Oct. 29, 2023

My description was so long that it broke the website

So I am posting it here.

Classical information theory, developed by Claude E. Shannon in the 1940s, seeks to find the maximum possible rate of information transfer ("capacity") of a a channel or system of channels of classical bits. By the fundamental theorem of a channel with noise, it is possible to transfer an amount of information at a rate less than or equal to the capacity with arbitrarily low error. Of course, with a noisy channel, it is impossible to reach an error rate of zero, but using error correction techniques like Hamming codes, we can get very close. The amount of information is measured as entropy, and uses bits (base 2) or "nats" (base e) as its units. There is a direct conversion between information theoretic entropy and thermodynamic entropy, so information theory is intrinsically connected to thermodynamics. Classical information channels can be analyzed by relatively simple methods of linear algebra and multivariable calculus.

Quantum information theory, on the other hand, uses qubits as its units. The probabilistic nature of qubits and their ability to entangle makes finding the capacity of a quantum channel much more difficult. Many of the properties of classical information theory that help simplify the math do not hold for quantum channels. Because of this, quantum information theory is far more complex than its classical counterpart. However, as quantum computing progresses, the need for efficient communication between quantum computers grows. By finding the capacity of different types of quantum channels, we can figure out which ones are most efficient. Z-channels, simple channels, timing channels; in this project, I hope to analyze these channel types and more to find an absolute limit on how much information a quantum channel can transmit.