Editing Quantum information (section)

=== Development from fundamental quantum mechanics ===
The history of quantum information theory began at the turn of the 20th century when [[classical physics]] was revolutionized into [[Quantum mechanics|quantum physics]]. The theories of classical physics were predicting absurdities such as the [[ultraviolet catastrophe]], or electrons spiraling into the nucleus. At first these problems were brushed aside by adding ad hoc hypotheses to classical physics. Soon, it became apparent that a new theory must be created in order to make sense of these absurdities, and the theory of quantum mechanics was born.<ref name="Nielsen2010" />

[[Quantum mechanics]] was formulated by [[Erwin Schrödinger]] using wave mechanics and [[Werner Heisenberg]] using [[matrix mechanics]].<ref name="Mahan2009"/> The equivalence of these methods was proven later.<ref name="Perlman1964"/> Their formulations described the dynamics of microscopic systems but had several unsatisfactory aspects in describing measurement processes. Von Neumann formulated quantum theory using [[operator algebra]] in a way that it described measurement as well as dynamics.<ref>{{Cite book|last=Neumann|first=John von|url=https://books.google.com/books?id=B3OYDwAAQBAJ&q=foundations+of+quantum+mechanics+von+neumann&pg=PR1|title=Mathematical Foundations of Quantum Mechanics: New Edition|date=2018-02-27|publisher=Princeton University Press|isbn=978-0-691-17856-1|language=en}}</ref> These studies emphasized the philosophical aspects of measurement rather than a quantitative approach to extracting information via measurements.

See: [[Dynamical pictures|Dynamical Pictures]]
{{Pictures in quantum mechanics}}

==== Development from communication ====
In the 1960s, [[Ruslan Stratonovich]], [[Carl W. Helstrom|Carl Helstrom]] and Gordon<ref name="Gordon1962"/> proposed a formulation of optical communications using quantum mechanics. This was the first historical appearance of quantum information theory. They mainly studied error probabilities and channel capacities for communication.<ref name="Gordon1962"/><ref name="Helstrom1969"/><ref name="Helstrom1976"/> Later, [[Alexander Holevo]] obtained an upper bound of communication speed in the transmission of a classical message via a [[quantum channel]].<ref name="Holevo1973"/><ref name="Holevo1979"/>

==== Development from atomic physics and relativity ====
In the 1970s, techniques for manipulating single-atom quantum states, such as the [[atom trap]] and the [[scanning tunneling microscope]], began to be developed, making it possible to isolate single atoms and arrange them in arrays. Prior to these developments, precise control over single quantum systems was not possible, and experiments used coarser, simultaneous control over a large number of quantum systems.<ref name="Nielsen2010" /> The development of viable single-state manipulation techniques led to increased interest in the field of quantum information and computation.

In the 1980s, interest arose in whether it might be possible to use quantum effects to disprove [[Theory of relativity|Einstein's theory of relativity]]. If it were possible to clone an unknown quantum state, it would be possible to use [[Quantum entanglement|entangled]] quantum states to transmit information faster than the speed of light, disproving Einstein's theory. However, the [[no-cloning theorem]] showed that such cloning is impossible. The theorem was one of the earliest results of quantum information theory.<ref name="Nielsen2010" />

==== Development from cryptography ====
{{See also|Quantum cryptography}}
Despite all the excitement and interest over studying isolated quantum systems and trying to find a way to circumvent the theory of relativity, research in quantum information theory became stagnant in the 1980s. However, around the same time another avenue started dabbling into quantum information and computation: [[Cryptography]]. In a general sense, ''cryptography is the problem of doing communication or computation involving two or more parties who may not trust one another.''<ref name="Nielsen2010" />

Bennett and Brassard developed a communication channel on which it is impossible to eavesdrop without being detected, a way of communicating secretly at long distances using the [[BB84]] quantum cryptographic protocol.<ref name="Bennett2014"/> The key idea was the use of the fundamental principle of quantum mechanics that observation disturbs the observed, and the introduction of an eavesdropper in a secure communication line will immediately let the two parties trying to communicate know of the presence of the eavesdropper.

==== Development from computer science and mathematics ====
{{See also|Quantum supremacy|Quantum algorithm}}
With the advent of [[Alan Turing]]'s revolutionary ideas of a programmable computer, or [[Turing machine]], he showed that any real-world computation can be translated into an equivalent computation involving a Turing machine.<ref>{{Cite web|last=Weisstein|first=Eric W.|title=Church–Turing Thesis|url=https://mathworld.wolfram.com/Church-TuringThesis.html|access-date=2020-11-13|website=mathworld.wolfram.com|language=en}}</ref><ref name="Deutsch1985"/> This is known as the [[Church–Turing thesis]].

Soon enough, the first computers were made, and computer hardware grew at such a fast pace that the growth, through experience in production, was codified into an empirical relationship called [[Moore's law]]. This 'law' is a projective trend that states that the number of transistors in an [[integrated circuit]] doubles every two years.<ref name="Moore1998"/> As transistors began to become smaller and smaller in order to pack more power per surface area, quantum effects started to show up in the electronics resulting in inadvertent interference. This led to the advent of quantum computing, which uses quantum mechanics to design algorithms.

At this point, quantum computers showed promise of being much faster than classical computers for certain specific problems. One such example problem was developed by [[David Deutsch]] and [[Richard Jozsa]], known as the [[Deutsch algorithm|Deutsch–Jozsa algorithm]]. This problem however held little to no practical applications.<ref name="Nielsen2010" /> [[Peter Shor]] in 1994 came up with a very important and practical [[Shor's algorithm|problem]], one of finding the prime factors of an integer. The [[discrete logarithm]] problem as it was called, could theoretically be solved efficiently on a quantum computer but not on a classical computer hence showing that quantum computers should be more powerful than Turing machines.

==== Development from information theory ====
Around the time computer science was making a revolution, so was information theory and communication, through [[Claude Shannon]].<ref name="Shannon1948a"/><ref name="Shannon1948b"/><ref name="Shannon1964"/> Shannon developed two fundamental theorems of information theory: noiseless channel coding theorem and [[Noisy-channel coding theorem|noisy channel coding theorem]]. He also showed that [[Error correction code|error correcting codes]] could be used to protect information being sent.

Quantum information theory also followed a similar trajectory, Ben Schumacher in 1995 made an analogue to Shannon's [[Shannon's source coding theorem|noiseless coding theorem]] using the [[qubit]]. A theory of error-correction also developed, which allows quantum computers to make efficient computations regardless of noise and make reliable communication over noisy quantum channels.<ref name="Nielsen2010" />