Since Bell’s death, interest in his work and quantum foundations in general, and the amount of application of his work, have grown steadily. Work on Bell’s inequality has continued, each loophole has been closed independently, and in 2015 it seems that a loophole-free test will be achieved very soon. Also stimulated by Bell, discussion of fundamental aspects of quantum theory, a discussion which was scarcely tolerated in the days of the supremacy of the Copenhagen interpretation, is widespread and productive. Bell’s work has stimulated the conception and growth of quantum information theory, which encompasses quantum computation (or quantum computing), quantum cryptography (or quantum key distribution), and quantum teleportation, and there is now an enormous amount of work, both theoretical and practical.
Since Bell’s death, interest in his work and quantum foundations in general, and the amount of application of his work, have grown steadily. Work on Bell’s inequality has continued, each loophole has been closed independently, and in 2015 it seems that a loophole-free test will be achieved very soon. Also stimulated by Bell, discussion of fundamental aspects of quantum theory, a discussion which was scarcely tolerated in the days of the supremacy of the Copenhagen interpretation, is widespread and productive. Bell’s work has stimulated the conception and growth of quantum information theory, which encompasses quantum computation (or quantum computing), quantum cryptography (or quantum key distribution), and quantum teleportation, and there is now an enormous amount of work, both theoretical and practical.
The rapid rise of quantum information For the last four chapters I have been describing what may be called the ‘fundamental’ or ‘foundational’ aspects of quantum theory. I have been explaining what happens when you penetrate deeper into the ideas of quantum theory than when you merely make use of it, when you try to understand its basic meaning and what, if true, it tells us about the physical nature of the Universe. As I said in Chapter 5, once Bohr had given his approach to these matters in his Como paper of 1927, general opinion was that his views were sacrosanct, and that no self-respecting physicist needed to return to discuss them further. It was Bell's great achievement to dent this complacency at least a little, and from the very end of the 1960s for the next quarter of a century or so, there were a few experimentalists keen to test the Bell inequalities with increasing stringency, and a few theoreticians with fresh ideas about how quantum theory should be interpreted. While it was generally admitted that Bell's work was a genuine and important contribution to our understanding of quantum theory, and eventually the ideas actually reached some of the textbooks, in the 1970s and 1980s the field was still very much a minority interest, and even those who found it interesting would scarcely have felt that it had, or was likely to have in the foreseeable future, practical application.
Alan Turing has certainly contributed to a widespread belief that the quest for a perfect, unbreakable, cipher is a futile pursuit. The ancient art of concealing information has, in the past, been matched by the ingenuity of code-breakers, but no longer! With the advent of quantum cryptography, the hopes of would-be eavesdroppers have been dashed, perhaps for good. Moreover, recent research, building on schemes that were invented decades ago to perform quantum cryptography, shows that secure communication certified by a sufficient violation of a Bell inequality makes a seemingly insane scenario possible-devices of unknown or dubious provenance, even those that are manufactured by our enemies, can be safely used for secure communication, including key distribution. All that is needed to implement this bizarre and powerful form of cryptography is a loophole-free test of a Bell inequality, which is on the cusp of technological feasibility. We provide a brief overview of the intriguing connections between Bell inequalities and cryptography and describe how studies of quantum entanglement and the foundations of quantum theory influence the way we may protect information in the future.
Since 2000, several landmark results in quantum information have catapulted the field to one of the most exciting in science. From the demonstration of Shor’s factorisation algorithm that threatens the long-term security of public-key cryptography, to the teleportation of super-position states, the demonstration of error-correcting codes and the development of topologically protected qubits, our ability to control the quantum world is ever increasing. Matched by elegant experiments to test the fundamentals of quantum physics, such as the recent demonstration of the loop-hole free violation of Bell's inequality, 1 , 2 these exciting achievements are all emerging just at the time when information technology is beginning to enter the quantum regime.
Device-independent quantum key distribution (DIQKD) is the art of using untrusted devices to distribute secret keys in an insecure network. It thus represents the ultimate form of cryptography, offering not only information-theoretic security against channel attacks, but also against attacks exploiting implementation loopholes. In recent years, much progress has been made towards realising the first DIQKD experiments, but current proposals are just out of reach of today's loophole-free Bell experiments. In this Letter, we close the gap between the theory and practice of DIQKD with a simple variant of the original protocol based on the celebrated Clauser-Horne-Shimony-Holt (CHSH) Bell inequality. In using two randomly chosen key generating bases instead of one, we show that the noise tolerance of DIQKD can be significantly improved. In particular, the extended feasibility region now covers some of the most recent loophole-free CHSH experiments, hence indicating that the first realisation of DIQKD already lies within the range of these experiments.
Finally, here is a modern, self-contained text on quantum information theory suitable for graduate-level courses. Developing the subject 'from the ground up' it covers classical results as well as major advances of the past decade. Beginning with an extensive overview of classical information theory suitable for the non-expert, the author then turns his attention to quantum mechanics for quantum information theory, and the important protocols of teleportation, super-dense coding and entanglement distribution. He develops all of the tools necessary for understanding important results in quantum information theory, including capacity theorems for classical, entanglement-assisted, private and quantum communication. The book also covers important recent developments such as superadditivity of private, coherent and Holevo information, and the superactivation of quantum capacity. This book will be warmly welcomed by the upcoming generation of quantum information theorists and the already established community of classical information theorists.
For practical applications of quantum randomness generation, it is important to certify and further produce a fixed block of fresh random bits with as few trials as possible.Consequently, protocols with high finite-data efficiency are preferred.To yield such protocols with respect to quantum side information, we develop quantum probability estimation.Our approach is applicable to device-independent as well as device-dependent scenarios, and it generalizes techniques from previous works [Miller and Shi, SIAM J. Comput. 46, 1304 (2017); Arnon-Friedman et al., Nat. Commun. 9, 459 (2018)].Quantum probability estimation can adapt to changing experimental conditions, allows stopping the experiment as soon as the prespecified randomness goal is achieved, and can tolerate imperfect knowledge of the input distribution.Moreover, the randomness rate achieved at constant error is asymptotically optimal.For the device-independent scenario, our approach certifies the amount of randomness available in experimental results without first searching for relations between randomness and violations of fixed Bell inequalities.We implement quantum probability estimation for device-independent randomness generation in the CHSH Bell-test configuration, and we show significant improvements in finite-data efficiency, particularly at small Bell violations which are typical in current photonic loophole-free Bell tests.