The notion of quantum information as explained in this primer was established in the 1990s. It emerged from research focused on understanding how physics affects our capabilities to communicate and to process information. The recognition that usable types of information need to be physically realizable was repeatedly emphasized by R. Landauer who proclaimed that ``information is physical'' [22]. Beginning in the 1960s, R. Landauer studied the thermodynamic cost of irreversible operations in computation [23]. C. Bennett showed that by using reversible computation, this cost can be avoided [24]. Limitations of measurement in quantum mechanics were investigated early by researchers such as J. von Neumann [25,26], and later by A. Holevo [27] and C. Helstrom [28]. A. Holevo introduced the idea of quantum communication channels and found bounds on their capacity for transmitting classical information [29]. Initially, most work focused on determining the physical limitations placed on classical information processing. The fact that pairs of two-level systems can have correlations not possible for classical systems was proven by J. Bell [30] in 1964. Subsequently, indications that quantum mechanics offers advantages to information processing came from S. Wiesner's studies of cryptographic applications [1] in the late 1960s. S. Wiesner's work was not recognized until the 1980s, when C. Bennett, G. Brassard, S. Breidbart and S. Wiesner [2] introduced the idea of quantum cryptography, which can be used to communicate in secret.
Initially, the term ``quantum computation'' was mostly used to refer to classical computers realized using quantum mechanical systems. In the 1980s, P. Benioff [31], R. Feynman [3] and Y. I. Manin [32] introduced the idea of a quantum computer based on quantum information. They noted that the apparent exponential complexity of simulating quantum mechanics on a classical computer might be overcome if we could use a computer that is itself based on quantum mechanics. A formal model of quantum Turing machines was soon defined by D. Deutsch [33], who later also introduced quantum networks [34]. D. Deutsch and R. Jozsa [35] were the first to introduce a black box problem that can be solved deterministically on a quantum computer in fewer steps than on a classical computer.
In spite of suggestions that it could lead to large efficiency improvements in simulating physics, quantum information processing was still largely an academic subject. Based on work by E. Bernstein and U. Vazirani [13] that formalized quantum complexity theory, D. Simon [14] showed that, for black-box problems, quantum computers can be exponentially more efficient than classical deterministic or probabilistic computers, giving the first indication of a strong advantage for quantum information processing. It was Shor's algorithm for factoring large whole numbers [4,5] that finally convinced a larger community that quantum information was more than just a tool for realizing classical computers. This change in attitudes was in no small part due to the fact that the security of commonly used cryptographic protocols is based on the hardness of factoring.
At that point, it was still generally believed that the fragility of quantum states made it unlikely for reasonably large quantum computers to be realized in practice. But the discovery by Shor [36] and A. Steane [37] that quantum error-correction was possible soon changed that view, see [12] for an introductory overview.
As a result of the recognition of the utility and realizability of quantum information, the science of quantum information processing is a rapidly growing field. As quantum information becomes increasingly accessible by technology, its usefulness will be more apparent. The next few sections briefly discuss what we currently know about applications of quantum information processing. A useful reference text on quantum computation and information with historical notes is the book by M. Nielsen and I. Chuang [38].