Over the past decade, quantum information theory has developed into a vigorous field of research despite the fact that quantum information, as a precise concept, is undefined. Indeed, the very idea of viewing quantum states as carriers of some kind of information (albeit unknowable in classical terms) leads naturally to interesting questions that might otherwise never have been asked, and corresponding new insights. We discuss some illustrative examples, including a strengthening of the well-known no-cloning theorem leading to a property of permanence for quantum information, and considerations arising from information compression that reflect on fundamental issues.
Over the past decade, quantum information theory has developed into a vigorous field of research despite the fact that quantum information, as a precise concept, is undefined. Indeed, the very idea of viewing quantum states as carriers of some kind of information (albeit unknowable in classical terms) leads naturally to interesting questions that might otherwise never have been asked, and corresponding new insights. We discuss some illustrative examples, including a strengthening of the well-known no-cloning theorem leading to a property of permanence for quantum information, and considerations arising from information compression that reflect on fundamental issues.
Quantum information theory represents a rich subject of discussion for those interested in the philosphical and foundational issues surrounding quantum mechanics for a simple reason: one can cast its central concerns in terms of a long-familiar question: How does the quantum world differ from the classical one? Moreover, deployment of the concepts of information and computation in novel contexts hints at new (or better) means of understanding quantum mechanics, and perhaps even invites re-assessment of traditional material conceptions of the basic nature of the physical world. In this paper I review some of these philosophical aspects of quantum information theory, begining with an elementary survey of the theory, seeking to highlight some of the principles and heuristics involved. We move on to a discussion of the nature and definition of quantum information and deploy the findings in discussing the puzzles surrounding teleportation. The final two sections discuss, respectively, what one might learn from the development of quantum computation (both about the nature of quantum systems and about the nature of computation) and consider the impact of quantum information theory on the traditional foundational questions of quantum mechanics (treating of the views of Zeilinger, Bub and Fuchs, amongst others).
Quantum information theory represents a rich subject of discussion for those interested in the philosphical and foundational issues surrounding quantum mechanics for a simple reason: one can cast its central concerns in terms of a long-familiar question: How does the quantum world differ from the classical one? Moreover, deployment of the concepts of information and computation in novel contexts hints at new (or better) means of understanding quantum mechanics, and perhaps even invites re-assessment of traditional material conceptions of the basic nature of the physical world. In this paper I review some of these philosophical aspects of quantum information theory, begining with an elementary survey of the theory, seeking to highlight some of the principles and heuristics involved. We move on to a discussion of the nature and definition of quantum information and deploy the findings in discussing the puzzles surrounding teleportation. The final two sections discuss, respectively, what one might learn from the development of quantum computation (both about the nature of quantum systems and about the nature of computation) and consider the impact of quantum information theory on the traditional foundational questions of quantum mechanics (treating of the views of Zeilinger, Bub and Fuchs, amongst others).
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.
Recent research in the fields related to the quantum information theory (QIT) is becoming some of the most intriguing and promising investigations in contemporary physics. Many novel QIT concepts are discussed in the literature, and the broad range of new models of quantum optics and solid-state physics have been recently considered in the context of QIT. Theideas of symmetry are widely discussed in all physical sciences, becoming keystones of various concepts and considerations, leading to novel discoveries in physics. Thus, this Special Issue is devoted to the broad range of QIT topics that are related to the ideas of symmetry. It covers a broad range of ideas that can develop upon the basic research and applications in the field of quantum information, and in general, quantum theory.
Introduction The quantum information theory began to rise in the end of 20th century. The EPR (relation)really is quantum entanglement, Consequently, it makes the concept of information in science expand from classical information theory to quantum information theory, and a new concept of quantum information formed. The primary concept of information faced to new challenges and produced some important philosophical questions. For example, can we set up the concept of quantum information? What is the nature of quantum information? The past common concept of information (the information is the elimination of uncertainty) could be used in quantum information? Whether does the emergence of quantum computation mean to eliminate no-boundaries between the quantum and the classical? My aim in this paper is to discuss these questions. My philosophical analysis focuses, however, on the basic quantum information theory. Methods The research method is analytical philosophy and logic that make quantum conception more clear and accurate. Results and Discussion The concept of information could be set up. fundamentally speaking, it did be supported by the Shannon information theory and further philosophical reflections. According of information theory, (classical) information concept could be set up, and there are two necessary preconditions: (a) the premise is a set of possible events, and they can be described by the probability. (b) the information is the elimination of uncertainty. Fundamentally, quantum information is also satisfied with the family-resemblance two preconditions: (1) Quantum information describes the possibility of microscopic things, and quantum information is the expression of wave function. The wave function describes the state of microscopic particles, and presentation of the possibility of microscopic objects. (2) On the aspect of eliminating the uncertainty, the quantum communication is same as classical communication. The signal receiver once received quantum signals transmitted, and the receiver eliminates the corresponding uncertainty of quantum. Therefore, the quantum information is the elimination of quantum uncertainty, and which is called quantum information I. From two point of views, the possible events and eliminate uncertainty, the quantum information and classical information have family resemblance. Quantum information like Classical information way of transmission, it is delivered by the information source, and is received by recipient through the information channel. Quantum Information is similar to classical information, but more essential difference between them, specifically in the following three aspects: (1) The probability directly describe the possibility of classic events, while wave function (or probability amplitude) describes quantum events in the quantum world, and the absolute square of wave function is corresponded to classical probability. (2)There have the essential difference between qubits (quantum qits) and classical bits. (3) Classical information can be completely cloned or deleted. nevertheless, quantum information is neither cloned (no-cloning), nor removed completely. To my point of view, through the analysis of the process of quantum teleportation, a quantum uncertainty can be divided into three categories: the first is the external uncertainties of microscopic particles; the second the uncertainty of the superposition state; the third the inherent uncertainty of microscopic particles. These three uncertainties can be eliminated by three different ways that are transmission of quantum information, accurate quantum transformations and the creations of quantum entanglement. Therefore we can give the general definition of certainty: a situation (the state of events, things) is of certainty, if they are satisfied with the following conditions: (a) a situation is entirely determined by n events parameters; (b) n parameters of events has an accurate values simultaneously. The existences of quantum states form quantum facts. Quantum states show themselves, and therefore it releases the information to the outside world. For this reason, there have two aspects of quantum state which need to express: existence of quantum state is the quantum fact, here we emphasize "existence"; and quantum state can show to the external world, which is the quantum information, here we emphasize "Show". Hence, quantum information is the show(Zeigt) of quantum state, which is called quantum information II. The nature of quantum information is the show of quantum events and their correlated ways. Quantum information is a kind of certainty and order. Quantum information can be divided into quantum informationⅠand quantum informationⅡ.. Quantum InformationⅠjust only a phenomenonal definition, it does not go deeply into the nature of the information. Therefore, the elimination of uncertainty can not be seen as the nature of quantum information itself . In the process of quantum teleportation, the source of quantum information (such as quantum state , a and b are coefficients) is delivered to the receiver, what is the essence of quantum information? From the point of view of quantum information theory, quantum state represents quantum information, quantum state is the state of quantum system (or microscopic particles) or quantum events. in the quantum state , what quantum states disclose the quantum information does not be the absolute size of quantum information, but the relationship, since the coefficients a and b satisfy the condition , and it do not be important numerical a and b, but between their relative size and relationship, which reflects the correlated ways between a and b. The connotation of quantum InformationⅠand quantum information Ⅱ offers support for the common view of classical information concept. Which is more deeply to disclose the nature of quantum information for both of them? Obviously, quantum information Ⅱ reflects the nature of quantum information. Quantum reality and quantum information are unified. What the wave function expresses is quantum reality. The wave function is unified of quantum information and quantum reality. There is no quantum reality, there is no quantum information. Because of the information and reality are unified, and quantum information different from classical information, so we can deduce that quantum reality is different from classical reality, and quantum computing differs from classical computing. In the classical parallel computing, the value calculated in different circuits respectively, but in parallel quantum computing the value calculated in one circuit, which is the essential difference between classical and quantum parallel computing. Many worlds interpretation of quantum mechanics does not mean that the difference between quantum and classical disappears: (1) Superposition in the microscopic world is very different from classical macroscopic physical world, so it is impossible that the superposition principle is fit for quantum world used for the classical world; (2) "To perform a quantum measurement, quantum world can be split up numerous classical world" is not supported by any experience and evidence; (3) Each branches of quantum computing are in quantum states, and quantum states are coherent, holistic, and some even entangled. Nevertheless, it is impossible for classical computing to achieve the quantum computing’s specific features; (4) The essential differences between quantum and the classical are decided by the development history of quantum mechanics and quantum information theory. The differences between quantum and the classical is really established by the quantum theory, concepts and their experiments that include Heisenberg’s matrix mechanics of Schrodinger’s wave equation, uncertainty principle of quantum mechanics and quantum entanglement phenomena and so on. They are completely different from the classical physical theories, concepts and experiments. Figure 1. Quantum information processing (see PDF version for the Figure). Conclusions This fruitful work gives an discussion of quantum concept that is the quantum information is the elimination of quantum uncertainty, which is called quantum information I and quantum information is the show (Zeigt) of quantum state, which is called quantum information II. Quantum information II reflects the nature of quantum information. The nature of quantum information is the show of quantum events and their correlated ways. Acknowledgments This research work of this paper is supported by 2011 the Philosophy and Social Sciences Foundation of the Ministry of Education of P. R. China (Project Number: 11JZD007) " Studies of the development trend of contemporary technological philosophy" . References and Notes Weiner, N., Cybernetics and Society. Houghton Mifflin Company, 1950. Shannon, C. E., The Mathematical Theory of Communication. The Bell System Technical Journal. 1948, Vol.27, pp.379-423, 623-656. Kornwachs K., Jacoby K., Introduction: What’s new about information? In Kornwachs K., Jacoby K.eds. Information. Berlin: Akademic Verlag GmbH. 1996. Bouwmeester, D. Pan, J.-W.，et al. Experimental Quantum Teleportation. Nature. 1997. 390. Bennett C. H. and Di Vinecenzo D. P. quantum information and computation, Nature, 2000, 404. Einstein, A. Podolsky B., and Rosen, N. Can Quantum-Mechanical Description of Physical Reality Be Considered Complete? Physical Review. 1935,47. Nielsen, M. A. Chuang, I. L., Quantum Computation and Quantum Information. Cambridge University Press, 2000. Duwell, A. Quantum information does not exist. Studies in History and Philosophy of Modern Physics，2003, (34). Berta, M. Christandl, M. Colbeck, R., et al. The uncertainty principle in the presence of quantum memory. Nat. Phys., 2010, (6). Caves， M. and Fuchs，C. A. 1996. Quantum information：how much information in a state vector?. preprint quant-ph/9601025. Barrow, J., et al, Science and Ultimate Reality: Quantum Theory, Cosmology and Complexity. Cambridge University Press. 2004. Yongde Zhang, Principles of Quantum Information Physics. Beijing: Science Press. 2006. Wheeler, J. A., At Home in the Universe. New York: Springer-Verlag. 1996. Guolin Wu, Quantum Entanglement And Its Philosophical Meaning, Studies in Dialectics of Nature, 2005, (7). Guolin Wu, A Detailed Philosophical Inquiry of the Quantum Information, Philosophical Researches. 2014, (8). Guolin Wu, Philosophical Connotation of quantum information Technology. Philosophical Trend. 2013, (8).
Information is a physical. Physical systems register and process information. These facts generated enormus interest in the development of novel quantum tecnologies, especially because the construction of smaller electronic devices ultimately leads to a consideration of quantum mechanical effects in electronic and computer desingns. The notion of the classical bit of information theory was formally pushed into the realm of the quanta with the introduction of the quantum bit or qubit, in the seminal works of Deutsch (Deutsch, 1985) and Shor (Shor, 1994). They demostrated that, indeed, controlled multipartite qubit interference effects could provide the means for a radical new way of computing, allowing the computation of many intractable computational problems, such as the factoring of large number or exact simulation of large quantum systems. The field of experimental and theoretical research in quantum information and computation has emerged as very important player in the understanding of quantum phenomena the both the basic and technological levels. This has attracted the attention of numerous researchers with backgrounds ranging from computer science, mathematics and engineerin, to the physical sciences, and we now have an interdisciplinary field where great efforts are being made in order to build devices that allow the progressing of information at a quantum level. A concise introduction to the field of quantum information and quantum computation is presented. This stars with the bassic definitions of bits, quantum registers, through to the universal gate-set for building the universal quantum computer, from a quantum network model of computation. The work shows how two-qubit gates suffice for quantum computation, emphasing the power of the quantum circuit representation for entagling and disentagling quantum states. This leads to the “no-cloning theorem”, which leads us to many interesting applications, such as quantum cryptography. Two alternative approaches or performing quantum computation are also described i) the one-way or measurement based quantum computer method, and ii) holonomic or geometric quantum computation. Following this, quantum entaglement quantification is highlighted, particulary its usefulness as a communication resource, in order to describe some of its most celebrated practical applications to date: quantum teleportation, cryptography, dens coding, and data compression. Deutsch’s concept of quantum parallelism is enphasized in order to gain insight into the potential for efficiently solving certain classically intratable algorithms. A subject central to the field of QIP- quantum decoherence- is then introduced.. Possible ways to overcome it, in particular quantum error correction, are discussed. A descriptios of some of the currently available hardware of the practical implementation of quantum computation is provided with a discussion of the main physical quantum bits that are currently employed (or proposed) for a such a purpose.