#### Quantum Science Seminar

# Quantum data compression for ensembles of mixed states

An interdisciplinary group of faculty & students studies problems in the theory of quantum information processing. A brief review of the most recent publications will be followed by a presentation on a specific paper or set of papers. All faculty and students are welcome.

Data compression is an important fundamental problem in information theory. The classical data compression problem (also known as source coding) was solved by Shannon in 1948. Analogously, we can consider the problem of quantum data compression. That is, the minimal number of quantum resources required for faithful transmission of the states produced by the source. This problem was stated and solved for the first time by Schumacher.

In this presentation we discuss a particular form of quantum data compression in which the encoding states are indexed by classical variables. This problem, which is known as mixed-state quantum data compression, has been open for long time. After precisely defining the problem, we discuss the different techniques used for deriving the lower and upper bounds. Next, we'll talk about the relation between this problem and classical probability distribution compression. Finally, we show the connection between the mixed-state compression rate, and approximate sign rank of the density matrix, and compare the rates with previously known results.