Simple construction of quantum universal variable-length source coding

TL;DR

This paper presents a simple, universal quantum variable-length source coding scheme that minimizes error and rate over all sources, using a measurement technique that balances estimation accuracy and state preservation.

Contribution

It introduces a novel quantum source coding method that estimates entropy without destroying the input state, applicable to entangled states and improving compression efficiency.

Findings

Error and rate tend to zero regardless of source

Estimation of entropy is achieved with minimal state disturbance

Applicable to Schumacher's scheme and entangled state compression

Abstract

We simply construct a quantum universal variable-length source code in which, independent of information source, both of the average error and the probability that the coding rate is greater than the entropy rate $H(rho_p)$, tend to 0. If $H(rho_p)$ is estimated, we can compress the coding rate to the admissible rate $H(rho_p)$ with a probability close to 1. However, when we perform a naive measurement for the estimation of $H(rho_p)$, the input state is demolished. By smearing the measurement, we successfully treat the trade-off between the estimation of $H(rho_p)$ and the non-demolition of the input state. Our protocol can be used not only for the Schumacher's scheme but also for the compression of entangled states.