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I've received an offer to work my master's thesis on an approach to black holes with quantum information. In that setting, before accepting, I'm trying to understand what this is all about really, since I know nothing yet of quantum information.

At first I thought that quantum information was somehow related to statistical mechanics because of dealing with things like entropy.

But searching more about this, it seems it is almost entirely about quantum computing. It seems to deal with circuits, gates, bits, and lots of other stuffs that seem at first to be extremely quantum computing related. And it seems to be extremely focused on more "practical issues" of quantum computing instead on, what I personaly find more interesting, issues of fundamental physics.

To make my point clear, I mean, Quantum Mechanics allows us to understand the dynamics of atoms and subatomic particles. Quantum Field Theory allows us to understand the dynamics of relativistic fields and treat these phenomena as the interactions of relativistic particles. Statistical Mechanics allows us to understand how macroscopic degrees of freedom are related to microscopic ones and make sense of how temperature, for example, affects systems. General Relativity gives us a description of spacetime itself and the interaction between spacetime and matter.

I'd say that all these seem to be concerned with "how nature works and how those phenomena we observed actually can be described".

Now, quantum information is just concerned with quantum computers, bits, and things like that?

I do understand all this is important and I'm in no means disputing this. I just don't like quantum computing (I tend to prefer more abstract mathematical-physics problems), and I'm trying to understand whether or not quantum information and quantum computing are the same thing.

It is just that I have a feeling that although the heavy usage of quantum mechanics is physics, the objectives themselves of quantum information, are closer to computer science than to physics.

My current impression is that quantum information is a particular usage of physics to achieve practical results. But it might be wrong, and that is the reason of this question.

What is quantum information really about? How does it fit physics in general? Is it really majorly related to quantum computers or it tries to answer question from fundamental physics?

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No, quantum information has nothing to do with quantum computing necessarily. In theory, quantum information deals with questions of information theory, which is a branch of computer science.

Quantum information primarily deals with a number of tasks:

  • Storage of (quantum) information in quantum mechanical systems
  • Communication of (quantum) information over noisy quantum channels, i.e. sending bits or qubits (that is the basic unit in information theory) over quantum channels. Here, quantum channels are maps on quantum states fulfilling some properties (you can think of them as time evolutions on some system taking the environment into account)
  • Secure communication as in cryptography

The answer of what are the best rates for communication often rely on entropies. Note that these are (a priori) not the entropies you are used to from statistical mechanics. They are information entropies defined independently of statistical mechanics although the quantum analogue of the classical von Neumann entropy does turn out to be equivalent to some statistical mechanics entropy.

By the nature of these problems, they touch on different fields of physics, depending on what you are interested in. For noisy channels of real systems, you will often use tools also applied in statistical mechanics such as master equations and you might want to learn some quantum optics, as a lot of systems are quantum optical systems. You can also study a whole bunch of mathematically hard questions related to capacities (rates of error-free information that can be sent over a channel), or you can study "codes", i.e. ways how to really send the information over channels, a topic that is usually more prominent in computer science. Since cryptographic protocols as well as a whole bunch of interesting communication protocols rely on entangled states, entanglement is also mostly studied in quantum information. If you are interested in storage, since the main theoretical tasks have been solved, you might want to study condensed matter systems for instance.

Since the main challenges involve quantum states, quantum information is usually done in the physics department and not so much in the computer science department.

However, historically quantum information (much like information theory itself) developed closely to the idea of a quantum computer. This is why many books on the topic such as Nielsen & Chuang group the two together. However, in contrast to quantum information, quantum computing is focussed more on:

  • Quantum complexity theory (which is the quantum analogue of complexity theory and is often studied in computer science departments)
  • Building a quantum computer
  • Envisioning schemes for quantum computation and devising algorithms

While building a quantum computer is a physical engineering challenge mostly done in condensed matter, statistical physics or quantum optical systems, devising algorithms and schemes (such as the quantum circuits you talked about) is done in theory departments both in physics and in computer science.

However, quantum information is not as clear a discipline as for instance particle physics or cosmology and at the moment, a lot of people who started out working in quantum information have diverged to other topics such as quantum thermodynamics (which applies quantum information methods combined with statistical physics) or tensor network systems (which are studied heavily in condensed matter physics). In the same vein, there are applications to black hole physics.

  • For one, there is the well known "Firewall paradox" related to the "Black hole information paradox" although I must say that it is debated how important these paradoxes are or whether there really is a paradox.
  • A second application in the veil of applications of tensor network systems to AdS/CFT is pioneered by, I believe, Swingle and many others mor recently.
  • A third application, this time of quantum computing, has been put forth by Dvali and Pachenko, Dvali et. al. They believe a black hole to be a quantum computer (without having read the paper I confess).

In other words, there is no way of knowing what you'll be working on. Ask the people who made you an offer!

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  • $\begingroup$ As far as I know, there are some works recently to understand the dynamics of blackhole from the quantum information point of view. They concern problems such as if the evolution of BH is unitary, how the information escapes from BH during evaporation, if we can recover the in-falling information from the BH radiation, how to explain the geometry of BH by quantum computation. $\endgroup$ – XXDD Jun 10 '17 at 11:57
  • $\begingroup$ That is true. In principle, the information problem is very much related (and quoted in) the papers on the Firewall paradox. However, if you have anything specific in mind that you do not see covered at all, feel free to write another answer! $\endgroup$ – Martin Jun 10 '17 at 12:43

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