Just published in Physical Review A!

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Overview

Our previous paper Occam's Quantum Strop showed how to compress the state of a classical stochastic process for transmission through a quantum channel down to size \(C_q(L)\) where \(L\) is the length of encoding words used. The compression improves with longer lengths.

In the new publication, we show how to compute this quantum compression curve (\(C_q(L)\)) in closed form for all lengths including infinite.

Obviously this provides a great new tool for exploring this idea of quantum compression.

Additionally, the calculation provides more insight into what is going on. For instance, it shows how the curve can be nicely thought of as coming from two components. The first of which only yields a contribution the the compression curve for \(L\) less than some cutoff. This cutoff length is related to the nilpotent index of an important transition matrix.

The second yields an exponentially decaying contribution that persists for all lengths. This part has to do with cycles in the same transition matrix.