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'''[[Quantum mechanics]] and [[Theory of relativity|relativity]] theory''' are two of the foundational stones of [[theoretical physics]], while [[information theory]] is one of the most widely applied of all theories in [[mathematics]].

(contracted; show full)beginning of the twentieth century to give answers to unexplained issues in [[physics]]: the [[black body]] [[spectrum]], the structure of [[atom]]s and [[Atomic nucleus|nuclei]], the [[electrodynamics]] of moving bodies. Many years later, [[information theory]] was developed by [[Claude Shannon]] [1948] for analyzing the efficiency of communication methods. How do these seemingly disparate disciplines affect each other? In this review, we shall show that they are inseparably related.
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==What is Information?==

===Information about What?===

Chris Fuchs [2004] says that quantum information is “the potential consequences of our experimental interventions into nature.”

===Interventions and observations===
[[Werner Heisenberg]] in a quote that he attributed to [[Albert Einstein]] many years after the fact stated [Heisenberg 1971]:

:It is quite wrong to try founding a theory on observable magnitudes alone. In reality the very opposite happens. It is the theory which decides what we can observe. You must appreciate that observation is a very complicated process. The phenomenon under observation produces certain events in our measuring apparatus. As a result, further processes take place in the apparatus, which eventually and by complicated paths produce sense impressions and help us to fix the effects in our consciousness.  Along this whole path—from the phenomenon to its fixation in our consciousness—we must be able to tell how nature functions, must know the natural laws at least in practical terms, before we can claim to have observed anything at all. Only theory, that is, knowledge of natural laws, enables us to deduce the underlying phenomena from our sense impressions. When we claim that we can observe something new, we ought really to be saying that, although we are about to formulate new natural laws that do not agree with the old ones, we nevertheless assume that the existing laws—covering the whole path from the phenomenon to our consciousness—function in such a way that we can rely upon them and hence speak of “observation.”

===Incompleteness===
Chris Fuchs [2004] states:

:He [Einstein] was the first person to say in absolutely unambiguous terms why the quantum state should be viewed as information (or, to say the same thing, as a representation of one’s beliefs and gambling commitments, credible or otherwise).  His argument was simply that a quantum-state assignment for a system can be forced to go one way or the other by interacting with a part of the world that should have no causal connection with the system of interest. The paradigm here is of course the one well known through the [[EPR paradox|Einstein, Podolsky, Rosen [1935] paper]], but simpler versions of the train of thought had a long pre-history with Einstein himself (see [Fine 1986] and [Jammer 1985]).

:The best was in essence this. Take two spatially separated systems ''A'' and ''B'' prepared in some entangled quantum state |&psi;<sup>''AB''</sup>>. By performing the measurement of one or another of two observables on system ''A'' alone, one can immediately write down a new state for system ''B''. Either the state will be drawn from one set of states {|&phi;<sub>i</sub><sup>''B''</sup>>} or another {|&eta;<sub>i</sub><sup>''B''</sup>>}, depending upon which observable is measured. The key point is that it does not matter how distant the two systems are from each other, what sort of medium they might be immersed in, or any of the other fine details of the world. Einstein concluded that whatever these things called quantum states be, they cannot be “real states of affairs” for system ''B'' alone. For, whatever the real, objective state of affairs at ''B'' is, it should not depend upon the measurements one can make on a causally unconnected system ''A''.

:Thus one must take it seriously that the new state (either a |&phi;<sub>i</sub><sup>''B''</sup>> or |&eta;<sub>i</sub><sup>''B''</sup>>) represents information about system ''B''. In making a measurement on ''A'', one learns something about B, but that is where the story ends. The state change cannot be construed to be something more physical than that.  More particularly, the final state itself for ''B'' cannot be viewed as more than a reflection of some tricky combination of one’s initial information and the knowledge gained through the measurement.  Expressed in the language of Einstein, the quantum state cannot be a “complete” description of the quantum system.
:...
:The last seventeen years have given confirmation after confirmation that the [[Bell's theorem|Bell inequality]] (and several variations of it) are indeed violated by the physical world. The [[No-communication theorem|Kochen-Specker no-go theorems]] have been meticulously clarified to the point where simple textbook pictures can be drawn of them [ [[Asher Peres]] 1993]. Incompleteness, it seems, is here to stay: The theory prescribes that no matter how much we know about a quantum system—even when we have maximal information about it—there will always be a statistical residue. There will always be questions that we can ask of a system for which we cannot predict the outcomes. In quantum theory, maximal information is simply not complete information [Caves and Fuchs 1996]. But neither can it be completed. As [[Wolfgang Pauli]] once wrote to Markus Fierz in [1954], “The well-known ‘incompleteness’ of quantum mechanics (Einstein) is certainly an existent fact somehow-somewhere, but certainly cannot be removed by reverting to classical field physics.” Nor, I would add, will the mystery of that “existent fact” be removed by attempting to give the quantum state anything resembling an ontological status.

:The complete disconnectedness of the quantum-state change rule from anything to do with [[spacetime]] considerations is telling us something deep: The quantum state is information. Subjective, incomplete information. Put in the right mindset, this is not so intolerable. It is a statement about our world. There is something about the world that keeps us from ever getting more information than can be captured through the formal structure of quantum mechanics.

==Unsolved problems==
In [Asher Peres and Daniel Terno 2004] the following unsolved problems (among others) are pointed out:

*There is a trade-off between the reliability of detectors and their localization. This is an important practical problem.
*Progressing from special to general relativity, what is the meaning of parallel transport of a spin?
*We still need a method for detection of relativistic entanglement that involves the spacetime properties of the quantum system,
(contracted; show full)
* Christopher Fuchs, ''Quantum mechanics as quantum information (and only a little more)'' in A. Khrenikov (ed.) Quantum Theory: Reconstruction of Foundations (Växjo: Växjo University Press, 2002).
*Asher Peres and Daniel Terno. ''Quantum Information and Relativity Theory'' Rev.Mod.Phys. 76 (2004) 93.

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