Quantum Information Theory

Full Title or Meme

Quantum Information Theory (QIS) is a further abstraction of an abstract model of real-world physics.

Context

• QIS was first suggested by Richard Feynman as a means to model the real quantum work of subatomic interactions in Information Theory.

Information Rules

Reconstructing quantum mechanics from informational rules

1. Information capacity: The most elementary component of all systems can carry no more than one bit of information.
2. Locality: The state of a composite system made up of subsystems is completely determined by measurements on its subsystems.
3. Reversibility: You can convert any "pure" states to another such state and back again.

These rules apply to classical physics if a bit can be only 1 or 0. They apply to quantum physics if a bit can have any value from 0 to 1. In other word classical = boolean logic and quantum = fuzzy logic.

Reversibility

• The current model of physical reality (some call the model a set of laws) shows no preference between moving forward versus backwards in time. Particles' "motions" can be predicted either way.
• What is most interesting is that Landauer's principle was originally developed in 1961 to predict the lower theoretical limit of energy consumption of computation. It holds that "any logically irreversible manipulation of information, such as the erasure of a bit or the merging of two computation paths, must be accompanied by a corresponding entropy increase in non-information-bearing degrees of freedom of the information-processing apparatus or its environment". So, A reversable computation is one in which no information is erased and, in principle, may be carried out without releasing any heat.
• In 2022 we could say the same about quantum processes. In particular quantum error codes are very efficient at encoding information which comes from the fact that "quantum mechanics is reversible, and thus information must be preserved somewhere." This leads to description of how information that falls into a black hole is theoretically recoverable.
• Since 2020 efforts to reduce the power consumption of computing are moving in the directions of reversible computing. See the wiki page on What Purpose do Clocks Serve for more information on low power computing.
• While Physics since Hawking has held that information is preserved, it does not prevent information from disbursing to the point of irrelevance to us humans.

Three Areas of QIS

These areas were taken from Hoofnagle and Garfinkel's book

Quantum Communication

See the wiki page on the Quantum Computing Threat to existing cryptography.

Quantum Computing

• Most closely tracks the original suggest from Richard Feynman in modeling the physical reality of Quantum Mechanics.
• The first proposal for a quantum computer was made by Seth Lloyd in 1993 and described in Scientific American in 1995.
• Note that some would place the Quantum Computing Threat in this category as well. Any taxonomy such as this runs into classification ambiguity.
• It's hard in 2023 to disentangle the hype from the reality. What are the promising applications to realize a quantum advantage? Perhaps the largest problem is getting data into and out of the quantum circuity. The best advantage would limit data flow for such application like search where data flow are high. Other problems like cryptography and physical reality seem like areas where quantum approaches are practical.

References

Other Material

• See the wiki page on Second Law of Thermodynamics