideas of quantum mechanics into the context of general culture. For decades, physicists have flaunted the kind of esotericism of quantum mechanics. Journalists love to quote the classics of quantum physics: “Those who are not shocked when they first come across quantum theory cannot possibly have understood it” (Niels Bohr); “I think I can safely say that nobody understands quantum mechanics” (Richard Feynman); “Quantum mechanics is absolutely meaningless” (Roger Penrose) [1]. Indeed, for many quantum-scale phenomena, no analogues have yet been found in the everyday world, and they are difficult to express in our everyday language. As a result, the introduction to quantum mechanics begins with a description of the mathematical formalism, which becomes an obstacle for the untrained listener and is not suitable for popularization. Moreover, such an approach creates problems for physicists themselves: many of them, studying the mathematical formalism of quantum mechanics and being convinced in practice of its effectiveness, do not ask the question of how the founders of this science were able to go in the opposite direction and, starting from experience, find the required formalism. As a result, important problematic and heuristic aspects of the development of science may drop off even professional physicists’ radar. In view of the above, an important task is to find effective explanatory techniques that allow one to talk about quantum phenomena without resorting to mathematical apparatus and without abuse of doubtful metaphors. This article attempts to find such an approach to explaining quantum cryptography. The choice in its favor is determined by the fact that it is one of the most mature quantum technologies of the second generation, which is already beginning to generate a demand for technical specialists to set up and maintain secure quantum communication lines. This activity requires a general understanding of the ideas of quantum mechanics underlying the technology, but at the same time, it does not require full knowledge of the mathematical apparatus that is used in research and development. In accordance with this, the task was set to outline the principle of quantum cryptography without resorting to such abstract concepts as the state space of a quantum system, its bases and the choice between them in quantum measurement. In a popular scientific sense, the advantage of quantum cryptography is a simplicity for understanding. Our experience shows that its main points can be explained to students in about half an hour without extraordinary mental effort. It is also enigmatical and fascinating, since, on the one hand, it is associated with spy codes, and on the other hand, it provides protection based on the laws of nature. Methodologically, the positive aspect of quantum cryptography is valuable. Many fundamental premises of quantum physics are negative: the impossibility of making any measurement without affecting the system, the Heisenberg uncertainty principle, the nocloning theorem. At the same time, quantum cryptography, on the contrary, allows an absolutely secure distribution of the encryption key.
The difficulties of the old quantum theory were largely dispelled by the development of quantum mechanics in the 1920s. First Heisenberg (1925) developed the rather abstract matrix mechanics and soon after Schro¨dinger (1926; see also Eckart, 1926) developed the physically more appealing wave mechanics. Subsequently he showed them to be mathematically equivalent. The physicists were greatly relieved; now they had once again a mathematical formalism that enabled the results of experiments to be calculated. It was possible to move forward. It is certainly a very elegant and indeed beautiful formalism, and does enable the results of many physical measurements to be calculated with great accuracy. It is used daily by atomic and nuclear physicists; there is no other way to make calculations. From the earliest days there has been intense debate about the interpretation of quantum mechanics, and it shows no signs of being settled; if anything it is becoming more intense over the years. As Penrose has remarked, no one understands quantum mechanics. Feynman (1967; see also Sykes, 1994) also admitted that ‘nobody understands quantum mechanics’, and Einstein once remarked: ‘I have thought a hundred times as much about the quantum problems as I have about general relativity theory’ (Pais, 1994, p. 57). It should therefore be evident that the most that can be done here is to try to show where the real difficulties lie, and how the failure to recognize that quantum mechanics is an essentially statistical theory has led to a series of confusing quantum paradoxes. It is just these paradoxes that have often been used to support theological speculations. It is useful to ask what ‘understanding quantum mechanics’ actually means. Certainly it means being able to calculate the results of many measurements. The same applies to Newton’s theory of gravitation, which we understand in the sense that we can use it as a basis of calculation, although we do not really understand the gravitational force itself. Very often, especially in modern physics, the mathematical formalism does not give us the sort of intuitive physical feeling for what is going on that we often obtain from classical mechanics. Perhaps we can never achieve more than this for quantum mechanics. In classical mechanics we can assume that a property that is measured objectively exists prior to the interaction of the measuring apparatus with the observed system. Quantum mechanics, however, ‘is incompatible with the proposition that measurement discovers some unknown but pre-existing property’ (Peres, 1997, p. 14). There is an important distinction between mysteries and absurdities. We may be forced to live with mysteries, but there is no reason why we should put up with absurdities such as the wave-particle duality, tunnelling through potential barriers, acausal events and the collapse of the wave function. These are the quantum paradoxes that will be discussed later on. They arise within the Copenhagen interpretation of quantum mechanics and are solved by other interpretations. These alternative interpretations enable us to make conjectures about what is going on, even though we cannot understand it in detail. This is acceptable and a stimulus to further research. It is certainly difficult enough to understand quantum mechanics, but there is no need to try to visualize logical absurdities in the effort to do so. Quantum mechanics is a mathematical formalism that makes it possible to calculate the results of some experiments. Anything more than this, such as questions about the interpretation of what is measured and whether it tells us what is actually going on in the system being studied, belongs to philosophy. Thus we are concerned here with what is essentially a philosophical debate; if it were just a matter of physics the debate would have been settled long ago. One of the difficulties is that it invokes the results of experiments and uses the language of quantum mechanics. Inevitably this language uses philosophical terms and then it is easy to give the impression that the philosophical propositions are in some way entailed by the physical results. These in turn can influence theological thinking. In order to be quite clear which arguments are justified and which are not, it is essential to separate the three levels of discourse: physical, philosophical and theological. Our task is to relate these together, and this immediately raises the traditional problems of the philosophy of science, including the relation of experiment to theory, and of theory to explanation. We begin by discussing experiments, distinguishing between those that are real and those that are imaginary.
The aura of mystery surrounding quantum physics makes it difficult to advance quantum technologies. Demystification requires methodological techniques that explain the basics of quantum technologies without metaphors and abstract mathematics. The article provides an example of such an explanation for the BB84 quantum key distribution protocol based on phase coding. This allows you to seamlessly get acquainted with the real cryptographic installation QRate, used at the WorldSkills competition in the competence of "Quantum Technologies".
Introduction Chapter 1 dealt with one of the deepest mysteries in modern science: how to explain consciousness. This Part deals with another mystery: how to make sense of quantum mechanics. Both involve a problem of reconciliation with the classical worldview, which is one hint that the two mysteries might be related. A second is that, unlike classical physics, which makes no reference to or allowance for consciousness, quantum theory raises the issue of consciousness and its relationship to the physical world in a very direct way. These hints do not necessarily mean there is a connection between the two mysteries, but by the end of this Part I hope to have shown why it would be natural to look for one. My more immediate aim here is to give the social scientific reader an introductory understanding of the experimental findings of quantum theory, its key concepts, and the debates about its interpretation. The discussion assumes no prior knowledge of quantum physics and makes no use of mathematics. Quantum theory without equations might seem like an oxymoron, and certainly reading this Part will not enable anyone to use quantum theory. But to a perhaps surprising degree it is possible to understand quantum theory without being able to use it. Its findings can be communicated in ordinary language, and the same goes for its main concepts and interpretive debates. One consequence of this has been the emergence of a virtual cottage industry of books on quantum theory for a lay audience. Most are written by physicists, and many are quite good. However, it is not just popular treatments that do without equations: much of the professional philosophical literature does as well. (I draw on both kinds of literature below.) Philosophers of physics are trained to understand the math, of course, which is necessary for a full appreciation of the issues.
The ability to transfer information securely is essential in the modern world we live in. While the field of cryptography has long researched ways to do this, events over the last couple of years have brought the issues of secure information transfer squarely into the public eye. As a consequence, security and cryptography have quickly become issues of social and political importance, sparking debates about the values of privacy and the role of government. An essential ingredient of modern cryptography is the generation of randomness: cryptographic techniques are built on the premise that one has access to random bits. It is well known, however, that computers cannot produce algorithmically random sequences – that is, sequences with maximal algorithmic information content – but are doomed to produce ‘pseudorandomness’. This lack of randomness can be, and has been, exploited to compromise security, see [4]. The active field of quantum information theory has proposed approaches to provide supposedly ‘unbreakable’ security by exploiting various quantum phenomena. This security unfortunately relies on assumptions about the nature of quantum measurements and their ability to generate random bits. Anton Zeilinger summarises this by postulating that the simplest quantum systems, qubit, can hold only one bit of classical information [6]. This foundational principle is in line with a wider paradigm shift to view quantum information as an extension of classical information, but it is nonetheless unsatisfying to simply postulate this principle, given its importance in determining the practical advantages of quantum information theory. In order to understand better how quantum mechanics can help generate meaningful information, we instead look to relate the outcomes of quantum measurements to formal properties of the system based on more fundamental assumptions. Indeed, we have shown that a) some of the postulated properties of quantum information follow from the formal structure of the theory and b) a purely formal notion of information within a quantum world can generate, via measurement, meaningful and useful information in the macroscopic world (for example, in cryptography). The indeterminism of quantum measurements can be formalised via the notion of value indefiniteness. To explain this concept, let us consider an arbitrary quantum system and ask whether the outcome of a measurement of any observable quantity A (such as the energy of the system, its angular momentum (spin), etc.) is determined prior to the measurement. If this is the case, then we say the observable is value definite with value v(A); otherwise, the observable is value indefinite and v(A) is undefined. Mathematically, one can reduce all observable quantities to so-called projection observables, which can only take the values 0 or 1. Thus, the question of whether the outcome of several measurements can be simultaneously determined in advance can be rephrased in terms of the information ‘carried’ by a particular system in a definite quantum state. Classically, one expects that all quantities are determined in advance, and hence all observables are value definite. Quantum mechanically, however, the belief is that this is not the case, and the information content of quantum systems is limited. Formulating carefully the notion of value indefiniteness allows us to formalise the notion of (quantum) indeterminism; however, this doesn’t help clarify whether quantum systems are indeed value indefinite or not. Staying in this formal framework, the Kochen-Specker theorem [5] provides a first positive result, showing that at least some observables must be value indefinite if one makes the assumption known as non-contextuality, which states that any definite values that exist must be independent of other compatible measurements that may or may not be performed on the system. Under the same assumption, this theorem can be strengthened to show that only one single observable can have the definite value 1 (see [2]). Furthermore, only observables that can be measured simultaneously with this single one can have the definite value 0; the rest must all be value indefinite. Since the preparation of a system involves precisely ensuring that, usually via measurement, the system is in a definite state with respect to some desired observable, this result shows that no other incompatible observable can be value definite. That is, preparing a system in a definite state by making the ‘preparation’ observable value definite specifies completely the information content of the quantum system. This is an example of syntactical quantum information acquiring meaning at the level of the quantum itself. Can the syntactical information at the level of the quantum generate meaning outside the quantum, that is, at the macroscopic level? The results cited above hold in the Hilbert-space framework of quantum mechanics and are formulated only in terms of a syntactical notion of information. Their real importance becomes evident when one interprets them in the context of quantum measurements. Specifically, if we prepare a quantum system in a known state, they allow us to ‘locate’ observables which we can measure, but which are value indefinite; that is, observables whose measurement results are not specified by any pre-existing property of the quantum system. Furthermore, with respect to a mathematical model of unpredictability which we developed in [3], the results of these measurements can be shown to be absolutely unpredictable. In this way we get a mathematical explanation and justification of the largely accepted intuition that quantum mechanics is inherently unpredictable, and that this unpredictability arises from the phenomenon of indefiniteness within the quantum world. Furthermore, if one considers a hypothetical infinite sequence generated by the repeated measurement of a quantum value indefinite observable, one can prove that these sequences must be strongly incomputable, technically ‘bi-immune’ [1]. Such sequences cannot be generated by any Turing machine or classical computer, showing that value indefiniteness leads to a clear classical/quantum split in a purely algorithmic context. Importantly, bi-immunity is a property of observed, macroscopic quantities, quite separate from the quantum framework in which the value indefiniteness is formalised. This form of macroscopic meaning created from the lack of syntactic information is precisely the scenario that quantum random number generators try to create, and which is essential for the development and certification of quantum cryptographic systems. The fact that the macroscopic information created goes beyond anything classically obtainable serves as a valuable practical resource, outside of and removed from the quantum formalism. To conclude, quantum information creates meaning within the quantum and via measure- ment, the lack of information within the quantum, creates meaning and valuable information at the macroscopic level. Acknowledgments The second author thanks Prof. S. Marcus for useful conversations on quantum information theory. This work was supported in part by Marie Curie FP7-PEOPLE-2010-IRSES Grant RANPHYS. References and Notes Abbott, A.A.; Calude, C.S.; Svozil, K. Strong Kochen-Specker theorem and incomputability of quantum randomness. Physical Review A 2012, 86, 062109. Abbott, A.A.; Calude, C.S.; Svozil, K. Value-indefinite observables are almost everywhere. Physical Review A 2013, 89, 032109. Abbott, A.A.; Calude, C.S.; Svozil, K. On the unpredictability of individual quantum measurement outcomes. CDMTCS Research Report 2014, 458. Calude, C.S. Quantum randomness & cryptology. CyberTalk 2013, 3, 42–43. Kochen, S.; Specker, E. The problem of hidden variables in quantum mechanics. Journal of Mathematics and Mechanics 1967, 17, 59–87. Zeilinger, A. A foundational principle for quantum mechanics. Foundations of Physics 1999, 29(4),631–643.
Quantum cryptography is a new and exciting area that uses quantum physics to protect communication lines from being spied on or intercepted. Fundamental ideas in this field, like the uncertainty principle and the fact of quantum entanglement, are used to achieve levels of security that have never been seen before. Our in-depth study, "Quantum Cryptography: Mathematical Foundations and Practical Applications for Secure Communication Protocols," looks at both the math behind quantum cryptographic protocols and how they are used in the real world. Our study goes into great detail about the theories behind quantum cryptography. It explains ideas like quantum key distribution (QKD), quantum teleportation, and quantum secure direct communication (QSDC). One of the main ideas behind quantum cryptography is the idea of qubits, which are like regular bits but in quantum mechanics. They can be in more than one state at the same time because of superposition. Quantum cryptographic methods use this property to make sure communication is safe by putting data in quantum states and taking advantage of the fact that quantum measures are inherently unpredictable. The study we're doing looks at how to use quantum cryptography in typical everyday situations. We look at the problems that come up when you try to build infrastructure for quantum transmission, such as noise, decoherence, and scale. We make a plan for making strong and trustworthy quantum cryptographic systems by giving details about how experiments are set up and how technology is improving. Our study looks into how quantum cryptography could be used for things other than just keeping communications safe. We look into what it means for new technologies like quantum networks, quantum computing, and safe multi-party processing. We hope that by explaining the bigger effects of quantum cryptography, we can encourage more study and new ideas in this ground-breaking area.
The quantum cryptography approach is a significant change in secure communication in the sense that quantum cryptography bases its security on the law of quantum physics as opposed to computation difficulty. With classical encryption methods rapidly losing their resistance to the power of the underlying computers as well as the expected possibilities of the quantum computers, quantum cryptography comes into the limelight as a possible method of securing information in the long term. The paper is a detailed and systematic review of quantum cryptography along with the fundamentals of this practice, the way it works, and its practical implementation. It describes the ability of quantum phenomena to be unique (including superposition, uncertainty, and disturbance of measurement) and able to secure a key exchange as well as ensure any attempt of eavesdropping would be automatically noticed.In the review, the authors mainly discuss quantum key distribution (QKD) protocols, their functioning principles, security assurances, and the benefits of quantum over classical key exchange schemes. Besides that, the paper critically evaluates the real issues surrounding the implementation of quantum cryptographic systems such as hardware limitations, transmission range, environmental noise, and compatibility, to existing compatibility infrastructures. Recent advances in the field of experiments and pilot implementations are presented to determine the maturity of new technologies, and their suitability to be used on a large scale. Through its analytical review of theoretical assets, as well as practical constraints, this paper offers a definite and equalist view of the state of quantum cryptography today and also explains the research priorities important in its scale, moving away of the test production systems to the dependable and extensive security measures.