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I am wondering how fundamental the study of quantum information theory and computation is, in the sense of contributing to our understanding of the basic laws of nature. Will quantum information theory give us new insights into fundamental physics, or is it "merely" an application of quantum mechanics to information theory and computation? I find this to be a very interesting question, but can find very few sources that comment on it. I am currently reading Nielsen and Chuang's quantum information textbook, but I haven't seen this point addressed. There's a 2012 article by Aram Harrow (Why now is the right time to study quantum computing) which posits in the abstract that "quantum computing is not merely a recipe for new computing devices, but a new way of looking at the world", but sadly it is behind a paywall. In section 5 of this 1999 article, John Preskill briefly talks about how he thinks quantum information will contribute to fundamental physics, and says "I am anticipating a much broader interface between quantum information science and fundamental physics in the future". I am basically wondering what the current status of this interface is 15 years later, if there is any at all, and if the quantum information community still believes that quantum information may play an important role in fundamental physics.

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  • $\begingroup$ I will write an answer but if you're interested in chatting I will go to the hbar chat room right now. Here's a link: chat.stackexchange.com/rooms/71/the-h-bar $\endgroup$ – DanielSank Dec 17 '14 at 6:40
  • $\begingroup$ Has conventional computing given us any insights about nature? Not really. It has given an incredible boost to experiments, though. Modern physics would not be possible without automated data collection and storage and the computing power of modern computers. Quantum computing may, eventually, do the same thing. Will it give us any further information about nature? Unlikely, since it does the same thing as conventional information processing, merely in a certain parallel way. Everything a quantum computer can do, can be simulated on a conventional one... it might just take a long time. $\endgroup$ – CuriousOne Dec 17 '14 at 6:59
  • $\begingroup$ @CuriousOne: Strongly disagree. See my answer. $\endgroup$ – DanielSank Dec 17 '14 at 7:31
  • $\begingroup$ @DanielSank: You may disagree, that doesn't change anything about the historical impact of computing on physics. Nor does it change anything about the 100% equivalence of classical and quantum computing. There is nothing that can be computed with a quantum computer that couldn't be computed with a classical computer. $\endgroup$ – CuriousOne Dec 17 '14 at 8:41
  • $\begingroup$ @CuriousOne: First of all, you note the contributions of computing to experiments but ignore their impact on theory, which is odd. Second, OP asks "will quantum information theory give us new insights into fundamental physics". Do you not think that understanding the relationship between information extracted from a system and the precise details of its wave function collapse is "new insight"? Finally, what would you consider to be the last two "insights about nature" delivered by the physics community? $\endgroup$ – DanielSank Dec 17 '14 at 9:14
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Quantum computing research already has improved our understanding of the basic laws of nature in what I think are several important ways.

"Quantum" does not mean "microscopic"

One of the types of system used to implement quantum bits (qubits) is a superconducting resonant circuit. These circuits are large enough to see with your naked eye, yet they exhibit true quantum effects such as the violation of the Bell inequality. The fact that essentially macroscopic systems can exhibit quantum behavior runs against decades of history of quantum mechanics research, theory, and pedagogy in which we are constantly told, incorrectly, that quantum mechanics is the theory of the very small.

Now, you aksed about new laws of nature. You could argue that a statement about the applicability of quantum mechanics to various systems isn't a new law of nature, but I'd disagree :) When you "do" quantum mechanics you may be used to just writing down a Hamiltonian and solving for various properties. However, a good theory should tell you what it describes. If quantum mechanics is a law of Nature then I say quantum computing has at least modified and solidified that law by showing us that physical size is not the factor determining that's law's realm of applicability.

What does "quantum" mean?

In fact, quantum computing has given us an extremely clear picture of when a system is quantum. By now countless experiments in systems conceived for the purposes of quantum computing have shown us that what really matters is how strongly the system under consideration is coupled to other systems of which you aren't keeping track, i.e. how strongly your system is coupled to the "environment". If a potentially quantum system, like an atom, an electron, or a superconducting qubit is well isolated from any other nearby degrees of freedom, then that system will indeed behave quantum-mechanically. If, on the other hand, the atom (for example) interacts strongly with a bunch of air molecules whose states you are not paying attention to, then from your point of view the quantum state of the atom will collapse. The rate at which the quantum state collapses increases as the atom interacts with more air molecules or interacts with each one more strongly.

Did you notice that I said the wave function collapses only from your point of view, and only because you aren't paying attention to the air molecules? It's true, and in fact this fact provides us with the clearest understanding of what the wave function really means: it is a representation of the information in a physical system available to you. If you have a complete system such as the atom and the air molecules, there's a certain amount of information there. You can represent this as a wave function. If you ignore the air molecules, you lose some information and you can no longer represent what you do know with a quantum state vector; you have to use a density matrix. If too much of the quantum information leaves the atom and goes into the environment, what you do know about the atom is essentially classical information. In other words, the wave function collapsed. This understanding that the quantum state is a statement of available information makes us realize that in a very real sense quantum mechanics is a theory about information. I think that if quantum computing research pushed us to understand that fact then it has made real contributions to fundamental physics.

While this was theoretically sort of understood decades ago, it's only now that we have controllable quantum systems that we've been able to actually do experiments. Serge Haroche and Dave Wineland won the Nobel in 2012 for pioneering this field of single degree of freedom quantum systems where these kinds of experiments are possible.

And even the nature of quantum measurement is now the subject of daily experiments

One of the most "mysterious" parts of quantum mechanics is the so-called "measurement". There are countless questions on Physics.SE asking about the relationship between wave function collapse and measurement and what "measurement" even really means. I think quantum computing has blown these questions wide open. Folks in the quantum computing field can literally track the evolution of a quantum system's wave function as it collapses. We can measure how different kinds of measurements and different measurement strengths$^{[a]}$ cause the quantum state to collapse in different way$^{[b]}$.

Finale

Now, you may be more asking if quantum computing as an abstract field has offered us any insight into the laws of Nature. I still say it has. Quantum computing protocols for fault tolerance like the surface code use quantum measurement and wave function collapse as an integral part of processing information. This is really kind of amazing. We all learn that quantum measurements are random and that they sort of screw up the system you measured. However, brilliant folks have discovered a way to make certain very special kinds of measurements which, while they are random and while they do cause part of the wave function to collapse, they don't cause the part of the wave function which stores your information to collapse. The way that works relies on specific forms of quantum entanglement and very interesting ways of doing measurement. This is a new idea and one that has significantly affected how a lot of people even think about quantum mechanics, wave functions, measurement, and information.

$[a]$: By measurement strength I mean the rate at which our knowledge of the state increases. This is partially dependent on the physical strength with which the measurement apparatus interacts with the system under observation, but also depends on more subtle things like the commutation relations between the measurement operator and the Hamiltonian of the observed system.

$[b]$: If you're interested, take a look at section 3.6, and then the discussion leading up to and including figure 6.11 in this thesis (It's my thesis. I'm posting a link because it's a resource with which I happen to be intimately familiar even though it's probably not the best reference for this topic).

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The quantum theory of information and computation sheds light on many issues in fundamental physics.

First, it explains that any physical system can be simulated by a universal computer. This sheds some light on the issue of whether we can expect to be able to understand the laws of physics.

Second, such a computer can be constructed by composing almost any single two-qubit gate:

http://arxiv.org/abs/quant-ph/9505018.

Third, thinking of quantum mechanical processes in terms of information flow in quantum computational networks can help explain experiments that have often been regarded as baffling or paradoxical, see

http://arxiv.org/abs/quant-ph/9906007

http://arxiv.org/abs/1109.6223.

There are also some limits to what we should expect the theory to explain. For example, it can't explain the second law of thermodynamics since it doesn't explain why any process would be irreversible:

http://www.ipod.org.uk/reality/reality_deutsch.pdf.

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    $\begingroup$ Those arguments that you can't explain irreversible processes don't make sense to me. Doesn't irreversibility just come from insanely long recurrence time? $\endgroup$ – DanielSank Dec 17 '14 at 17:00
  • $\begingroup$ You're right. I formulated that badly. The actual problem is why some processes occur but their reverses do not. Consider a universe in which there are two kinds of mugs. One kind of mug starts out unbroken on a table and then falls onto the floor and breaks. The other starts out broken on the floor and leaps onto the counter and reassembles. The recurrence time for each process is the same since one is just the time reverse of the other, but one happens and the other doesn't. $\endgroup$ – alanf Dec 18 '14 at 11:56
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    $\begingroup$ The reason mugs don't unbreak is because there are more arrangements of the atoms which we label as "broken" than there are arrangements of the atoms which we call "intact". This is the key point which, for some reason, everyone ignores. $\endgroup$ – DanielSank Dec 18 '14 at 17:28

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