General Mixed State Quantum Data Compression with and without Entanglement Assistance

General Mixed State Quantum Data Compression with and without Entanglement Assistance

Seminar author:Zahra Baghali Khanian

Event date and time:11/03/2020 11:00:am

Event location:GIQ VIRTUAL SEMINAR

Event contact:zbkhanian@gmail.com

We consider the most general (finite-dimensional) quantum mechanical information source, which is given by a quantum system 

$A$ that is correlated with a reference system $R$. The task is to compress $A$ in such a way as to reproduce the joint source state 

$\rho^{AR}$ at the decoder with asymptotically high fidelity. This includes Schumacher's original quantum source coding problem of a 

pure state ensemble and that of a single pure entangled state, as well as general mixed state ensembles. 

Here, we determine the optimal compression rate (in qubits per source system) in terms of the Koashi-Imoto decomposition of the 

source into a classical, a quantum, and a redundant part. The same decomposition yields the optimal rate in the presence of unlimited 

entanglement between compressor and decoder, and indeed the full region of feasible qubit-ebit rate pairs.